Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Extraction of shape skeletons from grayscale images
Computer Vision and Image Understanding
Fundamenta Informaticae - Special issue on mathematical morphology
A Computationally Efficient Shape Analysis via Level Sets
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Local Symmetries of Shapes in Arbitrary Dimension
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
An Axis-Based Representation for Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Shape Representation and Classification Using the Poisson Equation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dissimilarity between two skeletal trees in a context
Pattern Recognition
3D shape recursive decomposition by Poisson equation
Pattern Recognition Letters
Disconnected Skeleton: Shape at Its Absolute Scale
IEEE Transactions on Pattern Analysis and Machine Intelligence
The eccentricity transform (of a digital shape)
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
From a modified ambrosio-tortorelli to a randomized part hierarchy tree
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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A new tool for shape decomposition is presented. It is a function defined on the shape domain and computed using a linear system of equations. It is demonstrated that the level curves of the new function provide a hierarchical partitioning of the shape domain into visual parts, without requiring any features to be estimated. The new tool is an unconventional distance transform where the minimum distance to the union of the shape boundary and an unknown critical curve is computed. This curve divides the shape domain into two parts, one corresponding to the coarse scale structure and the other one corresponding to the fine scale structure. The connection of the new function to a variety of morphological concepts (Skeleton by Influence Zone, Aslan Skeleton, and Weighted Distance Transforms) is discussed.