The image processing handbook (2nd ed.)
The image processing handbook (2nd ed.)
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Directional Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vessel Tracking in Peripheral CTA Datasets -- An Overview
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Simplifying curve skeletons in volume images
Computer Vision and Image Understanding
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
The Use of Size Functions for Comparison of Shapes Through Differential Invariants
Journal of Mathematical Imaging and Vision
A review of vessel extraction techniques and algorithms
ACM Computing Surveys (CSUR)
Journal of Mathematical Imaging and Vision
Pattern recognition based on homology theory
Machine Graphics & Vision International Journal
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Border and Surface Tracing - Theoretical Foundations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels
Journal of Mathematical Imaging and Vision
Computation of homology groups and generators
Computers and Graphics
Computing homology group generators of images using irregular graph pyramids
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Detecting pathologies with homology algorithms in magnetic resonance images of brain
Machine Graphics & Vision International Journal
Coreduction homology algorithm for inclusions and persistent homology
Computers & Mathematics with Applications
Coreduction Homology Algorithm for Regular CW-Complexes
Discrete & Computational Geometry
3D topological thinning by identifying non-simple voxels
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Branch voxels and junctions in 3d skeletons
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
Suspension models for testing shape similarity methods
Computer Vision and Image Understanding
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We show that the problem of extracting linear features from a noisy image and counting the number of branching points may be successfully solved by homological methods applied directly to the image without the need of skeletonization and the analysis of the resulting graph. The method is based on the superimposition of a mask set over the original image and works even when the homology of the feature is trivial and in arbitrary dimension. We tested the method on computer-generated data, 2D images of blood vessels, 2D satellite images and 3D images of collagen fibers.