Conclusions and future work

Our modified segmentation method successfully tracked the salt boundaries in our test cases. These test cases present challenges including non-continuous salt boundaries with noise. An interpreter would still have to slightly adjust the tracking result in a few places.

Because of this method's excessive storage requirements, a multi-scale approach will be necessary. The size of the weight matrix in equation (2) is $({\tt m} \times {\tt n})^{\tt 2}$ where m and n are the dimensions of the image. Even using sparse matrices in 2 dimensions, this matrix can be prohibitively large. In 3D, things get much worse as the matrix is now $({\tt m} \times {\tt n} \times o )^{\tt 2}$, where o is the 3rd dimension. The segmentation method applied to a coarsely sub-sampled input cube will still select the salt boundary as long as it is the brightest amplitude in the cube. Smaller, more finely sampled cubes can then be segmented along the boundary.

Application of this method to 3D datasets is going to be a computational challenge that will require us to take advantage of maximizing the sparseness of the weight matrix, using accurate starting solutions, and taking a multi-scale approach.