Chapter

Scale Space and Variational Methods in Computer Vision

Volume 4485 of the series Lecture Notes in Computer Science pp 687-696

Piecewise Constant Level Set Method for 3D Image Segmentation

  • Are LosnegårdAffiliated withDepartment of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen
  • , Oddvar ChristiansenAffiliated withDepartment of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen
  • , Xue-Cheng TaiAffiliated withDepartment of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen

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Abstract

Level set methods have been proven to be efficient tools for tracing interface problems. Recently, some variants of the Osher- Sethian level set methods, which are called the Piecewise Constant Level Set Methods (PCLSM), have been proposed for some interface problems. The methods need to minimize a smooth cost functional under some special constraints. In this paper a PCLSM for 3D image segmentation is tested. The algorithm uses the gradient descent method combined with a Quasi-Newton method to minimize an augmented Lagrangian functional. Experiments for medical image segmentation are shown on synthetic three dimensional MR brain images. The efficiency of the algorithm and the quality of the obtained images are demonstrated.