Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Graphical Models and Image Processing
FORMS: a flexible object recognition and modeling system
International Journal of Computer Vision
Extraction of shape skeletons from grayscale images
Computer Vision and Image Understanding
VIS '97 Proceedings of the 8th conference on Visualization '97
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Concepts of use in contour map processing
Communications of the ACM
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Local Symmetries of Shapes in Arbitrary Dimension
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
An Axis-Based Representation for Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Image Deblurring in the Presence of Impulsive Noise
International Journal of Computer Vision
Shape Representation and Classification Using the Poisson Equation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Level Lines Selection with Variational Models for Segmentation and Encoding
Journal of Mathematical Imaging and Vision
Multiscale Joint Segmentation and Registration of Image Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Disconnected Skeleton: Shape at Its Absolute Scale
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Mumford-Shah regularizer with contextual feedback
Journal of Mathematical Imaging and Vision
Color Image Restoration Using Nonlocal Mumford-Shah Regularizers
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Hierarchical Shape Decomposition via Level Sets
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Shape analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
Extended Phase Field Higher-Order Active Contour Models for Networks
International Journal of Computer Vision
Mumford-Shah regularizer with spatial coherence
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding
International Journal of Computer Vision
International Journal of Computer Vision
Ambrosio-tortorelli segmentation of stochastic images
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Beyond pairwise shape similarity analysis
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
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
Distance images and intermediate-level vision
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
IEEE Transactions on Image Processing
Variational approach for edge-preserving regularization using coupled PDEs
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
Densifying Distance Spaces for Shape and Image Retrieval
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
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In its most widespread imaging and vision applications, Ambrosio and Tortorelli (AT) phase field is a technical device for applying gradient descent to Mumford and Shah simultaneous segmentation and restoration functional or its extensions. As such, it forms a diffuse alternative to sharp interfaces or level sets and parametric techniques. The functionality of the AT field, however, is not limited to segmentation and restoration applications. We demonstrate the possibility of coding parts--features that are higher level than edges and boundaries--after incorporating higher level influences via distances and averages. The iteratively extracted parts using the level curves with double point singularities are organized as a proper binary tree. Inconsistencies due to non-generic configurations for level curves as well as due to visual changes such as occlusion are successfully handled once the tree is endowed with a probabilistic structure. As a proof of concept, we present (1) the most probable configurations from our randomized trees; and聽(2)聽correspondence matching results between illustrative shape pairs.The work is a significant step towards establishing exponentially decaying diffuse distance fields as bridges between low level visual processing and shape computations.