before describing in detail the particular method of achieving an extended range of original scene exposures over which the image captured on film retains its linear character , it should be observed that the present invention resides primarily in a novel combination of steps to generate and utilize an inverse shaping lut which are readily executed using conventional digital image scanning and processing circuit and components . accordingly , the structure , control , and arrangement of such conventional circuits and components have been illustrated in the drawings by readily understandable block diagrams which show only those specific details that are pertinent to the present invention , so as not to obscure the disclosure with structural details which will be readily apparent to those skilled in the art having the benefit of the description herein . thus , the block diagram illustrations of fig1 does not necessarily represent the mechanical structural arrangement of the exemplary system , but are primarily intended to illustrate the major structural components of the overall image scanning and processing system in a convenient functional grouping , whereby the present invention may be more readily understood . fig1 is a block diagram of an overall digital image processing system . an image scanner 10 outputs digitally encoded values representative of the r , g , b color content at an nxm array of spatial sampling points taken from film image 12 . these r , g , b digital values are coupled to a programmed digital processor 14 , which could be , for example , a general purpose vax digital computer sold by the digital equipment corporation or a special purpose computer designed for a specific image processing system . in any case the computer is programmed to perform the steps to be described below with reference to fig .&# 39 ; s 2 and 3 , and through which the r , g , b digital values are controllably modified in order to effect the extension of the linear range desired . the modified r , g , b values may be further processed to affect other desired improvements in the processor 14 before being sent to a digital recorder 16 for digital encoding and storage for later use , or before being sent to a digital - to - analog converter 18 , and then sent to a writer or display device 20 , such as a color print engine or display , whereat the contrast adjusted image is reconstructed . the first step of constructing an inverse look - up table which is to reside in processor 14 in fig1 is illustrated in fig2 . curve 1 shows an example of the &# 34 ; toe &# 34 ; region of a plot of the negative density versus incident log exposure to the film . curve 2 is formed by extending the straight line central portion ( not shown ) of curve 1 . only the toe region is shown for clarity . a single set of curves are shown for the purposes of illustration , however it should be understood that three sets of curves are to be employed , one each for the red , the green , and the blue digital images . the dashed lines show the separation of the densities that would result from two neighboring exposures both on to the real film , exemplified by curve 1 , and an ideal &# 34 ; linearized &# 34 ; film , exemplified by curve 2 . the ratio given in equation ( 1 ) is a measure of the adjustment in contrast which would result at the indicated point in the &# 34 ; toe &# 34 ; resulting from linearizing curve 1 . ## equ1 ## where δd1 is the density difference which would result in the actual film ( curve 1 ) from two nearly equal exposures , δd2 is the corresponding density difference which would result in the linearized film ( curve 2 ) from the same two exposures , γ is the contrast adjustment factor required to linearize curve 1 . as the slope of curve 1 approaches 0 at low exposures , δd1 also approaches 0 , and in this idealization the contrast adjustment would increase without limit . however , this is not practical when applied to an actual film converted to an actual digital image . all real films exhibit grain noise when scanned with apertures of a practical size , and furthermore all digital images will contain some noise due to being forced to represent their magnitude at each point using numbers of finite precision ( i . e ., quantization noise ). these two sources of noise remain of finite extent even in the portion of the toe of curve 1 which has a vanishingly small slope . thus if the straightening processes exemplified by curve 2 were carried to its extreme limit , this noise would be magnified by an unlimited amount . of course , this would have a negative impact on image quality . however , this problem can be controlled while much of the benefit to the tone scale of the image can be achieved by limiting the contrast adjustment to some maximum upper limit , such as 4 . 0 . this partial linearization can be represented in the following functional form : ## equ2 ## where γ , δd2 , and δd1 have the same meaning as in equation ( 1 ), γ &# 39 ; is contrast adjustment to apply to curve 1 to achieve the partially linearized density , γ max is the maximum value which should be used to achieve the partial linearization of curve 1 . the maximum limit , γ max , is set at a different level depending on the noise contained in the digital image . thus for low noise film such as kodak ektar25 negative film recorded with 10 bits of precision , the upper limit to the adjustment may be as high as 8 . conversely with higher noise film such as kodak gold1600 or film recorded with a lower bit resolution , the upper limit to the adjustment may be only 2 . in order to achieve the improvement , an estimate of the minimum density from the film used to capture the image must be obtained . this may be done by scanning an unexposed portion of the same film strip as that upon which the image was captured , and by converting those scan signals to a digital image which has been converted from the film &# 39 ; s r , g , b transmission to it &# 39 ; s r , g , b density using means such as described in fig1 . any convenient area may be scanned in order to find the minimum density . for instance , one could scan the narrow regions between the frames , or in clear areas along the edge of the film , or on the leader before the first image or after the last image . when the scanning is done using a relatively large aperture which would be satisfactory to generate a digital image for output to a relatively low resolution reproduction medium such as standard broadcast video , then the density data so generated may then be searched for its lowest r , g , and b values . these values may then be used as the estimate the minimum density . however if the scanning is done using a relatively small aperture which would be needed to generate a digital image for output by a high resolution output device , then for each of the r , g , b images an nxn array of neighboring scan values should be averaged together in transmission space and that average value reconverted to density . the value of &# 34 ; n &# 34 ; will usually lie in the range from 4 to 32 . this process will result in a second lower resolution r , g , b image which can be searched for its lowest r , g , and b values . these values may then be used as a less noisy estimate of the minimum density . after the minimum density is found , the image bearing portion of the film must also be scanned and converted to an r , g , b digital density image using the same means as described for fig1 . the digital image may then be shifted in such a way that after the shift it would have the same density values as if it had been captured on the standard film exemplified by curve 1 in fig2 . finally , the digital image must be adjusted by a function which increases the slope according to the functional form given in ( 2 ) above . this may be done by passing the digital image through an lut . referring to fig3 curve 1 is a graphical representation of such a lut with the contrast adjustment having an upper limit of 4 . 0 . the table may be generated by a numeric integration of the function ( 2 ) to create a lut relating the measured density to the &# 34 ; linearized &# 34 ; density . this may be followed by a shifting of the output values of the table so that for at least one midscale input density the same output density is obtained . as would be understood by those skilled in digital image processing art , the range of input values to the lut is determined by the range of numeric values which characterize the input medium . as would be further understood by those skilled in digital image processing art , if in following the above method , some output values from the lut turn out to be negative , and if the digital processing system can not tolerate such negative values in the output image , then a further shift may be introduced into the lut output values in order to insure that the output image contains only positive values . this would , of course , necessitate that all subsequent processing steps anticipate the occurrence of numeric values for the digital image which will be larger than otherwise would have been the case . furthermore , it should be noted that the lut values could be adjusted up or down to accommodate the actual minimum density of the film being scanned instead of adjusting the density of the image to accommodate the location of the minimum density in the lut . a second embodiment to the contrast adjustment can be obtained in the following way . at a some point on the toe of curve 1 , which depends on the noise in the digital image , the signal to noise ratio of a digital image of low modulation will reach a value below one . when this occurs , the potential benefit of an improved tone scale will be more than offset by the increased visibility of the noise . thus below this point , not only is there no advantage of further increasing the contrast , but there is no advantage of increasing the contrast at all . thus instead of maintaining the contrast adjustment at a constant value , the contrast adjustment should be gradually cut back in magnitude . one preferred example of a function which would gradually reduce the contrast adjustment back to 1 is given by the following equations : ## equ3 ## where γ , δd2 , and δd1 have the same meaning as in equation ( 1 ), γ &# 39 ; is the contrast adjustment to apply to curve 1 to achieve the partially linearized density , γ max is the maximum value which should be used to achieve the partial linearization of curve 1 . a , b , c , d are constants which depend upon the maximum contrast adjustment . for instance if the maximum contrast adjustment were to be 4 . 0 , then a would equal 3 . 0 and b would about equal 0 . 632 , if c were equal to 1 . 0 and d were equal to 5 . 0 . as with the first embodiment of the contrast adjusting function , equation ( 2 ) above , in which a maximum contrast adjustment was used , this improvement can also be achieved using a look - up table . this may be done by employing the procedure given above for the first embodiment except that the contrast adjusting function given by equation ( 3 ) is used in the numerical integration . curve 2 in fig3 is a graphical representation of such a lut with the contrast adjustment having a maximum value of 4 . 0 . as would be appreciated by those skilled in the art , other functions may also be employed to gradually reduce the contrast adjustment , all of which would still be within the scope of this invention . furthermore additional functionally may be built into the linearization lut . for instance , the output values could all be multiplied by a constant which would adjust the overall image contrast to accommodate a standard data metric or to accommodate the down stream output device . in addition , the dynamic range of the contrast adjusted image can be limited as required by simply limiting the range of the output values from the lut . furthermore , the number of bits representing the image can be conveniently reduced by consolidating a number of input values into a single output value . finally , the output image can be non - linearly transformed by the linearization lut if required by the output device . so for instance , the lut output values can be the negative anti - log of the negative of the contrast adjusted densities . as would be apparent to those skilled in the art , any mixture of this additional functionality may be obtained when using the linearization lut . while i have described the invention in reference to representative values for the image being digital values , as would be understood to those skilled in the manipulation of images , the invention could be practiced using any form for the representative values , including analog representations . while i have shown and described the present invention in accordance with a preferred embodiment , it is to be understood that the same is not limited thereto but is susceptible to numerous changes and modifications as known to a person skilled in the art , and i therefore do not wish to be limited to the details shown and described herein but intend to cover all such changes and modifications as are obvious to one of ordinary skill in the art .