Simple Amplitude Boundary

 

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Figure 1 Left is a simple model of a high amplitude salt boundary. Right is the partitioned output of the segmentation method.

On the left in Figure is a simple model of a salt boundary. The vertical stripe in the middle is the high amplitude salt reflection. The results of the segmentation method can be seen on the right. The pixels have been partitioned into two groups, one on either side of the boundary.

 

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Figure 2 Left is a simple model of a high amplitude discontinuous salt boundary. Right is the partitioned output of the segmentation method.

On the left in Figure is the same simple model as Figure yet with a discontinuity. Notice that the output result on the right partitions the image across the discontinuity. Although only a simple test case, this demonstrates that this segmentation method can successfully partition data where the amplitude is discontinuous.

The resulting ${\bf y_2}$ eigenvector for the discontinous model is shown on the left in Figure . It is this eigenvector that is used to partition the data. The splitting point is at zero. All values greater than zero will be in one group and all values less than zero in the other group. However, a practical measure recommended by Shi and Malik (2000) is to calculate the normalized cut at several splitting points across the eigenvector and take the minimum. On the right in Figure is a contour plot of the ${\bf y_2}$ eigenvector. Each contour can be thought of as the partition for a different splitting point. Notice that the contours are spread out in the area of the discontinuity. Here the algorithm is unsure of where to track the salt boundary and basically opts for the shortest distance.

 

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Figure 3 Left the ${\bf y_2}$ eigenvector of Figure . Right is a contour plot of the ${\bf y_2}$ eigenvector.

 

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Figure 4 A 2D seismic section from Unocal. The major reflection at 3200 ms is the salt boundary.

 

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Figure 5 This is the instantaneous amplitude of the seismic section in Figure .

 

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Figure 6 ${\bf y_2}$ eigenvector calculated from the data in Figure .

 

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Figure 7 A contour plot of the ${\bf y_2}$ eigenvector in Figure . Notice the areas of uncertainty where the contours are spreading.