To conduct a formal comparison of DIC methods, we used synthetic images that we could freely manipulate. We created a series of images where we introduced simulated deformation and noise. Thereby, the real displacement was exactly known and we were able to evaluate the outcomes' correctness. We produced a 540 × 434 px shaded relief based on a DSM of a natural slope. Characteristics and geographical context of the DSM are shown in Figure S1 from the Supplementary Materials. The lighting position of the shaded relief has been set to (0◦, 90◦) (azimuth, elevation). The intensity range of the reference image (refIm) varied between [0, 255]. Then, we moved the pixels within a region of interest (ROI) using non-linear transformations, in the form:

$$\text{motIm}(i + f(i), j + \mathfrak{g}(j)) = \text{reflm}(i, j) \tag{7}$$

where motIm is the image with simulated motion and *f*(*i*) = *g*(*j*) = 0 outside the ROI. According to Equation (7), the produced displacement is not a rigid translation, but it is a non-linear surface deformation that simulates real cases. Therefore, within every template couple in the DIC calculus, displacement gradients are present. Before to apply Equation (7), we upsampled the images of a factor of 10. Subsequently, we resampled to the original size. Thereby, we were able to simulate a 1/10th pixel displacement. We conducted the resampling operation using the *imresize* Matlab function using bicubic interpolation.

Then, we introduced various types and magnitudes of noise into motIm (Table 1): (i) speckling, (ii) blurring, (iii) different positions of light source and iv) illumination intensity changes. The Speckle noise is defined in the form IN = IN + n · IN, where n varies uniformly with mean 0 and a given variance. We considered speckle variances of 0.03, 0.05 and 0.07. The Blur noise has been produced with a low-pass mean filter of different sizes: 3 × 3, 5 × 5 and 7 × 7 pixels. We simulated Light noise by using three positions of the light source to create the shaded relief: (10◦, 80◦), (30◦, 60◦) and (50◦, 40◦).

**Table 1.** List of the synthetic images used in this study.

Light noise is feature-based spatially-coherent noise. The Dark noise has been produced by subtracting from the intensity image an oblique plan that linearly varied from 0 to 100, 0 to 150 and 0 to 200 (from left to right). Examples of synthetic images are shown in Figure 2. The considered noises concern typical disturbing effects that might occur in real surveys. Light noise well simulates the shadow pattern change caused by the different sun position or the presence of isolated clouds. In contrast, Dark noise represents homogeneously-varying illumination intensity. These are known issues in operative surveys [7,11,12,17,31]. Blur noise simulates image defocusing that can occur for many reasons: e.g., incorrect manual or autofocusing, low illumination, presence of haze or precipitation, condensation of the optical objective or camera vibration. To our knowledge, the influence of image defocusing has never been studied, but, according to our experience, it is a quite frequent disturbing effect. Finally, Speckle is a pseudo-random multiplicative noise that is typical of coherent waves. Probably, this phenomenon is less recurring in visual-based surveys. However, it can occur when DIC is applied to satellite SAR images [32]. We did not use combinations of different noises because the aim of our study was to evaluate the influence of specific disturbances on the DIC calculation.

**Figure 2.** Examples of synthetic images with different types of noise. (**A**) Reference image; (**B**) image with displacement and without noise (motIm); (**C**–**F**) motIm plus Blur5, LightB, Speckle5 and Dark150 noise respectively. The region of interest (ROI) with simulated displacement is delimited in black. (**G**) Map of simulated displacement and (**H**) displacement distribution in the ROI.

In total, we analysed 13 versions of motIm with different types and levels of noise (Figure S2). The DIC was calculated on a regular grid of 8000 nodes and the ROI contained 628 nodes.

#### *3.3. Real Images*

We conducted a similar analysis using real images acquired in natural environments (Table 2). We considered two examples of image data adopted in DIC applications. We used ground-based photographs of an Alpine glacier and satellite panchromatic images of a desertic area. These sites concern diverse environments, but both characterised by high ranges of deformation, with a maximum displacement of ~10 px.

The ground-based dataset refers to oblique 18 Mpx photographs of the Montitaz Lobe of the Planpincieux Glacier (PG), in the Mont Blanc area [31]. The reference image was acquired in optimal conditions in 27 September 2019 at h12.00. To assess the different methods' performances, we calculated the DIC using three distinct search images that have been acquired in 28 September 2019 at h12.00, h08.00 and h19.00 (Figure 3). Therefore, respectively with (1) same illumination conditions, PGopt; (2) different light source position, PGlight and (3) different illumination intensity, PGblur. In PGblur, the scarce illumination also introduced a slight blurring.

Between the acquisitions of the reference and the other three images, some snow melting occurred in the upper part of the images, while a small ice break-off detached from the glacier terminus. We were able to evaluate the robustness of different DIC methods also against these kinds of disturbance. We adjusted the displacement in order to normalise the different time gaps between the three couples of photographs. The DIC processing was conducted using 64 × 64 template size.

**Table 2.** Specifics of the real images couples.

**Figure 3.** Images of the Planpincieux Glacier: (**A**) reference image; (**B**) image acquired in similar illumination conditions; (**C**) image acquired with different lighting position; (**D**) image acquired with diffuse illumination and slight blurring. The pairs AB, AC and AD are indicated as PGopt, PGlight and PGblur respectively.

The satellite dataset is composed of a pair of Sentinel 2B images (image codes: T33QZU\_20191008T090849 and T33QZU\_20201002T090719), which targeted the Bodélé Depression (BOD) in Chad [33]. We considered a portion of 400 km2 centred approximately in 17.02◦ N–18.02◦ E. Such an area presents isolated sand dunes and clusters of small dunes and a homogeneous background (Figure 4). The environmental conditions of the first image showed strong wind and partial cloudiness. Therefore, the image appeared slightly blurred and the illumination was not uniform. We applied the DIC using templates of size 32 × 32 and 64 × 64 px.

To the real images, we applied four exemplar DIC methods (1) FFT-OR, (2) DOT-OR, (3) ZNCC-IN and (4) PC-GR.

#### *3.4. Criteria for the Comparison*

To evaluate the performances of the DIC methods, we used specific criteria for the comparison. Since the true displacement is known in the synthetic case, we defined a series of quantitative metrics. By contrast, in both the PG and BOD cases, ground-truth measurements were not available. Therefore, we conducted a qualitative analysis based on the visual identification of outliers, spatial resolution and displacement pattern.

The metrics adopted to examine the results obtained with the synthetic images are the following. Outside the ROI, where the theoretical displacement is zero, we calculated mean (*μ*) and standard deviation (*σ*) of the displacement as an estimate of accuracy and precision. In motIm, (*μ*) and (*σ*) are ideally zero. However, since the displacement is evaluated on templates that can be over the ROI limits, non-zero values could verify in the neighbourhood of the ROI. This behaviour is expected to be more evident with larger templates. Within the ROI, we calculated the mean absolute difference (MAD) and the linear correlation coefficient (CORR) between the obtained displacements and the mean theoretical displacement included in the template. We considered the mean value because the displacement is not uniform within the templates and the DIC measures a sort of averaged displacement [18]. For this reason, the DIC might misestimate the real displacement. We investigated this aspect considering the bias between the 1st, 2nd and 3rd quartiles of the distributions of the measured and theoretical displacements.

**Figure 4.** Sentinel 2B images of the Bodélé Depression. They were acquired in 8 October 2019 and 2 October 2020, respectively. In 2019, one can note the inhomogeneous illumination due to thin clouds and some apparent blurring caused by the strong wind.

We noticed that sometimes, even though the overall quality of the results was good, the presence of a few outliers in the residuals strongly affected in a negative way the MAD and CORR metrics. Therefore, we decided to analyse the results also excluding the outliers (MAD\* and CORR\*). Usually, these outliers concern areas near the ROI boundaries where the investigated templates lie over the ROI edges. When this happens, no displacement is detected near the ROI boundaries. We refer to the ability to correctly identify the displacement in the ROI limits' vicinity as "spatial resolution". Simultaneously, we reported the percentage of outliers (%OUT) in the results. We defined an outlier a value that is more than three scaled median absolute deviation (sMAD) away from the median, where sMAD is defined as ∼1.5 median (*xi* − median(*x*)). According to the outlier definition, this metrics has to be evaluated carefully. A small number of outliers could entail a very scattered distribution of the residuals and therefore results of low quality. However, a large percentage of outliers is certainly an indicator of poor performances.

Since we are presenting a certain amount of data, the reader might find hard to examine all the results. Therefore, besides the quantitative parameters, we defined a simple qualitative metrics which assigns a negative/neutral/positive score depending on the visual analysis of the results. We used the following notation: a minus (−) is given when the results contain so much noise that the displacement pattern is not yet recognisable or the pattern is still recognisable, but the values are strongly over/underestimated or the spatial resolution is very poor. A zero (o) is assigned when the displacement pattern is maintained and the values are approximately correct, but many outliers are present. A plus (+) is assigned when the results show good spatial resolution, the displacement values and pattern are correct and the number of outliers is limited.

Finally, we examined the computational time required to operate the various DIC correlations. Even though the computational time is not related to the quality of the results, it is an important parameter that can be relevant in applications that require fast processing or that have to elaborate very large amount of data.

#### **4. Results**

In this chapter, we present the results of 15 DIC combinations of correlation functions and image representations. Every combination has been applied to 13 images characterised by various noise types and magnitudes. The analysis has been conducted using four distinct template sizes. In total, we compared 780 results. Furthermore, we examined the results of four model DIC approaches (i.e., ZNCC-IN, DOT-OR, FFT-OR and PC-GR) applied to four couples of images of various real environments. The results of NCC, ZNCC, SSD and ZSSD in combination with OR image provided poor results and they will be not shown. Since DOT is valid for complex numbers, it has been applied exclusively to OR images.

#### *4.1. Methods' Comparison Using Synthetic Images*

In the following, we shall present the results obtained with the considered DIC methods applied to the synthetic images. In Figures 5 and 6, we report the displacement maps, the distributions of the displacement of the stable areas and the scatterplots between the measured and theoretical data obtained with every DIC combination for (i) Speckle3 noise calculated with 32 × 32 template size and (ii) Blur5 calculated with 16 × 16 template, respectively. In these figures, we also report the values of CORR, MAD, *μ* and *σ*. In Figure S3, we report analogue figures concerning every combination of the correlation function, image representation, noise and template size (i.e., 780 outcomes).

using 32 × 32 template size and with Speckle3 noise. The ROI is delimited in black.

distributions

 outside the ROI for every DIC approach

231

Besides, we prepared a series of figures containing the metrics present in Section 3.4. An example is presented in Figures 7 and 8, which show the outcomes of LightB noise calculated with 16 × 16 and 64 × 64 template size, respectively. We realised one similar figure for every combination of noise type and magnitude and template size (i.e., 42 figures). All the figures can be found in Figure S4.

