Fast, Quality, Segmentation of Large Volumes – Isoperimetric Distance Trees
For many medical segmentation tasks, the contrast along most of the boundary of the target object is high, allowing simple thresholding or region growing approaches to provide nearly sufficient solutions for the task. However, the regions recovered by these techniques frequently leak through bottlenecks in which the contrast is low or non-existent. We propose a new approach based on a novel speed-up of the isoperimetric algorithm  that can solve the problem of leaks through a bottleneck. The speed enhancement converts the isoperimetric segmentation algorithm to a fast, linear-time computation by using a tree representation as the underlying graph instead of a standard lattice structure. In this paper, we show how to create an appropriate tree substrate for the segmentation problem and how to use this structure to perform a linear-time computation of the isoperimetric algorithm. This approach is shown to overcome common problems with watershed-based techniques and to provide fast, high-quality results on large datasets.
KeywordsGaussian Elimination Laplacian Matrix Graph Partitioning Cholesky Factor Distance Tree
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- 1.Grady, L., Schwartz, E.L.: The isoperimetric algorithm for graph partitioning. SIAM Journal on Scientific Computing (2006) (in press)Google Scholar
- 14.Boykov, Y., Jolly, M.-P.: Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In: Proc. of ICCV 2001, pp. 105–112 (2001)Google Scholar
- 17.Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. In: Gunning, R. (ed.) Problems in Analysis, pp. 195–199. Princeton University Press, Princeton (1970)Google Scholar
- 19.Gremban, K.: Combinatorial preconditioners for sparse, symmetric diagonally dominant linear systems. Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, PA (October 1996)Google Scholar
- 20.Branin Jr., F.H.: The inverse of the incidence matrix of a tree and the formulation of the algebraic-first-order differential equations of an RLC network. IEEE Transactions on Circuit Theory 10(4), 543–544 (1963)Google Scholar
- 21.Gibbons, A.: Algorithmic Graph Theory. Cambridge University Press, Cambridge (1989)Google Scholar