Registering Interferometric SAR Images by Applying the Marr- Hildreth
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Registering Interferometric SAR Images by Applying the Marr- Hildreth Operator to Interpolated Windows Shyamalee Mukherji Centre of Studies in Resources Engineering Indian Institute of Technology, Bombay India. ABSTRACT The Marr-Hildreth operator first smoothes the image with a Gaussian function and then finds the laplacian of the smoothed image. The resulting image has both positive and negative values. This image is thresholded at zero to produce a binary image. These binary images are used to match the original images. Since the windows to be matched are binary, the number of matching pixels in the windows is the metric used for matching and there are fast algorithms to compute this metric. The number of matching pixels for one offset between the windows is computed and then the change in this number as one of the windows is translated across the other is computed. For horizontal offsets, the scan-lines of the windows are run-length encoded. The number of matching pixels changes only when the pixels underlying the end-pixels of the runs of the window being translated change. Since the end- pixels of the runs, except for the first and last pixels of the scan-lines occur in pairs and are complementary, the change in the number of matching pixels can be computed by considering only the right-end pixels of the runs. Further, the change in the number of matching pixels increases or decreases only when right-end pixels of the runs of the window being translated cross over left-end pixels of the runs of the underlying window. Therefore, the change in the number of matching pixel pairs is computed for the first shift of the master window and the increase or decrease in the change is computed for the other positions. The same algorithm can be applied for shifts in the vertical direction. we showed that registering interferometric SAR images using the Marr-Hildreth operator yields an interferogram that is comparable to that obtained using cross-correlation to find the matching points. Sub-pixel precision in matching was obtained by interpolating the matching-metric matrix. In this paper, we apply the Marr-Hildreth operator to interpolated windows of the images and compare the results with those obtained by applying cross-correlation to the windows. The windows to be matched are interpolated using cubic B-splines, the Marr- Hildreth operator is applied to these interpolated windows, the resulting windows are thresholded at zero to obtain binary windows and then the binary windows are matched using the fast algorithm to find the matching points with sub-pixel precision.