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Graph Algorithmic Techniques for Biomedical Image Segmentation
Book chapter

Graph Algorithmic Techniques for Biomedical Image Segmentation

Mona K Garvin and Xiaodong Wu
Advanced Computational Approaches to Biomedical Engineering, pp.3-45
Springer Berlin Heidelberg
11/11/2013
DOI: 10.1007/978-3-642-41539-5_1

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Abstract

After presenting an introduction to a more traditional graph-based 2D segmentation technique, this chapter presents an in-depth overview of two state-of-the-artgraph-based methods for segmenting three-dimensional structures in medical images: graph cuts and the Layered Optimal Graph Image Segmentation of Multiple Objects and Surfaces (LOGISMOS) approach. In each case, an overview of the underlying optimization problem is presented first (i.e., the formulation of an energy/cost function and the specified constraints), followed by the graph-based representation of the optimization problem which enables the globally optimal solution to be found in polynomial time. In particular, in the 2D case, a 2D boundary segmentation optimization problem is transformed into that of finding a minimum-cost path in a graph. In the graph-cuts approach, a 3D object/background labeling problem is transformed into that of finding a minimum s–t cut in a graph, and in the LOGISMOS approach, a single or multiple 3D surface segmentation problem is first transformed into that of finding a minimum-cost closure in a graph (which is further transformed into finding a minimum s–t cut in a graph). For each approach, example applications and extensions are also presented.
 Graph Construction Neighboring Column Optimal Surface Separation Constraint Smoothness Constraint

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