In Table 3, we report the qualitative metrics based on the visual analysis of the displacement maps. The rightmost column contains the sum of the scores obtained with each template size.

*Image intensity*. DIC applied to IN image provides the best results in the presence of Blur and Speckle noise. On the other hand, Light noise can provoke large pixel differences that can influence the correlation calculus. Dark noise introduces a bias that affects nonzero-centred correlation functions.

*Image gradient*. The use of GR images provides poor results in the presence of Blur and Speckle noise. On the contrary, GR images appear less affected by Light noise and are almost unaffected by Dark noise. GR images return acceptable outcomes only using NCC and ZNCC correlations. With large templates, GR images provide a lower spatial resolution compared to the other image representations. The outcomes obtained with GR images are concentrated on integer displacement values, especially when combined with PC.

*Image orientation*. OR images yield very high performances in combination with DOT technique. Also, FFT and PC return better results when applied to OR images than IN and GR cases. OR is unaffected by Dark noise and it is resistant against Light noise.

FFT and PC. The performances of frequency-based methods with templates of size 8 × 8 are poor because the displacement is relatively large with respect to the template size. Therefore, signal decorrelates. This is more evident for IN images. However, FFT correlation performs generally better compared to PC for every template size and in combination with every image representation. A remarkable observation is that the frequency-based methods underestimate the displacement. The underestimation is more evident for IN images with Blur noise. The degree of underestimation seems independent from the template size (Figure S4).

NCC and ZNCC show similar results. However, since NCC is calculated using values that are not centred in zero, it is very affected by changes of illumination, because the difference of the mean value of the image can dominate. Therefore, NCC performs badly with Dark noise. Both NCC and ZNCC provide accurate values of displacement. However, in the presence of Blur noise, the spatial resolution decreases and they tend to spread the displacement when calculated with large templates (Figure S3).

**Table 3.** Performance score based on the qualitative analysis of the results. The rightmost column reports the total score obtained for every template size separately (i.e., 8 × 8/16 × 16/32 × 32/64 × 64).

**Figure 7.** Outcomes of DIC processing with LightB noise using 16 × 16 template size. (**A**) mean absolute error with and without considering outliers, black and white bars respectively. (**B**) Pearson coefficient with and without considering outliers, black and white bars, respectively. (**C**) Percentage of outliers. (**D**) Boxplot of the residuals. (**E**) Difference between the 1st, 2nd and 3rd quartiles, black, grey and white bars, respectively. (**F**) Standard deviation and mean of the displacement in the stable area (i.e., outside the ROI), white and black bars respectively.

**Figure 8.** Outcomes of DIC processing with LightB noise using 64 × 64 template size. (**A**) mean absolute error with and without considering outliers, black and white bars respectively. (**B**) Pearson coefficient with and without considering outliers, black and white bars, respectively. (**C**) Percentage of outliers. (**D**) Boxplot of the residuals. (**E**) Difference between the 1st, 2nd and 3rd quartiles, black, grey and white bars, respectively. (**F**) Standard deviation and mean of the displacement in the stable area (i.e., outside the ROI), white and black bars respectively.

SSD and ZSSD. SSD is the weakest method among those considered. It performs acceptably only for IN images and slight Blur noise. However, the subtraction of the template mean value allows at reducing the impact of the quadratic term. Accordingly, ZSSD shows results similar to NCC and ZNCC. Nevertheless, it is less performing when applied to GR images. ZSSD is less robust against Speckle noise, in particular when calculated with small templates.

DOT works with OR images and it is more performing than FFT-OR and PC-OR. DOT is unaffected by Dark noise and very robust against Light noise. It performs similarly to NCC in the presence of Speckle and limited Blur noise. Poor results are obtained in the presence of strong blurring. DOT results are quite smooth and the fraction of outliers is generally lower compared to other methods.

In Figure S5, we report examples of IN images of motIm with and without noise. Besides, we show also the power spectra of each image. In this analysis, we considered only the bounding box of the ROI. We report the same analysis for GR and OR images in Figure S5. The power spectra of motIm IN and GR are similar, while in that of OR, the signal appears less defined. Blur noise smooths the edges and makes the image features less clear. This is particularly evident in GR image. The spectra of every blurred image representation have lowered high frequencies. Dark noise does not influence GR and OR images and their power spectra, while it introduced a bias in IN, as expected. Light noise tends to strengthen the features in GR image, while OR image seems to maintain the main pattern. Speckle noise introduces random scattered noise, which makes OR and GR images more disturbed. With Speckle noise, the higher frequencies strongly increase their power in IN and GR images. In general, higher frequencies of OR spectra are less influenced by any kind of noise.

#### *4.2. Methods' Comparison Using Real Images*

The maps of the vertical displacement component of the PG images are shown in Figure 9. From left to right, the columns report the results obtained with DOT-OR, ZNCC-IN, PC-GR and FFT-OR techniques. The results of PGopt, PGlight and PGblur images are reported respectively in the upper, middle and lower row. As one can note, the performances with PGopt images are approximately the same for every DIC method. PC-GR map is less smooth and several scattered outliers are present. In the upper part of the image, some noise appeared in the maps obtained with every DIC method, in correspondence of fresh snow melting (Figure 3). However, DOT-OR and FFT-OR appear less affected by this phenomenon. Similarly, DOT-OR and FFT-OR perform better with PGlight images. In this case, DOT-OR is slightly more performing compared to FFT-OR. ZNCC-IN and PC-GR are both influenced by Light noise, but the effects are different. In general, PC-GR shows scattered outliers, while ZNCC-IN decorrelates in the form of stains. DOT-OR, ZNCC-IN and FFT-OR methods performed equally well with PGblur images. They show lower displacement values compared to those measured with PGopt images. However, ZNCC-IN underestimates at a slightly less extent compared to the other methods, especially in the horizontal component (Figure S6). The underestimation confirms the observations obtained with the synthetic images, even though a slight slowing down of the glacier motion cannot be excluded. PC-GR results with PGblur images are quite poor. All the DIC methods decorrelate in the area corresponding to the break-off.

In Figure 10, we report the scatterplot of the outcomes obtained with PGopt images, which can be considered as reference, versus the outcomes of PGlight and PGblur. It is evident that DOT-OR and FFT-OR behave almost equally with all the images, while ZNCC-IN shows some random noise with PGlight images. PC-GR performs satisfactorily with PGlight, while most of the results with PGblur appear random. PC-GR outcomes present a regular grid-like distribution.

The results of BOD images partially follow those of PG. Concerning the outcomes obtained with the template of size 32 × 32 (Figure S6), DOT-OR and FFT-OR show similar results. The contours of the largest dune clusters are well defined and the presence of outliers very limited. Both methods detect single dunes, but with a narrow spatial resolution. On the contrary, ZNCC-IN identifies the displacement of small isolated dunes, but it presents scattered outliers. With PC-GR, the areas corresponding to the dunes appear as clusters of random noise and only the displacement of the largest groups of dunes is correctly measured. The presence of clouds strongly impacts over ZNCC-IN, while DOT-OR and FFT-OR appear almost unaffected. The inhomogeneous illumination does not alter the results of FFT-OR, PC-FR and DOT-OR significantly, while ZNCC-IN fails in correspondence of the edges of the shadows cast by the clouds.

The outcomes obtained with 64 × 64 template size are slightly different (Figure 11). DOT-OR and FFT-OR show very smooth maps. The largest groups of dunes are correctly identified with good spatial resolution. However, the smallest dunes are not entirely detected, especially by DOT-OR. Any trace of the cloud presence does not appear in these cases. In the ZNCC-IN maps, the noise is slightly lower compared to that of 32 × 32 template. However, outliers remain in correspondence of clouds and shadows. The displacement of the isolated dunes is identified, but it is largely spread around in the form of stains. PC-GR performs better compared to the case with 32 × 32 template. All the dunes are identified and the spatial resolution is fair, but the displacement appears slightly underestimated. The presence of outliers is significantly reduced and are much less than in ZNCC-IN results. Like ZNCC-IN, the displacement appears slightly spread around the dunes, but at a smaller degree.

**Figure 9.** Displacement values obtained with the images of the Planpincieux Glacier. Rows A–C refer to PGopt, PGlight and PGblur images pairs respectively. Results \*1 (**A1**–**C1**) are obtained with DOT-OR method, while \*2 (**A2**–**C2**), \*3 (**A3**–**C3**) and \*4 (**A4**–**C4**) are obtained with ZNCC-IN, PC-GR and FFT-OR respectively.

**Figure 10.** First row: scatterplot between the outcomes of PGopt vs. those of PGlight. Second row: same as the first row, but PGopt is shown against PGblur. Third row: outcomes of BOD images obtained with the template size of 32 × 32 vs. template of 64 × 64. From left to right, the results have been obtained with DOT-OR, FFT-OR, ZNCC-IN and PC-GR method, respectively.

The scatterplots in Figure 10 show that the adoption of 64 × 64 template with DOT-OR, FFT-OR and PC-GR reduces notably the occurrence of displacements greater than 70–80 m, which are very likely errors. On the contrary, the displacement distributions of ZNCC-IN remain almost the same and show a strong presence of outliers using both 32 × 32 and 64 × 64 templates. Like in PG images, PC-GR outcomes present a regular grid-like shape.

#### *4.3. Computational Time*

According to our analysis, the computational complexity varies largely depending on the domain where the correlation is calculated. We examined the aspect of the computational time using random templates of size 8 × 8, 16 × 16, 32 × 32 and 64 × 64 px. For the space-based correlation methods, we used search bands of half the size of the template. The results are shown in Figure 12. We used an eight-core CPU AMD Ryzen 7 1800X. SSD is the fastest method among the space-based ones, while NCC, ZSSD, DOT and ZNCC are approximately 2, 3, 4 and 6 times slower, respectively. We observed that the computational time of NCC, ZSSD and DOT tend to uniform for large sizes. On the other hand, frequency-based functions require a computational time three to five orders of magnitude lower, depending on the template size.

**Figure 11.** Displacement magnitude and direction obtained with images of the Bodélé Depression using 64 × 64 template size. Only the areas with displacement >20 m year−1 are shown. DOT-OR and FFT-OR fail to detect isolated dunes. By contrast, ZNCC-IN spreads the displacement around and it suffers the presence of thin clouds and slight blurring. PC-GR performs well, it shows the best spatial resolution, even though it slightly underestimates the displacement.

