Book Review: Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science

We review recent work on level set methods for following the evolution of complex interfaces. These techniques are based on solving initial value partial differential equations for level set functions, using techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The methodology results in robust, accurate, and efficient numerical algorithms for propagating interfaces in highly complex settings. We review the basic theory and approximations, describe a hierarchy of fast methods, including an extremely fast marching level set scheme for monotonically advancing fronts, based on a stationary formulation of the problem, and discuss extensions to multiple interfaces and triple points. Finally, we demonstrate the technique applied to a series of examples from geometry, material science and computer vision, including mean curvature flow, minimal surfaces, grid generation, fluid mechanics, combustion, image processing, computer vision, and etching, deposition and lithography in the microfabrication of electronic components.

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A Hybrid Method for Pancreas Extraction from CT Image Based on Level Set Methods

Computational and Mathematical Methods in Medicine ◽

10.1155/2013/479516 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

Huiyan Jiang ◽

Hanqing Tan ◽

Hiroshi Fujita

Keyword(s):

Level Set Method ◽

Level Set ◽

Negative Impact ◽

Level Set Methods ◽

Region Growing ◽

Ct Images ◽

Medical Image Segmentation ◽

Initial Contour ◽

Ct Image ◽

Fast Marching

This paper proposes a novel semiautomatic method to extract the pancreas from abdominal CT images. Traditional level set and region growing methods that request locating initial contour near the final boundary of object have problem of leakage to nearby tissues of pancreas region. The proposed method consists of a customized fast-marching level set method which generates an optimal initial pancreas region to solve the problem that the level set method is sensitive to the initial contour location and a modified distance regularized level set method which extracts accurate pancreas. The novelty in our method is the proper selection and combination of level set methods, furthermore an energy-decrement algorithm and an energy-tune algorithm are proposed to reduce the negative impact of bonding force caused by connected tissue whose intensity is similar with pancreas. As a result, our method overcomes the shortages of oversegmentation at weak boundary and can accurately extract pancreas from CT images. The proposed method is compared to other five state-of-the-art medical image segmentation methods based on a CT image dataset which contains abdominal images from 10 patients. The evaluated results demonstrate that our method outperforms other methods by achieving higher accuracy and making less false segmentation in pancreas extraction.

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