Shape Bottlenecks and Conservative Flow Systems

This paper proposes an alternative to mathematical morphology to analyze complex shapes. This approach aims mainly at the detection of shape bottlenecks which are often of interest in medical imaging because of their anatomical meaning. The detection idea consists in simulating the steady state of an information transmission process between two parts of a complex object in order to highlight bottlenecks as areas of high information flow. This information transmission process is supposed to have a conservative flow which leads to the well-known Dirichlet-Neumann problem. This problem is solved using finite differences, over-relaxation and a raw to fine implementation. The method is applied to the detection of main bottlenecks of brain white matter network, namely corpus callosum, anterior commissure and brain stem.

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