A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual reconstruction
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gradient flows and geometric active contour models
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Fast Extraction of Tubular and Tree 3D Surfaces with Front Propagation Methods
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Isoperimetric Graph Partitioning for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
On two multigrid algorithms for modeling variational multiphase image segmentation
IEEE Transactions on Image Processing
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Segmentation of regions of interest in an image has important applications in medical image analysis, particularly in computer aided diagnosis. Segmentation can enable further quantitative analysis of anatomical structures. We present efficient image segmentation schemes based on the solution of distinct partial differential equations (PDEs). For each known image region, a PDE is solved, the solution of which locally represents the weighted distance from a region known to have a certain segmentation label. To achieve this goal, we propose the use of two separate PDEs, the Eikonal equation and a diffusion equation. In each method, the segmentation labels are obtained by a competition criterion between the solutions to the PDEs corresponding to each region. We discuss how each method applies the concept of information propagation from the labelled image regions to the unknown image regions. Experimental results are presented on magnetic resonance, computed tomography, and ultrasound images and for both two-region and multi-region segmentation problems. These results demonstrate the high level of efficiency as well as the accuracy of the proposed methods.