Figure 1: The log-Gabor transform compared to other multiresolution schemes. a. Schematic contours of the log-Gabor filters implented in Fischer (2007) in the Fourier domain with 5 scales and 8 orientations (only the contours at 78% of the filter maximum are drawn). b. The real part of the corresponding filters is drawn in the spatial domain. The two first scales are drawn at the bottom magnified by a factor of 4 for a better visualization. The different scales are arranged in lines and the orientations in columns. The low-pass filter is drawn in the upper-left part. c. The corresponding imaginary parts of the filters are shown in the same arrangement. Note that the low-pass filter does not have imaginary part. Insets (b) and (c) show the final filters built through all the processes described in Section II. d. In the proposed scheme the elongation of log-Gabor wavelets increases with the number of orientations nt . Here the real parts (left column) and imaginary parts (right column) are drawn for the 3, 4, 6, 8, 10, 12 and 16 orientation schemes. e. As a comparison orthogonal wavelet filters ’Db4’ are shown. Horizontal, vertical and diagonal wavelets are arranged on columns (low-pass on top). f. As a second comparison, steerable pyramid filters [30] are shown. The arrangement over scales and orientations is the same as for the log-Gabor scheme.

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