**Figure 12.** Computational time (in milliseconds) necessary to process one template of various sizes using different correlation functions.

It is worth noting that the computational time of space-based methods depends mostly by the size of the search band. Probably, most of the circumstances do not require as large search bands as those we used in this experiment.

#### **5. Discussion**

The results of our experiment using synthetic images demonstrated that IN images are quite resistant to Blur and Speckle noise. Nevertheless, frequency-based methods still fail in the presence of blurring, probably because it introduces strong low-frequency components that dominate over the high-frequency features. On the other hand, IN images are more sensitive to Light noise, because it can produce coherent areas of large pixel difference. GR images do not suffer changes in illumination and they provide acceptable results in the presence of Light noise. However, they are more sensitive to Blur and Speckle noise, in accordance to the observation of Sjödahl [25]. This could appear in contrast with the findings of Martin and Crowley [20], which observed more stable correlation indexes using GR images. However, their study was only focused on index stability, rather than on the results' effectiveness. We noticed a peculiar behaviour of PC-GR method. The obtained displacements were concentrated on integer values (the dimension of one pixel of Sentinel-2 images is 10 m). This occurs because the autocorrelation function of GR images has a narrow prominent peak which makes the signal well-defined [25]. However, such a sharp peak probably concentrates all the information into integer shift values. As a consequence, GR images are less suitable for detecting sub-pixel displacements. OR images behave similarly to GR, but they return much better results. Since OR images are complex, a single element of the matrix is composed of two components. Therefore, OR images contain more information compared to IN and GR. Consequently, the original pattern information is less corrupted by noise and the signal-to-noise ratio maintains higher.

Concerning the correlation methods, space-based correlations non-centred in zero (i.e., SSD and NCC) fail in the presence of a change in illumination. Results strongly improve by considering the zero-mean values and adopting normalised function. As a matter of fact, ZNCC outperforms the other space-based methods. In general, SSD and ZSSD are more sensitive to large pixel variations, because the quadratic form enhances the largest differences. Among the space-based correlations, SSD appears the least effective method, particularly when adopted with GR images. This result differs from the finding of Martin & Crowley (1995) [20]. A possible reason, as also suggested by Pust [22], is that they analysed the performances of SSD without any source of noise. NCC and ZNCC return similar results, but NCC strongly suffers changes of average intensity using IN images. Space-based methods fail when applied to OR images. Probably, this happens because OR images are complex and the space-based functions are well defined only for real numbers. In general, we observed that space-based methods (excluding SSD in general and NCC for Dark noise) are more robust compared to frequency-based ones, confirming the observations of Pust [22]. On the other hand, Bickel et al. [19] obtained slightly better results with FFT compared to ZNCC using large template size.

Formally, DOT correlation is calculated in the space domain, but we describe its behaviour individually for two reasons: first, it differs from classical space-based functions as it operates with complex numbers; second, we want to highlight the high performances of this original method that we developed. In principle, DOT may be applied to whatever image representation composed of two separate components: e.g., the first derivatives of the image intensity (like in this study) or two different bands of multispectral images. This opens new possibilities of investigation for defining original DIC approaches. In general, DOT-OR appears quite robust against every source of considered noise. It is unaffected by dark noise and it provides the best outcomes in the presence of Light noise. We observed acceptable results with Speckle and weak Blur noise. The higher performances of DOT probably depend on two elements: (i) DOT applies to OR images, which are less corrupted by noise and (ii) DOT correlation operates in Lagrangian specification. Therefore, it is less sensitive to decorrelation respect to frequency-based methods [30].

Compared to space-based methods, normalisation worsens the performances of frequency-based correlations. Indeed, FFT outperforms PC in every situation we examined. Probably, this happens because in PC, the contribution of the amplitude signal is ignored and all the phase components have the same weight in the correlation calculus. Therefore, the presence of noise that alters the frequency spectrum can easily limit the performance of PC. Similarly, Heid and Kääb [18] observed better outcomes from FFT, especially in the presence of homogeneous texture. Probably, as suggested by Lewis [29], since in PC all the frequencies are weighted equally, it fails when a predominant frequency is lacking, which is the case of homogeneous areas. As a consequence, PC is more prone to artefacts. We observed a general underestimation of frequency-based methods. Heid and Kääb [18] noticed the same behaviour in areas with the presence of displacement gradients. They suggested that this occurs because the features that move slower change less their texture (i.e., they decorrelate to a lesser extent). Therefore, the slower features' contribution weights more in the correlation calculus. This hypothesis seems confirmed by the fact that the underestimation is less evident in OR images, whose intrinsic normalisation limits this effect. Frequency-based correlations suffer limitation concerning the template size. In our experiment, both FFT and PC failed when applied with 8 × 8 templates. Theoretically, the dimension must be at least twice larger as the maximum displacement for correctly detecting it. In practice, Bickel et al. [19] suggested as a rule of thumb to use a template size 6 to 17 times larger than the maximum displacement. We observed acceptable results with templates four times larger than the maximum displacement.

It is worth noting that normalised functions (i.e., PC, NCC, ZNCC and DOT) have the advantage of outputting an image-independent similarity index. This permits to compare the results between different attempts of the DIC calculus [18] and makes the similarity matrix much easier to understand. For example, this may allow to define heuristic criteria of data quality and help in the outlier detection [7].

The outcomes obtained with PG images agree with those observed with synthetic images. DOT-OR and FFT-OR return similar high-quality results. ZNCC-IN performs well with PGopt and PGblur, but it suffers the Light noise in the PGlight images. This confirms the lower robustness of the IN images against Light noise, as also observed by Dematteis et al. [17], who analysed the effects of lighting change using FFT-IN approach. Besides, ZNCC-IN fails in the areas where snow melting occurs, as already noticed by Heid & Kääb (2012) [18]. As expected, PC-GR shows acceptable results with PGlight images, as it is less affected by Light noise, while it totally fails with PGblur.

On the other hand, the outcomes of BOD dataset have some interesting difference. DOT-OR and FFT-OR perform well with 32 × 32 template. They both show smooth results with few outliers. However, they cannot detect small isolated dunes adopting 64 × 64 template. Probably, small features disappear in OR images. ZNCC-IN correctly detects single dunes, but it spreads the displacement. Such behaviour is more evident with a larger template. We observed a similar effect with blurred synthetic images. Finally, PC-GR performs differently depending on the template size. With 32 × 32 template it fails, while it returns fair results with 64 × 64 template. This behaviour was unexpected, as PC-GR has never shown robust outcomes. However, it confirmed that the adoption of larger templates ensures a lower impact of the noise [18,30].

#### *5.1. Influence of the Template Size*

In general, larger template sizes provide better results in the presence of strong noise. This behaviour was expected, because the signal-to-noise ratio increases. As a matter of fact, using synthetic images, most of the considered methods perform better with 32 × 32 template size and a minority returns better outcomes with 64 × 64 template. However, larger sizes tend to produce underestimated values and coarser spatial resolution. It is possible to appreciate such differences from the comparison of Figures 7 and 8. Similar considerations also hold for the BOD case study (Figure 11 and S6). There, the reduced spatial resolution is particularly evident with template sizes of 32 × 32 and 64 × 64.

GR images and OR images provide the worst and the best spatial resolution, respectively. Frequency-based methods do not detect displacement near the ROI boundaries using wide templates. When applied to blurred images, SSD, ZSSD, ZNCC and NCC spread the displacement out of the ROI and underestimate the results.

As mentioned before, FFT and PC perform very badly when applied to templates of size 8 × 8. However, FFT-IN and FFT-OR provide good results with larger sizes. DOT-OR, ZNCC-IN and ZSSD-IN returned similar high-quality outcomes for every template size. In general, the performances of PC correlation and GR images appear more dependent on the template size.

#### *5.2. Possible Uses of Specific DIC Methods*

Applying exemplar DIC methods to couples of real images that present some forms of noise, we observed the same effects that we obtained using the synthetic dataset where we introduced known and controlled types of noise. This demonstrates that the analysis conducted on the synthetic images was able to successfully describe the influence of typical disturbances that can occur in operative surveys in the geoscience field. Our study shows that various kinds and levels of noise affect differently the outcomes of the most commonly adopted DIC methods. However, we noticed that specific methods generally perform better.

The results of our analysis evidence that ZNCC-IN is quite robust against many kinds of noise, even though it suffers a change of the shadow pattern (i.e., Light noise). ZNCC-IN is sensitive to weak features and it is suitable to use when dealing with homogeneous images (e.g., river flow, dune migration, ice caps), although it might spread the displacement around the objects. However, scattered changes of image intensity, like those caused by the presence of snow or isolated shadows, might hamper the ZNCC-IN calculus (Figures 9 and 11). The use of GR images could be a possible alternative to overcome light noise. But ZNCC-GR largely suffers blurring and speckling and the use of GR images could hamper the detection of sub-pixel displacement.

Instead, DOT-OR is generally more resistant against every noise source and more performing in images with high feature contrast. Since it considers only the gradient orientation, it is insensitive to changes of illumination and colour. Therefore, its use might be suggested in glaciological applications, where the presence of surface debris is possible and snow melting and unfavourable illumination may occur frequently. On the other hand, it is less performing with homogeneous images that do not show a well-defined pattern.

On the contrary, in general, frequency-based methods revealed worse performances. However, using large templates, FFT-OR is comparable with ZNCC-IN and DOT-OR techniques and its computational time is several orders of magnitude lower. Therefore, FFT-OR is a good option when fast processing is required, e.g., during an emergency or when dealing with large datasets. FFT-IN could be an alternative when dealing with Speckle noise, even though speckling is expected to occur less frequently. Besides, it must be considered that frequency-based methods tend to underestimate the displacement and provide a coarser spatial resolution of the displacement maps.

The remaining DIC methods we examined revealed various disadvantages compared to the abovementioned approaches. PC performed much worse than FFT with every image representation and it is more time-consuming. Instead, NCC, SSD and ZSSD require less computational costs compared to ZNCC, but they generally perform worse. If fast processing is really necessary, FFT-OR is a much more valid alternative.

