Unsupervised Optimal Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
How good are convex hull algorithms?
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Computer Vision and Image Understanding
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
A Generic Methodology for Partitioning Unorganised 3D Point Clouds for Robotic Vision
CRV '04 Proceedings of the 1st Canadian Conference on Computer and Robot Vision
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Journal of Visual Communication and Image Representation
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Milena: Write Generic Morphological Algorithms Once, Run on Many Kinds of Images
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Some morphological operators on simplicial complex spaces
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Morphological filtering on graphs
Computer Vision and Image Understanding
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Since image analysis techniques have come to maturity, mesh analysis has remained challenging requiring more and more efforts for elaborating an effective theoretical model. In this article, following algebraic mesh operators, we introduce algorithms that perform morphological transformations on unorganized point sets connected by their Delaunay triangulations. We show that these algorithms correspond to morphological operators like erosion, dilation or opening, acting as ''shape filters'' on meshes. More theoretically, a link is established between these algorithms and the formalisms of edge algebra and @a-objects. Then, the mesh operators are defined in terms of complete lattices. These algorithms are applied to the problem - among others - of scene reconstruction by stereoscopy in which objects are represented by unstructured and noisy clouds of 3D points. Rapid prototyping should also benefit from these algorithms.