Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
Readings in computer vision: issues, problems, principles, and paradigms
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Discrete Deformable Boundaries for the Segmentation of Multidimensional Images
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
International Journal of Computer Vision
Fast Constrained Surface Extraction by Minimal Paths
International Journal of Computer Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Active Contours Under Topology Control--Genus Preserving Level Sets
International Journal of Computer Vision
Hierarchy construction schemes within the scale set framework
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Digital homeomorphisms in deformable registration
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
First results for 3D image segmentation with topological map
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Multi-label simple points definition for 3D images digital deformable model
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Digital deformable model simulating active contours
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Active contours under topology control genus preserving level sets
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Digital Imaging: A Unified Topological Framework
Journal of Mathematical Imaging and Vision
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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We propose a purely discrete deformable partition model for segmenting 3D images. Its main ability is to maintain the topology of the partition during the minimization process. To do so, our main contribution is a new definition of multi-label simple points (ML simple point) that is easily computable. An ML simple point can be relabeled without modifying the overall topology of the partition. The definition is based on intervoxel properties, and uses the notion of collapse on cubical complexes. This work is an extension of a former restricted definition (Dupas et al., 2009) that prohibits the move of intersections of boundary surfaces. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. We illustrate the potential of our approach with the segmentation of 3D medical images with known expected topology.