#### **6. Conclusions**

Our study analyses the effects of four types of noise (i.e., Blur, Dark, Light and Speckle) and various template sizes on the performances of different DIC algorithms applied to synthetic and real images. We simulated the noise on a shaded relief into which we artificially introduced displacement. We considered six popular correlation functions (i.e., NCC, ZNCC, SSD, ZSSD, FFT and PC) plus an original correlation function (referred as

DOT) based on the scalar product of complex numbers. We applied every DIC method to three image representations (IN, GR and OR). In total, we analysed 800 combinations of correlation function and image representation (780 using synthetic images and 20 using real images). Concerning the image representations, GR images returned the poorest outcomes, although they appeared less sensitive by Light noise. In general, we observed that spacebased methods produced better results compared to frequency-based methods. Among the former ones, ZNCC-IN and DOT-OR are the most performing methods. Nevertheless, ZNCC-IN suffers Light noise and DOT-OR is less sensitive in homogeneous areas. The original DOT-OR method proved to be quite resistant against every type of considered noise and we registered low-quality results only with strong blurring. An advantage of DOT is that it employs two distinct components. This permits to exploit more information of the main signal and thus to be less affected by noise.

Frequency-based methods fail using small templates, but FFT-IN and FFT-OR provide good results with larger templates. However, they are in general less robust than ZNCC-IN and DOT-OR. Among the frequency-based methods, FFT-OR returned the best results, while PC underperformed with just weak noise. Nevertheless, we registered satisfactorily outcomes with PC-GR applied to Sentinel-2B images. We observed that frequency-based methods tend to underestimate the actual displacement.

We compared the results of ZNCC-IN, DOT-OR, FFT-OR and PC-GR applied to terrestrial images of the Planpincieux Glacier (Italy) and Sentinel 2B images of the Bodélé Depression (Chad). In general, the results obtained with the real photos confirmed those observed with the synthetic images.

The study shows that space-based methods should be adopted in applications where strong noise is expected. However, the change in the shadow pattern might negatively influence them. DOT-OR seems the more robust method, as it provides smooth displacement maps. Nevertheless, it may fail in homogeneous areas. FFT-OR and FFT-IN are more sensitive to noise, but they require much less computational time and they should be preferred in applications that need fast processing.

Therefore, the choice of the most suitable DIC method should be led by the expected environmental conditions and noise types. However, the results of our analysis suggest that such a choice should be made among one of these methods: ZNCC-IN, DOT-OR and FFT-OR.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/2072-4 292/13/2/327/s1, The interested reader can find supplementary material attached to this paper. Figure S1: The details of the DTM adopted to produce the synthetic images; Figure S2: the synthetic images used in the comparison analysis; Figure S3: the displacement map, scatterplot of theoretical vs. measured displacement and the distributions of the displacement of the stable areas for every combination of method, noise and template size; Figure S4: The metrics explained in Section 3.4. Every figure reports the metrics of all the considered methods for a specific noise and template size; Figure S5: the IN, GR and OR images of the ROI and the corresponding power spectra and Figure S6: the results obtained with the PG images (both horizontal and vertical displacement components) and with the BOD images (displacement fields with 32 × 32 and 64 × 64 template size).

**Author Contributions:** N.D. conceived the study, implemented the methodology and wrote the manuscript. D.G. contributed to writing the manuscript and supervised the research. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article or Supplementary Materials.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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Within this group, psalms 1 to 14 are commented upon verse by verse, whereas 15 to 32 are rather paraphrased briefly in one or two sentences; only now and then an allegorical explanation is added. Clemens Weidmann was struck by the syntactical chaos and disorder of many of the paraphrastical explanations, e.g. in 29/1,7sq.:

(7) Ego autem dixi in abundantia mea, Non movebor in aeternum: ego autem ille populus, qui ab initio loquebar, dixi in mea abundantia, iam nullam patiens egestatem: Non movebor in aeternum. (8) Domine, in voluntate tua praestitisti decori meo virtutem: sed hanc abundantiam, Domine, non ex me mihi esse, sed in voluntate tua praestitisse te decori meo virtutem ex eo didici, Avertisti autem faciem tuam a me, et factus sum conturbatus; quod avertisti aliquando a peccante faciem tuam, et factus sum conturbatus, recedente a me illuminatione notitiae tuae.

*Sed hanc abundantiam* does not fit well with the preceding psalm verse (*Domine, in voluntate tua praestitisti decori meo virtutem*), and the logical structure of the rest, i.e. *ex eo didici: Avertisti autem faciem tuam a me, et factus sum conturbatus, quod avertisti aliquando a peccante faciem tuam*, is not clear at all. Passages like this make perfect sense if one removes those quotations that are meant as lemmata, so that the text under discussion reads: *ego autem – ille populus, qui ab initio loquebar – dixi in mea abundantia iam nullam patiens egestatem: 'non movebor in aeternum'. Sed hanc abundantiam, domine, non ex me mihi esse, sed in voluntate tua praestitisse te decori meo virtutem ex eo didici, quod avertisti aliquando a peccante faciem tuam.* It is only thanks to this that *quod avertisti* can be identified so as depending on *ex eo*. Furthermore, in a manuscript from Echternach from the eleventh century,33 Clemens Weidmann found the remains of a numeric reference system. On this basis, he was able to reconstruct the text as follows: in *Enarrationes* 15–32 each psalm is first quoted in its full length, its verses are numbered all the way through. Then, in the explanation Augustine refers to the pertinent verse not by citing it but only by its number. We know that Augustine used this reference system in his *Contra sermonem Arrianorum* and the *Breviculus collationis cum Donatistis*. Hence, in CSEL 93/1A the text is constituted as follows:

33 Paris, BnF, lat.1983 (P11 in Weidmann's edition).

Again, it is worth noting that only one manuscript from the eleventh century has preserved part of the original reference system. If the editor had considered only the manuscripts predating the year 1000 – about 20 from before the eleventh century – he would not have been able to reconstruct the original arrangement of the text.

## **The organisation of the CSEL**

Up to 2012 the CSEL was funded and the editions were published by the Austrian Academy of Sciences. Since 2012 the CSEL has been part of the Department of Classics at Salzburg University, and the publisher is De Gruyter. The office, however, is still in Vienna. Our focus is on Augustine and Ambrose, but only as a guideline. Thus, within recent years, we have also published editions of an anonymous commentary on Job, two volumes on Prosper of Aquitaine, and the volume on Donatus mentioned above. The CSEL has volumes edited by the staff as well as by external editors. External editors receive advice and supervision whenever needed. Each volume is reviewed first by the CSEL staff, then by the advisory board, before it goes into print. Last but not least, the staff regularly gives courses on palaeography and editorial work in order to hand down the relevant skills and ultimately the pleasure of producing editions to the next generation of researchers.

## **Bibliography**

Ando, Clifford, 'Narrating Decline and Fall', in *A companion to Late Antiquity*, ed. by Philipp Rousseau (Chichester: Wiley-Blackwell, 2009), pp. 59–76.

# **Editing in Three Movements: Eriugena, Coleridge, Eliot**

*David Greetham†*

A strange triumvirate. What can Eriugena, Coleridge, and Eliot and the editions in which their work is enshrined have in common for me to bring them here to the closing conference of *Ars edendi* and then to the commemorative volume? Or, can the *differences* in the editing of the three inform our sense of the opportunities and challenges yet remaining in scholarly textuality? And, given the musical allusion in my title, is there some way in which each of these authors and their texts can be thought of as separate 'movements' each contributing to the total text (if you like, the harmony) that is editing and textual criticism?

Bearing in mind A. E. Housman's very neat formulation − 'textual criticism is a science, and, since it comprises recension and emendation, it is also an art. It is the science of discovering error in texts and the art of removing it,'1 − can all three authors and the editions of their works fit comfortably in the art/science dichotomy that we have inherited from Housman? Of course, the conference and the organisation sponsoring it, *Ars edendi*, recognize just one element of Housman's formulation, the 'arts' of editing, but perhaps for the moment it will suffice to recall that Housman's balanced formula was offered as a corrective to the Germanic dominance of *Altertumswissenschaft* and the imposition of a strict philology that left little room for the 'thought' in Housman's title. We have to remember that, based on a strict application of *recen-*

#### **How to cite this book chapter:**

On account of illness this lecture was not delivered by the author but read by one of the *Ars edendi* members at the concluding conference 17 August, 2016. In the final stages of editing this volume we received the sad news that David Greetham had passed away.

1 A.E. Housman, 'The Application of Thought to Textual Criticism', *Proceedings of the Classical Association*, 18 (1921), 67−84, p. 68.

Greetham, D. 2020. Editing in Three Movements: Eriugena, Coleridge, Eliot. In: Kihlman, E. and Searby, D. (eds.). *Ars Edendi Lecture Series. vol. V*. Pp. 109–122. Stockholm: Stockholm University Press. DOI: https://doi.org/10.16993/bbd.g. License: CC-BY

*sio*, Lachmann could claim that he could reconstitute not just the text but also the folio breaks in the manuscript archetype of Lucretius *De Natura Rerum*. Lachmann's 1850 edition of Lucretius demonstrated to his satisfaction that this archetype contained 302 pages of 26 lines per page and that this in turn was a copy (no longer extant) of a manuscript written in a minuscule hand, derived itself from a copy of a fourth-fifth-century manuscript written in rustic capitals.2

In the face of such sureties, Housman was very concerned that editors had been 'readily duped by […] scientific criticism or critical method',3 and that the Germans had mistaken textual criticism for mathematics.4 His promotion of 'thought' could be seen, if you like, as an early example of English compromise in the face of Teutonic *System*.

But why, indeed, these three authors and their texts? All three are representative of recent editing of documents from three periods − late classical, romantic, and modern. The edition of Eriugena by Édouard Jeauneau was published in 1996,5 the Coleridge by J.C.C. Mays in 2001,6 and the Eliot by Christopher Ricks and Jim McCue in 2015.7 As a group, they thus embody current theories and practices of the late twentieth and early twenty-first century. And while the methods and principles vary a good deal, all three stand at the end of a long tradition of editing in their respective fields and all three aim to provide a comprehensive, indeed exhaustive, access to the extant documents of their authors. This can be immediately seen in the range and sheer heft on display in the texts of Eriugena, Coleridge, and Eliot.

The Jeauneau edition of Eriugena's *Periphyseon* runs to five sturdy volumes, for a total of 3 293 pages, often with multiple parallel texts, where blank spaces indicate a gap in the text of that witness. The Mays edition of the *Poetical Works* of Coleridge occupies four volumes of the poetry in section sixteen of the Bollingen *Complete Works of Coleridge*,

2 K. Lachmann, *In T. Lucretii Cari De rerum natura libros commentarius* (Berlin: Georg Reimer, 1850).

3 A.E. Housman, *Selected Prose*, ed. by J. Carter (Cambridge: Cambridge University Press, 1961), p. 37.

4 Cf. Housman, *Selected Prose*, p. 132.

5 *Iohannis Scotti seu Eriugenae Periphyseon: editionem novam a suppositiciis quidem additamentis purgatam, ditatam vero appendice in qua vicissitudines operis synoptice exhibentur*, ed. by É. Jeauneau, 5 vols, CCCM 161−165 (Turnhout: Brepols, 1996−2003).

