Registering Interferometric SAR Images by Applying the Marr- Hildreth

							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.