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From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree (2011)
| Citations: | 2 - 1 self |
BibTeX
@MISC{Tari11froma,
author = {Sibel Tari and Murat Genctav},
title = { From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree},
year = {2011}
}
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Abstract
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 2) 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.
Keyphrases
non-local ambrosio-tortorelli phase field randomized part hierarchy tree phase field shah simultaneous segmentation restoration functional high level vision shape computation extracted part restoration application double point singularity part feature vision application level influence significant step towards widespread imaging probable configuration randomized tree diffuse alternative illustrative shape pair sharp interface level curve technical device visual change proper binary tree diffuse distance field low level visual processing poisson pde implicit representation parametric technique non-generic configuration level set gradient descent shape computation probabilistic structure low level