6 *The collected works of Samuel Taylor Coleridge* 16: *Poetical Works* I: *Poems*  (*Reading Texts*); *Poetical works* II: *Poems* (*Variorum Texts*), ed. by J.C.C. Mays (Princeton, NJ: Princeton University Press, 2001).

7 *The Poems of T.S. Eliot: [the annotated text]*, ed. by C. Ricks and J. McCue, 2 vols (London: Faber, 2015).

with two volumes of a 'reading text' and two volumes of a 'variorum text', for a total of 2 800 pages, in which, for example, *The Rime of the Ancient Mariner* takes up thirty-five pages of text historical collation, and notes; and while the Ricks and McCue Eliot seems almost abstemious with a mere 667 pages just on *Practical Cats*, and 1 311 pages on *Collected and Uncollected Poems*, the three publications cannot avoid being labelled monumental. These are weighty tomes, and it is unlikely that they will be superseded any time soon by rival editorial projects.

Given these determinations *and* uncertainties, can we find any cultural logic in regarding my first author, Johannes Scottus Eriugena, the ninth-century Irish philosopher, as emblematic of the early medieval period; Coleridgean plenitude as appropriate for the Romantic period, and the recent Eliot edition (as distinct from the Eliot corpus) for early twenty-first century textuality?

There is one immediate distinction that can be seen and that is important in the recent history of editing: that the Eliot edition exists at all is a reflection of the often fraught relations between the estates of modernist authors (notably Joyce, Laurence, and Eliot) and scholarly editors. Jonathan Bate records that '[f]or forty years the Eliot estate, in the form of the poet's widow, rigorously restricted quotation and limited cooperation with scholars,'8 leading Peter Ackroyd to explain in his biography, that 'I am forbidden by the Eliot estate to quote from Eliot's published work,'9 a restriction that Bate believes largely explains 'why Eliot's reputation took such a severe battering over the decades around the turn of the century.'10 Clearly, there were no such restrictions placed on the editing of the texts of Eriugena or Coleridge, so there was a celebratory mood about the Ricks and McCue edition of Eliot, a mood that was appropriate for the concluding conference of *Ars edendi*.

First, let us examine the format of these three editions. In an earlier discussion of Jeauneau's edition of Eriguena for a special commemorative issue of the *American Catholic Philosophical Quarterly*, 11 I made much of the fact that Jeauneau reflected a current concern with a 'rolling' postmodernist text in which the lure of the 'definitive' had been replaced by an 'open' edition *in qua uicissitudines operis synoptice exhibentur,* an exemplification of Bernard Cerquiglini's *L'éloge*

8 J. Bate, 'Fair enough?', *The Times Literary Supplement*, 6 August, 2010, 14–15, p. 15.

9 P. Ackroyd, *T.S. Eliot* (London: Hamilton, 1984), p.10.

10 Bate, p. 15.

11 D. Greetham, 'Édouard Jeauneau's Edition of the Periphyseon in Light of Contemporary Editorial Theory', *American Catholic Philosophical Quarterly* 79 (Fall 2005), 527−548.

*de la variante: Histoire critique de la philologie* (Paris: Seuil, 1989), and is to be compared with the immediately precedent edition by I.F. Sheldon-Williams, a volume in the series *Scriptores Latini Hiberniae,* in which the assertion *(desideratum?* hope? illusion?) was that 'the present edition attempts to present the text with which the author finally came to be satisfied, and at the same time to exhibit the stages of its development, through the creation of a "positive apparatus criticus".'12 Such desires for 'satisfaction' (the 'making complete' of a work as it progresses toward that most thorny of contemporary textual states, 'authorial final intention'), move Sheldon-Williams's edition in an epistemological direction in the reverse of Jeauneau. Similarly, the desire to construct a 'positive' apparatus (again, for the sake of 'fullness') and the expressed confidence that the 'scribal blunder' can be effectively distinguished from authorial idiosyncrasy are both evidence for the movement in the opposite direction of Jeauneau. Where Sheldon-Williams aims for teleology and completion, authorial and transmissional, the proliferation of textuality in the Jeauneau edition (what we might see as counterpoint or polyphony) sets out the 'critical' edition as only one state in the presentation of textual variation, and allows the 'synoptic apparatus' to become the 'fullest' part of the editorial enterprise (that is, four of the five volumes). Furthermore, what Sheldon-Williams hopefully enlists as a 'positive apparatus criticus' is nonetheless in his edition put in a conventional 'inferior' textual space, in reduced type at the *bottom* of the page, so that its positivism is in fact a mark of its degenerative status, again a conventional assumption. On the contrary, by freeing the synopticism from this mark of the 'inferior' and placing 'Versiones I–II, Versio II, Versio III, Versio IV, and Versio V' in a visual and spatial equality with one another (and by implication, with the 'critical' edition that sets the whole procedure in motion) Jeauneau forcibly moves the readerly eye (or ear) away from the plainchant of a single utterance into a polyphony with multiple voices and variance as a normative condition.

Thus, while he may be working from basically the same raw materials as Sheldon-Williams (no new witnesses of any significance have appeared of late, and Jeauneau's description of the redactions of *Periphyseon* is not substantially different from that of his immediate

12 I.P. Sheldon-Williams, ed., *Iohannis Scotti Eriugenae Periphyseon*, 4 vols, Scriptores Latini Hiberniae 7, 9, 11, 13 (Dublin: Dublin Institute for Advanced Studies, 1968−1995).

predecessor), Jeauneau holds the earlier editorial aims of 'satisfaction' and 'fullness' in abeyance, if they are accorded any value at all, in the face of textual fragmentation and proliferation. It is in the section of Jeauneau's editorial introduction designated as 'Les remaniements du Periphyseon' that the methodological and even ideological distance from Sheldon-Williams's 'satisfaction' is clearly marked:

Le *Periphyseon* nous a été transmis sous différentes formes, recensions ou versions. L'étude attentive de ces différentes versions nous permet de suivre, au moins en partie, l'évolution de l'œuvre. Nous sommes en présence, non d'un produit fini, mais d'une matière en fusion; non point d'un texte établi et fixé de façon canonique, mais d'un texte en perpétuel devenir.13

It is in this sense that *all* the variants, negative as well as positive, contribute to the *perpétuel devenir* of a text, that, as we have seen, a blank space (indicating a section that is not present in one of the versions) in the Jeauneau is just as much an authoritative variant as is one with a *different* text, even though it may be disturbing to the reader's navigation. A blank space in the Jeauneau is just as much a *presence* as is a positive textual variant. In the Eriugena edition for example, there are numerous occasions when the blank space is recorded as a 'negative reading' in one of the texts in parallel display, facing a passage from another version for which there is no equivalent in other witnesses.

And because Jeauneau believes that Eriugena 'se corrigeait constamment, ajoutant, retranchant, modifiant son texte'14 (in a manner that, as we shall see, is similar to Coleridge), Jeauneau's edition is the most expansive of the three authors and editions under review, since it aims to record the *complete* several different versions that cumulatively make up the documentary history of *Periphyseon*. 15

Jeauneau's decision to present the texts of Eriugena in facing-page parallel columns does of course place burdens on both the editor and the reader, and such parallel texts are not likely to become popular. The basic problem of creating and negotiating a parallel text is similar to that involved in the 'full score' of music, in which, as Roland Barthes notes, the reader has to negotiate both the horizontal (paradigmatic)

13 Jeauneau, vol. 1, p. xix.

14 Jeauneau, vol. 1, p. xxii.

15 Chaucerians will already be familiar with the device of the parallel text, as can be seen in the F and G versions of the *Prologue* to the *Legend of Good Women*, and parallel texts have a long and distinguished history, from Origen's *Hexapla* and on to the *Complutensian Bible*.

**Figure 1:** Pages 254–255 in *Iohannis Scotti seu Eriugenae Periphyseon: editionem novam a suppositiciis quidem additamentis purgatam, ditatam vero appendice in qua vicissitudines operis synoptice exhibentur,* ed. by É. Jeauneau, vol. 5, CCCM 165 (Turnhout: Brepols, 2003), License: CC BY-NC-ND.

for melody and the vertical (syntagmatic) for harmony.16 The reader confronted by such a 'full score' has to work in two modes, scanning *down* one text until a 'gross constituent'(in the terminology of structuralism) unit has been recognized and then moving *across* the page break to compare the gross constituent unit with a similar unit across the page example from Jeauneau. The movement downwards can be regarded as a search for *harmonics,* in a full score, and the horizontal movement a serial or narrative manoeuvre. A parallel text display works best when there is a basic accord in substantial units of a text, but not so much to obscure variation *within* a text or specific document.

As an experiment, a while back I constructed a parallel text based on the 1805 and 1850 versions of Wordsworth's *Prelude*, in which I attempted to show the complex (and not necessarily linear) relations between the two states.17 If the result is indeed a 'full score' it is a score in which elements duplicate each other, interrupt across the 'bar of difference,' and continually prevent a neat resolution of the harmonics. Such an interrupted score is to be seen in the five substantive versions of Eriugena.

Coleridge shares with Eriugena an almost obsessive involvement with change and revision. Indeed, Jack Stillinger adopts Coleridge as the *type* of the revising author, with an antitype in Keats, who very rarely returned to a poem after publication. And in Mays's edition of Coleridge, there is a similar acceptance of plenitude, reflecting the editor's view of Coleridge's composition techniques; 'Coleridge's mind operated at several levels, in several ways, and moved easily between them. An edition should display − not obscure − the variety and vitality of *his mind working*.'18 Mays's concentration on 'Coleridge's mind' is partly a reflection of the earlier Anglo-American intentionalism and partly an attempt to show that mind as it negotiates various social pressures, some quite intimate. Mays argues that '[a]n edition that displays Coleridge's working brain cannot use a "strictly synoptic procedure" because that won't do in charting that mazy mind, where "deliberation alternates with chance, and different intentions exist side by side" (cxx) or they shift and mutate haphazardly. "There is no clear tendency which

16 See for instance R. Barthes, *Elements of Semiology*, transl. by A. Lavers and C. Smith (London, Cape, 1967).

17 D. Greetham, *Theories of the Text* (Oxford: Oxford University Press, 1999), p. 316–319. [Editor's note: The Oxford University Press does not allow any content to be used under any form of open access license, which is why we have not been able to include an illustrative image of the result of Greetham's experiment.]

