From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree


TARI Z. S. , Genctav M.

JOURNAL OF MATHEMATICAL IMAGING AND VISION, vol.49, no.1, pp.69-86, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1007/s10851-013-0441-8
  • Journal Name: JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.69-86
  • Keywords: Bridging low level and high level vision, Shape computation, Screened Poisson PDE, Implicit representations, Linear model for reaction-diffusion, MUMFORD-SHAH REGULARIZER, CURVE EVOLUTION, SEGMENTATION, REPRESENTATION, RECOVERY, DISTANCE, MODELS

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.