Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Topological segmentation of discrete surfaces
International Journal of Computer Vision
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Journal of Mathematical Imaging and Vision - Special issue on mathematical imaging
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Octree-Based Topology-Preserving Isosurface Simplification
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
Diffeomorphic nonlinear transformations: a local parametric approach for image registration
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast parametric elastic image registration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Topology correction of segmented medical images using a fast marching algorithm
Computer Methods and Programs in Biomedicine
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
Statistical and topological atlas based brain image segmentation
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
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
Fully deformable 3D digital partition model with topological control
Pattern Recognition Letters
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
A multiple object geometric deformable model for image segmentation
Computer Vision and Image Understanding
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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A common goal in deformable registration applications is to produce a spatial transformation that is diffeomorphic, thereby preserving the topology of structures being transformed. Because this constraint is typically enforced only on the continuum, however, topological changes can still occur within discretely sampled images. This work discusses the notion of homeomorphisms in digital images, and how it differs from the diffeomorphic/homeomorphic concepts in continuous spaces commonly used in medical imaging.We review the differences and problems brought by considering functions defined on a discrete grid, and propose a practical criterion for enforcing digital homeomorphisms in the context of atlas-based segmentation.