18 Mays, *Poetical Works* I: *Poems (Reading Text)*, Part 1, p. lxxxviii (emphasis added).

could provide the basis of a rule" (cxxi).'19 Furthermore, Mays argues that 'Coleridge's materials are unruly. The editor must therefore be, like the poet, "fluid and opportunistic" (xv) and like the reader, "fixed in a permanent state of multiple vision"'.20 Even the 'reading text' does not imply finality, for it is often merely that text reflecting 'Coleridge's concern, up to the time he lost interest (as he so often did) (cxlvi).'21 The 'reading text' is simply a device to aid in the charting of variance in the historical collation and the 'variorum text'.

Thus, the insistent revision, according to Stillinger, shows Coleridge as a 'compulsive, wilful, out of control' tinkerer with his texts.22 Given what Mays characterizes as Coleridge's 'capaciousness,' with, for example, sixteen versions of the *Ancient Mariner*, ironically the advocate of 'unity' in poetry may be one of the most 'scattered and *dis*unified poets in English literature.'23 Stillinger speculates that 'perhaps he conspicuously featured his poetry's textual instability in order to imply that his poems were always in progress toward a never-to-be attained but increasingly approached perfection. Perhaps he wished to suggest that the perfect poem is a chimera and that authority itself is therefore a fiction. Perhaps he kept changing his poems to show that he was not dead.'24 In these circumstances, a multiform edition, like that of Mays, becomes the only honest way of representing Coleridge and his methods of composition.

The poem 'Dejection: An Ode', for example, first appeared in a nascent form in the so-called 'Letter' of 1802, which Mays insists should be seen as the muddled, unstructured first inspiration, 'never intended for publication.'25 The 'reading text' in the Mays edition, because it is clear text, does not allude to this muddle, but simply prints it as poem 289, the 'Letter' containing the stanza 'O Sara! we receive but what we give/And in *our* Life alone does Nature live,' which becomes 'O Lady' in poem 293 'Dejection: An Ode.'26 In the 'variorum text,' the very

19 J. McGann, *A New Republic of Letters: Memory and Scholarship in the Age of Digital Reproduction* (Cambridge, MA: Harvard University Press, 2014), p. 116.

20 McGann, p. 117.

21 McGann, p. 118.

22 J. Stillinger, *Coleridge and Textual Instability: The Multiple Versions of the Major*

*Poems* (Oxford: Oxford University Press, 1994), p. 117. 23 Stillinger, p. 117, original emphasis. 24 Stillinger, p. 117. 25 Mays, *Poetical Works* I: *Poems (Reading Text)*, Part 2, p. 677. The poem in this form, called 'A Letter to -', is on pp. 679–691. 26 Mays, *Poetical Works* I: *Poems (Reading Text)*, Part 2, p. 689 and pp.695–702.

much shortened poem lists an array of dedicatees: 'O Wordsworth,' 'Edmund,' 'William,' 'Edmund,' and 'Lady.' Coleridge was fortunate that all of these choices are disyllables, none of which would disturb the metrics of the line.27

In my correspondence with Mays, he tells me that the 'Letter' is part of the 'circular progression (Sara Hutchinson to Wordsworth in various guises and Edmund for the generic 'poet' − i.e. Spenser) and can be understood as the muddled, unstructured first inspiration reconceived and re-projected as 'Lady,' a version of the same imaginative ideal that is at the heart of the poem.'28 But while the poem, from the 1802 'Letter' to the 1817 first publication and beyond, may indeed have an 'imaginative ideal that is at the heart of the poem' each of the variant addressees represents a significant part of Coleridge's poetic conception and reconception.

Now, all of this cumulative variance does not completely answer the question already raised of why some authors can never let go of a text and continue to re-enter the text on numerous compositional stages. Just as Beethoven would frequently add another measure to an already engraved score from his publisher, so Coleridge would not regard a print proof as anything but a way-station and not the 'final word'. But it does provide evidence of the 'perpétual devenir' that Coleridge shares with Eriugena.

It would seem that the editors of both the Eriugena and the Coleridge have similar aims: to make available to the reader an enormous corpus of variants; but the methods are very different, Jeauneau opting for a series of parallel texts containing the various authoritative witnesses in full, but without attempting a reading text or a base manuscript for collation. But Mays creates (or selects) a 'reading text' and then provides a full documentary record of variants. It is important to note that the selection of the base manuscript for Coleridge does not confer any specific authority on this witness: it is simply a device to aid in the charting of variance in the historical collation and the 'variorum text'.

As I take titles seriously, I have to believe that Ricks and McCue's decision to call their edition 'the annotated text' rather than a 'critical' text or some such makes a statement about editorial policy and procedures.

27 Poem 293 in Mays, *Poetical works* II: *Poems (Variorum Texts)*, p. 890. [Editor's note: Princeton University Press does not allow any content to be used under any form of open access license, which is why we have not been able to include illustrative images of the different variants of the poem.]

28 J.C.C. Mays in private correspondence.

And because it is an 'annotated' edition not a 'critical' edition, the Ricks and McCue volumes do not present variance in the texts presented.

The Eliot corpus is a relatively invariant body of poetry, partly reflective of Eliot's diffidence about revision. As Ricks and McCue remark: 'Although Eliot was reluctant to revise after publication, examination has shown that even repeated impressions of the same edition diverge to an unexpected extent.'29 Variance exists in despite of authorial intention. Eliot is equally aggrieved about the state of his first editions: 'I have never succeeded in getting a first edition of one of my own books printed without some errors in it, and I sometimes find that when those are corrected new errors appear.'30

Why does this distinction of purposes and practice matter in this discussion of Eriugena, Coleridge, and Eliot? As has already been shown, the five volumes of Eriugena, displaying a vast array of texts and variants, fall in line with the usual procedures of the 'literary' editions, though we should be very clear that the accumulated evidence of these five volumes is not put in service of the establishment of a singular, authoritative text. Each of the versions recorded is given unique and specific authority and is not subordinated to the support of a 'critical' or 'eclectic' text. At best, they might be likened to *Leitmotifs* recognizable in various parts (and versions) of a musical text, but not establishing a specific authority. Or, they might be the variations (like Beethoven's Diabelli, Elgar's Enigma, or Bach's Goldberg) without the theme to which they would usually relate. The Coleridge is different, depending on where you look. The volumes of the 'variorum text' in the Coleridge consist entirely of the variants (there is no 'standard' text to which they can be compered), whereas the 'reading text' provides precisely that, a clear-text presentation of an editorially preferred text, unencumbered by the sort of record of variance in the 'variorum text.'

The Eliot volumes have a clear text up front (the equivalent of the 'reading text' in the Coleridge), followed by a series of interpretative texts recording the documentary history and a commentary which is the basic rationale for the edition, announcing itself as the 'annotated text.'

The Eliot edition is not immune from the sort of incorrigible error that often plagues standard editions, as when the last line of Part II ('with eyes I dare not meet in dreams') of 'The Hollow Men' is repeatedly omitted in several subsequent editions.

29 Ricks and McCue, vol. 1, p. xii

30 Letter to Djuna Barnes 15 Oct 1936, quoted in Ricks and McCue, vol. 1, p. xii.

Similarly, the error in the dedication to Jean Verdenal in 'Prufrock' (1889 instead of 1890) is retained, although the mistake was acknowledged by Eliot, on the grounds that 'the dedication has stood for almost a century and it has been thought best not to alter it'31 an argument that might seem to support the 'socialization' of the text or could be put down to editorial weariness.

Eliot was in general receptive to Pound's advice: 'He cut out a lot of dead matter. I think that the poem as originally written was about twice the length. It contained some stanzas in imitation of Pope, and Ezra said to me "Pope's done that so well that you had better not try to compete with him" which was sound advice'.32 Actually, Eliot's memory has exercised a little self-censorship, for Pound's intercession was less delicate than 'not try to compete'. What he actually warned Eliot was that 'you cannot parody Pope unless you can write better verse than Pope – and you can't.'33

Perhaps the most striking example of divergence between published text and drafts is the opening page for the 1922 *Waste Land* versus the 'same' text in the 'editorial composite'.34 Thus, we would not know from the clear text that the original title for the poem was 'He do the police in different voices' (a quotation from Dickens, *Our Mutual Friend,* bk 1, ch. xvi),35 though this reading is confirmed in the facsimile edition containing Eliot's original typescript or manuscript, Pound's annotations and the very occasional marginal comment by Vivienne Eliot ('Wonderful').36 The decision to omit any reference to pre-publication manuscript readings in Ricks and McCue is, if you like, a very powerful example of a 'final intentions' ideology, privileging later print over manuscript draft. It does not take much imagination to speculate on the likely social and canonical status of the poem if it were still called 'He do the police', and is another example of the importance of titles.

But there is more to it than just the title. We should not imagine that there is a linear progression from the so-called 'manuscript' to the print

31 Ricks and McCue, vol. 1, p. xiii. 32 Ricks and McCue, vol. 1, p. 581.

33 T.S. Eliot, *The Waste Land: A Facsimile and Transcript of the Original Drafts, Including the Annotations of Ezra Pound*, ed. by Valerie Eliot (London: Faber and Faber, 1971), p. 127.

34 Ricks and McCue, vol. 1, pp. 55–71 (published text), and pp. 324–346 (editorial composite). [Editor's note: Images of these pages have not been possible to include here since we could not obtain an Open Access license from Faber & Faber.]

35 Ricks and McCue, vol. 1, p. 324.

36 Eliot, *The Waste Land: A Facsimile*, pp. 10–11. [Editor's note: Images of these pages have not been possible to include here since we could not obtain an Open Access license from Faber & Faber.]

edition of 1922. For example, the passage beginning 'the typist home at teatime' occurs twice in the manuscript in very different contexts and in one such is the occasion for some of Pound's more caustic comments ('perhaps be damned', 'Make up your mind' and 'inversions not warranted by any real exegience [*sic*] of metre.').37 While Eliot was generally very receptive to the sort of revisions suggested by Pound; 'the typist' section, despite its dual prominence in the manuscript, is not carried forth into 1922, which remains the *de facto* terminus for the evolution of the poem and is thus very different from the sort of variance encountered in Eriguena and Coleridge.

