Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision, Graphics, and Image Processing
Generation of noise in binary images
CVGIP: Graphical Models and Image Processing
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Cluster Analysis by Binary Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The image processing handbook (2nd ed.)
The image processing handbook (2nd ed.)
r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computer Vision and Image Understanding
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Computer and Robot Vision
Consistent Set Estimation in k-Dimensions: An efficient Approach
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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Data visualization from a point set by estimating the underlying region is a problem of considerable practical interest and is an associated problem of set estimation. The most important issue in set estimation is consistency. Only a few existing point pattern shape descriptors that estimate the underlying region are consistent set estimators (a set estimator is consistent if it converges--in an appropriate sense--to the original set as the sample size increases). On the other hand, to be used as a shape descriptor, a set estimator should also satisfy several important criteria such as correct identification of number of components, robustness in the presence of noise and computational efficiency. Here we propose such a class of set estimators called s-shapes, which remain consistent in finite dimensions when the data are generated from any continuous distribution. These set estimators can be easily computed and effectively used for fast data visualization. Detailed studies on their performance such as error rates, robustness in presence of noise, run-time analysis, etc., are also performed.