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.

${\bf v}_{ij}$ is a vector representing the shortest path between two nodes ${\it i}$ and ${\it j}$ but excluding the nodes themselves. The weight connecting two nodes ${\it i}$ and ${\it j}$ is determined from the minimum of the negative instantaneous amplitude A sampled along ${\bf v}_{ij}$ and a user specified tolerance $\mu$ as:

$$W_{ij}=\left\{ \begin{array} {cc} 0 & \mbox{({min} A(${\bf v... ...< $\mu$\space }) \ 1 & \mbox{otherwise}. \end{array} \right.$$ (3)

The algorithm as designed by Shi and Malik (2000) is capable of using weights that are real-valued instead of binary as we are using here. We have found thus far that binary weights give the best results, but we still wish to experiment with real-valued weights. If we determine that binary weights are the best way to go, then we can take advantage of the cost savings of using logical arrays instead of real.