This potted history now means that I have to retract my earlier assumptions that the sheer weight of these three editions would mean that editing now stops. In fact, it might very well be the exact opposite: that the availability of the texts in these forms will encourage further textual examination based on the new information (specifically for Eliot). But there is another factor: before embarking on this investigation, I had worked on several previous editorial projects, separate from my writings on textual and editorial theory and history. These had included work on a) the collaborative edition of John Trevisa's *On the Properties of Things*, the fourteenth-century encyclopedia of, well, everything, in which the aim was to reconstruct the archetype lying behind and above the extant manuscripts, and b) the editing of Thomas Hoccleve's *Regement of Princes*, through the construction of an idiolect drawn from the practices in several autograph manuscripts of *other* Hoccleve's works. Neither of these projects is in any way similar to the conditions of the documents encountered in Eriugena, Coleridge, and Eliot, so I have learned a great deal in doing the research for this paper. The one underlying principle has been, and will continue to be, fidelity to the author, who, despite the dire claims of Roland Barthes, is very much alive, but alive through the loyalties and devotions (and sheer hard work) of editors working in the long tradition extending from the Alexandrian librarians to the present day. It is perhaps in this sense of a long tradition that I see these loyalties and devotions so much evident in the range and enthusiasms of this conference, and I am very grateful to have been able to add to these enthusiasms in working on this paper. I am now in a different place from before I started work on this report and thank you all for giving me the opportunity to demonstrate what I have learned from this experience.

37 Eliot, *The Waste Land: A Facsimile*, pp. 44–45.

### **Bibliography**

Ackroyd, P., *T.S. Eliot* (London: Hamilton, 1984).

#### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University* Nos. 1–22

#### Editor: Dag Norberg

#### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University*

#### Nos. 23–46

#### Editor: Jan Öberg

#### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University* Nos. 47–48 Editor: Monika Asztalos

#### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University*

#### Nos. 49–53

#### Editor: Hans Aili and Gunilla Iversen

### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University* Nos. 54–58

#### Editor: Hans Aili

54. *Alexander Andrée, Erika Kihlman*, ed. Hortus troporum. Florilegium in honorem Gunillae Iversen. A Festschrift in Honour of Professor Gunilla Iversen on the Occasion of her Retirement as Chair of Latin at Stockholm University. Stockholm 2008. Pp. XIX+384; 28 pl.

#### STUDIA LATINA STOCKHOLMIENSIA *Published by Stockholm University*

#### Nos. 59–

#### Editor: Maria Plaza

#### CORPUS TROPORUM

#### *Studia Latina Stockholmiensia* (SLS)*/Corpus Troporum* (CT)

CORPUS TROPORUM I, Tropes du propre de la messe. 1. Cycle de Noël, éd. Ritva Jonsson. SLS 21. Stockholm 1975.

CORPUS TROPORUM II, Prosules de la messe. 1. Tropes de l'alleluia, éd. Olof Marcusson. SLS 22. Stockholm 1976.

CORPUS TROPORUM III, Tropes du propres de la messe. 2. Cycle de Pâques, éd. Gunilla Björkvall, Gunilla Iversen, Ritva Jonsson. SLS 25. Stockholm 1982.

CORPUS TROPORUM IV, Tropes de l'Agnus Dei. Edition critique suivie d'une étude analytique par Gunilla Iversen. SLS 26. Stockholm 1980.

CORPUS TROPORUM V, Les deux tropaires d'Apt, mss. 17 et 18. Inventaire analytique des mss et édition des textes uniques par Gunilla Björkvall. SLS 32. Stockholm 1986.

CORPUS TROPORUM VI, Prosules de la messe. 2. Les prosules limousines de Wolfenbüttel, Herzog August Bibliothek Cod. Guelf. 79 Gud. lat., par Eva Odelman. SLS 31. Stockholm 1986.

CORPUS TROPORUM VII, Tropes de l'ordinaire de la messe. Tropes du Sanctus. Introduction et édition critique par Gunilla Iversen. SLS 34. Stockholm 1990.

CORPUS TROPORUM IX, Tropes for the Proper of the Mass. 4. The Feasts of the Blessed Virgin Mary. Edited with an Introduction and Commentary by Ann-Katrin Andrews Johansson. CT. Stockholm 1998.

CORPUS TROPORUM X, Tropes du propre de la messe. 5. Fêtes des Saints et de la Croix et de la Transfiguration. A Introduction et commentaires (Pp. 647 + carte + 13 photos). B Édition des textes (Pp. 560). Par Ritva Maria Jacobsson. CT. Stockholm 2011.

CORPUS TROPORUM XI, Prosules de la messe. 3. Prosules de l'offertoire. Édition des textes par Gunilla Björkvall. CT. Stockholm 2009. Pp. X + 254.

CORPUS TROPORUM XII, Tropes du Gloria, vol 1, Introduction et édition des textes, (428pp.), Vol. 2. Aperçu des manuscrits (2438pp.+32 planches), Par Gunilla Iversen, SLS 61, Stockholm 2014.

*Pax et Sapientia*. Studies in Text and Music of Liturgical Tropes and Sequences, in Memory of Gordon Anderson, ed. Ritva Jacobsson. SLS 29. Stockholm 1986.

*Recherches nouvelles sur les tropes liturgiques.* Recueil d'études réunies par Wulf Arlt et Gunilla Björkvall. SLS 36. Stockholm 1993.

This is the fi fth and fi nal volume of lectures on textual criticism and classical philology – broadly understood – given within the framework of the Ars edendi research programme (2008 – 2015).

Two of the six papers in this volume stem from a 2015 workshop on editorial theory and method, the theme of which dealt with fragments and the writing of commentaries. As regards the former, S. Douglas Olson problematizes the creation and continuation of scholarly knowledge concerning texts that have only come down to us in a fragmentary state, emphazising the challenges and pitfalls that lay in wait for the editor. Benjamin Millis offers a nuanced homage and apology for the traditional text edition with a scholarly commentary, especially underscoring its importance as a connective pathway between text and reader as well as the impetus it can give to scholarly research.

The other four lectures were given at the concluding conference of the Ars edendi programme, held in August 2016. In a case study Cynthia Damon shares her refl ections on how to digitally edit Pliny's *Natural History* in a form that will provide this work's rich reception history and at the same time its extensive use of sources, many of which are now lost. The digital component is also prominent in Odd Einar Haugen's contribution in which he shows that digital mark-up is also an editorial enterprise and how it can be useful for the textual scholar. Dorothea Weber gives an insider's view of the *Corpus Scriptorum Ecclesiasticorum Latinorum*, an editorial project on-going since 1864, and especially how improved cataloguing has led to numerous discoveries of texts by St. Augustine. As a conclusion to the volume, David Greetham, one of the founders of the Society for Textual Scholarship, refl ects on three different methods for editing texts that have undergone various degrees of rescription, namely the *oeuvres* of Eriugena, Coleridge, and Eliot.

Erika Kihlman and Denis Searby eds Ars Edendi Lecture Series Vol. V

STUDIA LATINA STOCKHOLMIENSIA

LXIII

Volume V

Edited by Erika Kihlman and Denis Searby


**2.1 Infinite horizontal slab equation (IHSE)**

The gravity effect or the Bouguer gravity anomaly can be calculated at any point of Cartesian coordinates (x, z) on the surface of the earth or reference measured datum, due to BHS or IHS is given by the Eq. (1) as follows:

$$\text{gB}(\mathbf{x}, \mathbf{z}) = 2\pi \text{phG} \tag{1}$$

where gB: is the gravity effect or Bouguer gravity anomaly due to slab in m. Gal (10�5 m/s2 ).

ρ: is the density of the horizontal slab in gm/cm3 (103 kg/m3 ).

h: is the thickness of the IHS in km (103 m).

G: is the Universal Gravitational Constant (6.67 � 10�11 Nm2 /kg2 ), N: is referring to Newton or force unit.

The Eq. (1) can be rewritten in a modified form for the new method purpose as follows:

$$\mathbf{gB(x,z)} = 2\pi \mathbf{G} \sum\_{i=1}^{N} \overline{\Delta \rho}(\mathbf{i}) \Delta \mathbf{z}(\mathbf{i}) \tag{2}$$

where Δρ: is the average vertical density-contrast in gm/cm3 (103 kg/m3 ). Δz: is the difference between the depth of top and bottom the IHS in km (103 m).

i: is the index number (i = 1, 2, 3 … N).

N: is the number of rocks 'formations, and

$$\overline{\Delta\rho} = \frac{\sum\_{i=1}^{N} \rho(\mathbf{i})}{\mathbf{N}} - \rho\_{\text{basement}} \tag{3}$$

where PN i¼1 ρð Þi N : is the average density, and ρbasement: is the density of basement rock.

In the proposed method, the Infinite Horizontal Slab Equation (IHSE) is used to calculate the gravity effects at the earth's surface (or any reference datum) for each subsurface rock' formation that, covering the basement rocks for any sedimentary basin area, and using the IHSE ability, efficiency in the estimating, tracing the formations' thicknesses (or depth), relative to the underlying basement rocks. By using the prior information of control point (or borehole), through profile (s) line (s) of Bouguer gravity anomaly which represents the vertical cross-section (s) for the area of study.

Simply the idea of the new method is based on the assumption that: the sedimentary rock' formations covering the basement rocks are the formations deposited individually in form of layers, or a group of HIS, of different densities distributions is being stacked in columns over the basement's rocks (**Figure 1**). And hence for any point (1, 2, 3, and 4) at the earth's surface (or datum), the total gravity effect is the summation of all gravity effects (at point 4) contributed by each individual slab (1, 2, and 3) along the vertical axis of that point at the earth's surface, were using the average vertical density-contrast (Δρ), between each formation's slab individually with basement rocks at points 1, 2, 3, and at point 4. Here is the new keen point of view that is: the average vertical densities'-contrasts between the stacked vertically of the IHSs and basement rocks are used in inversion calculations instead of densities'-contrasts between IHSs and their surrounding rock materials, through the

**Figure 1.**

*Bouguer gravity anomalies comparable to all possible rock' formations overlying the basement rocks.*

importance for this concept, it being became possible for some extent to separate of Bouguer gravity anomaly to its components that representing probably of all possible rock' formations overlying the basement rocks, according to the prior known information about those rock' formations (thicknesses, depths, and densities), either from subsurface (borehole, etc.) or the surface geology (field, etc.).


*3.4. Sterols*

The use of kiwi extract promoted the accumulation of a small (but not negligible) quantity of phytosterols: 1.00 and 3.81 mg/100 g of total lipids in buffalo and sheep cheeses, respectively. On the other hand, the sterol profile of the rennet cheeses was characterized by cholesterol alone (Table 3). The phytosterols we found in cheeses were stigmasterol, campesterol and β-sitosterol, which represent the most abundant sterols in kiwifruit [30].

