Figure 1 A cartoon illustrating some sample weights on the negative instantaneous amplitude. Several pixels are shown in squares and their corresponding weights in circles. The salt boundary is defined as areas where the negative instantaneous amplitude is below a threshold.
The top panel of Figure 2 shows the negative of the instantaneous amplitude of a synthetic salt boundary. This is the input for the weight calculation. The resulting weight matrix is extremely large: where m and n are the dimensions of the image. Because this matrix is so large, checking the quality of weights is problematic. We can however view all of the weights for particular pairs of pixels. For instance, the bottom of Figure 2 is the weight between each pixel and the adjoining pixel directly above it. Notice that it follows the peak of the amplitude.
Figure 3 A cartoon of the sampling of one pixel up to 16 samples. The black areas are sampled.
We found that the best results are obtained when the maximum search distance is greater than 30 pixels. The maximum search distance is the maximum distance between pixels, beyond which the weights are set to zero. Using large search distances causes two problems. First, the matrix becomes more dense and requires more storage space. Second, the weights of the pixels at greater distances far outnumber those at close distances causing a bias in the weight matrix. Shi and Malik (2000) used a decaying distance weight to reduce this bias. We found that if we only use windows that are centered at powers of 2, then the matrix is still sufficiently sparse while still benefiting from greater search distances. However, this obviously causes many distances to be not sampled at all. Figure 3 shows the sampling of one pixel up to a distance of 16 samples. To correct this, we plan to randomly sample from within the maximum search distance so that the number of non-zero points is approximately the same for all distances.