Application to seismic

To apply this segmentation method to seismic data, the weight calculation needs to be modified. Rather than looking for clusters of pixels with similar intensity, we are now looking for groups of pixels on each side of the bright amplitude salt boundary. Therefore, we want the weights connecting pixels on either side of the salt boundary to be low and the weights connecting pixels on the same side of the salt boundary to be relatively high. Taking the negative of the maximum amplitude along the shortest path between two nodes as the weight would insure that the weights connecting pixels on either side of the salt boundary will be low. However weights on the same side would be alternating from low to high as they go from peak to trough on the seismic data. This could make the grouping more uncertain. To correct this problem, we take the negative of the maximum of the absolute value of the complex trace (instantaneous amplitude) along the shortest path between two nodes.

If two pixels happen to be adjacent to each other, then it doesn't make sense to take the minimum of the two as the weight. This would make the weight connecting pixels within the boundary itself extremely weak, causing the segmentation algorithm to fail. Our solution is to set the weight equal to unity for adjacent pixels. This puts emphasis on the relative difference between weights calculated from pixels that are not adjacent to one another.

Alternatively, for pixels that are adjacent to one another, we can make the weight a function of similarity in intensity, similar to the standard implementation of the segmentation method. For instance, the weight connecting two adjacent pixels, Pixel₁ and Pixel₂ can be calculated as:  

$${\rm Weight(1,2)=1-\sqrt{(Amplitude(Pixel_1)-Amplitude(Pixel_2))^2}}.$$ (3)

This causes weights parallel to the reflections to be stronger, making it more likely to partition along reflections. Thus far, both of these approaches give similar results.