#### *3.5. Volatile Organic Compounds*

As expected, kiwifruit and cheeses were di fferent in terms of the quantity and quality of the odorant compounds (Table 4). The total amount of VOCs from the kiwifruits was about seven times higher than from the cheeses. The most represented category of odorants in kiwi were aldehydes (about 85% of total VOCs), and carboxylic acids and ketones in the cheeses (65% of total VOCs).

More specifically, (E)-2-hexenal and hexanal were the most abundant odorants in the kiwi extracts used in this experiment. These volatile aldehydes are produced during fatty acid oxidation by the lipo-oxygenase enzyme [31]. Other substances a ffecting odour were the ethyl esters of butyric and caproic acids, two alcohols (2-hexen 1-ol and 1-hexanol) and one ketone, 1-penten-3-one (Table 4).

In terms of cheese, the most represented odorant was 2-butanone (a ketone), which was above 25% of the total VOCs in all the cheeses, followed by acetic acid, 2,3-butenedione (another ketone), caproic, caprylic and nonanoic acids (carboxylic acids). 2-butanone and 2,3-butenedione were not detected in the kiwi pulp, while acetic, caproic, caprylic and nonanoic acids were identified both in the kiwi pulp and in the bu ffalo and sheep cheeses produced, and both using calf rennet and kiwifruit extract. On the other hand, caproic, caprylic and nonanoic acids are typical components of both bu ffalo [32] and sheep milk [33].

Terpenes are typical components of kiwi pulp but not of cheese (except for β-phellandrene).

Of the odorants that most characterize kiwifruit, in both bu ffalo and sheep cheeses we found only (E)-2-hexenal (representing about 80% of VOCs in pulp kiwifruit), ethyl caproate and 2-hexen-1-ol. Interestingly, in the kiwi-cheeses we found 3-methyl eicosane and dibutyl formaldehyde, which were found only in low quantities in the kiwi extract. Finally, cheesemaking was a significant variation factor for the total esters only in bu ffalo cheese, 3-pentanone 2-hydroxy and β-phellandrene, which was the only terpene we detected in the cheeses.

**Table 4.** Volatile organic compounds of cheeses made with kiwifruit extract or calf rennet (μg/kg of raw matter) (Part 1).

**Table 4.** *Cont.*

**Table 4.** *Cont.*

BMC, buffalo–calf rennet cheese; BMK, buffalo–kiwifruit cheese; SMC, sheep–calf rennet cheese; SMK, sheep–kiwifruit cheese; SEM, standard error medium; S, significance; ns, not significant; ne, not estimable. \*: 0.01 < *P* < 0.05; \*\*: 0.01 < *P* < 0.001; \*\*\*: *P* < 0.001;

## **4. Discussion**

#### *4.1. Tecnological Parameters*

Table 1 shows that the technological parameters were affected by the coagulant. As demonstrated by the mL of whey released (Table 1) and by the amount of total solid (Table 2), the higher initial cheese yield from calf rennet was due to a higher whey holding capacity and, consequently, a lower and slower curd syneresis. This result is due to the different proteinase action between actinidine and chymosin. Chymosin is an aspartate proteinase that hydrolyses the Met105–Phe106 linkage of K-casein, cleaving out glycol-macropeptide. This leads to a decreasing polarity of the casein micelle and thus promotes the coagulation of casein. On the other hand, actinidin is a cysteine proteinase that cleaves bonds with basic amino acids in position P1, especially in β-casein, with a consequent reduction in milk clotting [5]. Thus, chymosin hydrolysed k-casein only, generating a more elastic and structured curd. Actinidin, instead, cleaves bonds in different sites, producing a curd with small peptones and with a more rapid syneresis.

#### *4.2. Physic-Chemical Composition*

The higher syneresis of both buffalo and sheep curd from kiwi extract was responsible for the higher dry matter of these cheeses compared to those obtained by calf rennet (Table 2). Thus, the higher content of lipids and ashes in BM-K and in SM-K are due to a "concentration" effect. However, the cheese protein content was not affected by the type of coagulant used. This could be due to the higher proteolysis of cheeses obtained with kiwi extract, which produces small peptide fragments (5b), which, in turn, are soluble in whey, thus offsetting the wider syneresis of these kinds of cheeses.

The level of carbohydrates was expected to be lower in cheeses from kiwifruit, as these lose whey to a higher extent. In reality the level was higher than expected, perhaps because kiwi extract provided some sugars.

The mineral composition was in line with Cichoscki et al. [34] (Table 2). In spite of the wider syneresis of cheeses from kiwi and their solubility in water, except for sodium, none of the coagulants affected the mineral content of the cheese. Again, these minerals came to some extent from the kiwifruit extract. The fact that calcium was affected by the cheesemaking procedure is difficult to explain, as it is present in milk in three different forms: ionic, soluble as calcium phosphate and colloidal in apatite bridges within casein micelle.

The kind of coagulant affected the sodium content of the cheeses. In fact, cheeses produced by kiwifruit extract showed the lowest sodium amount. Calf rennet is rich in sodium chloride and sodium

benzoate, which are added as a preservative, thus partially explaining the different amount of sodium in the cheeses.

The different proteolytic activity of the two kinds of coagulant may explain the differences in colour of the cheese. In fact, both the lower lightness and the higher yellow index, might be related to the occurrence of proteolysis, which, in turn, is related to cheese browning [35]. Is worth noting that the colour differences between two coagulants were detectable only using instruments, as the total colour differences (ΔE) were much lower than 3, which is the discrimination threshold for the human eye [19].


**4. Phenolic**

*Saccharomyces*

**3. Alkaloids**

*in secondary metabolite formation.*

**Figure 1.**

hypertensive) [15].

The methods and technology used to improve pharmaceutical production of secondary metabolites in the *S. cerevisiae* have advanced rapidly in recent years. We discuss below the progress in developing biosynthetic pathways of *Saccharomyces cerevisiae*' secondary metabolites with anticancer potential: alkaloids,

*A short description of the formation pathways of secondary metabolites [11, 12]. Four sub-groups of microorganism and plant-generative metabolites involve terpenoids, polyketides, non-ribosomal peptides and alkaloids. Biosynthetic genes (BGC's) are structurally classified into the genes that encrypt major biosynthetic enzymes, supplementary enzymes, precursors in the process of biosynthesizing, resistance factors or transporters*

phenolic, terpenoids, polyketides, non-ribosomal peptides, and vitamin C.

Several studies have used *S. cerevisiae* in recent years as a host to engineer the biosynthetic process of alkaloids. Alkaloids are complex nitrogen molecules that are extremely bioactive. There are reportedly approximately 50 alkaloid medications, including vincristine (cancer drug), codeine (analgesic drug) and noscapine (antitussive drug). They are unique for the cell cycle and the process, because they block metaphase (M phase) in mitosis. They block tubulin's ability to form microtubules via polymerization. Dysfunctional spindle structures, avoid chromosome separation and cell proliferation. Strictosidine, which had been synthesized by novo, was the earliest study of alkaloid plant origin in *Saccharomyces cerevisiae* strains [14]. Strictosidine is a significant intermediate product in the terpenoids Indole alkaloids (TIAs) biosynthesis that include vincristine (antitumor) and ajmalicine (anti-

The metabolic course of *Saccharomyces cerevisiae* for protoberberine alkaloid (S) canadine from racnorlaudanosolin has been optimized by Galanie et al. [16]. The secondary metabolite of Berberine has numerous pharmacological effects, such as antidiabetics, antibacterial, anti-ulcerones and anti-inflammatory effects. In vivo and vitro experiments with berberine, the results of arresting cell cycle during G1 or G2/M and apoptosis of tumor cell were shown to be anti-cancer activity. Berberine also was found to induce autophagy and stress in the endoplasmic reticulum, resulting in the invasion and inhibition of the tumor cells. Berberine has been proven to lower angiogenesis by decreasing expression of VEGF in addition to its apoptotic effects. The cancer cell migration was also decreased. In the respective

**112**

Phenolic are a large category of secondary plant metabolites that have at least one hydroxylated ring. Flavonoids and stilbenes are two groups of metabolites highly appreciated as a nutrient and therapeutic agent among the phenolic developed by phenylpropanoid pathways in the plant [18]. As a host cell, *Saccharomyces cerevisiae* is well equipped to promote phenolic compound biosynthesis. The following phases include cancer development: initiation, development, proliferation, invasion and metastasis. Initiation links by free radicals, inflammatory mediators, radiation, smoke of cigarette that damage the DNA-product, which can cause genetic mutation and replication of cells which are mutated results to cause carcinogenesis [19].

It has been noted that phenolic compounds i.e. ellagic acid and delphinidin show significant protective effects for example, apoptotic activity in colon cancer cells. In prostate, liver and leukemia cancer cells, delphinidin also showed significant activity. Cell apoptosis can also be caused by phenolic compounds. The mechanisms of invasion and migration of human cancer are also updated (**Figure 2**) [20].

**Figure 2.** *Potential of secondary metabolite protective mechanisms for cancer management [17].*


*2.6. Performance Evaluation Indicators for the Model*

Confusion matrix, accuracy, precision, recall, and F1-score are usually used to evaluate the performance of models for single-label image classification issues [37]. The confusion matrix is mainly used to compare the objective results with the predicted results when evaluating the recognition accuracy of the images. Accuracy refers to the probability of predicting correct samples among all samples. Precision indicates the proportion of samples with positive predictions that are correctly predicted. Recall denotes the proportion of correctly predicted outcomes in the actual sample of true examples. In the actual situation, precision and recall are mutually "restricted". Therefore, we need the F1-score, a weighted average of precision and recall, to comprehensively evaluation the performance of models. The higher the F1-score, the better the performance of the model. The calculation formula of each indicator is as follows.

$$\text{Precision (P)} = \frac{TP}{TP + FP} \tag{5}$$

$$\text{Recall (R)} = \frac{TP}{TP + FN} \tag{6}$$

$$\text{Accuracy (Acc)} = \frac{TP + TN}{TP + TN + FP + FN} \tag{7}$$

$$\text{F1-score} = \frac{2 \times \text{P} \times \text{R}}{\text{P} + \text{R}} \tag{8}$$

Here, *TP* is the number of samples where the actual case is true, and the predicted outcome is positive. *TN* is the number of samples where the actual case is true and the predicted outcome is negative, and the same for *FP* and *FN*. They can be calculated by a confusion matrix.