Differential equations and dynamical systems
Differential equations and dynamical systems
Simulating the Grassfire Transform Using an Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ridge points in Euclidean distance maps
Pattern Recognition Letters
Topological segmentation of discrete surfaces
International Journal of Computer Vision
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
A parallel thinning algorithm for medial surfaces
Pattern Recognition Letters
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Skeletonizing Volume Objects Part 2: From Surface to Curve Skeleton
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
Proceedings of the Workshop on Geometry and Robotics
Segmentation of Carpal Bones from 3d CT Images Using Skeletally Coupled Deformable Models
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
3D/2D Registration via Skeletal Near Projective Invariance in Tubular Objects
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Characterization and Recognition of 3D Organ Shape in Medical Image Analysis Using Skeletonization
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
M-Reps: A New Object Representation for Graphics
M-Reps: A New Object Representation for Graphics
A Skeletal Measure of 2D Shape Similarity
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
The Shock Scaffold for Representing 3D Shape
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Hippocampal Shape Analysis Using Medial Surfaces
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Reversible Surface Skeletons of 3D Objects by Iterative Thinning of Distance Transforms
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Automatic and reliable extraction of dendrite backbone from optical microscopy images
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
Computation of the shock scaffold for unorganized point clouds in 3D
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Curvature correction of the Hamilton-Jacobi skeleton
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Computation and evaluation of medial surfaces for shape representation of abdominal organs
MICCAI'11 Proceedings of the Third international conference on Abdominal Imaging: computational and Clinical Applications
MPRSS'12 Proceedings of the First international conference on Multimodal Pattern Recognition of Social Signals in Human-Computer-Interaction
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The medial surface of a volumetric object is of significant interest for shape analysis. However, its numerical computation can be subtle. Methods based on Voronoi techniques preserve the object's topology, but heuristic pruning measures are introduced to remove unwanted faces. Approaches based on Euclidean distance functions can localize medial surface points accurately, but often at the cost of altering the object's topology. In this paper we introduce a new algorithm for computing medial surfaces which addresses these concerns. The method is robust and accurate, has low computational complexity, and preserves topology. The key idea is to measure the net outward flux of a vector field per unit volume, and to detect locations where a conservation of energy principle is violated. This is done in conjunction with a thinning process applied in a cubic lattice. We illustrate the approach with examples of medial surfaces of synthetic objects and complex anatomical structures obtained from medical images.