IEEE Trans Image Process - The elastic ratio: introducing curvature into ratio-based image segmentation.

Tópicos

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Resumo

We present the first ratio-based image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio [Formula: see text] that depends, given an image I, on the oriented boundary C of the segmented region candidate. Minimizing this ratio amounts to finding a curve, neither small nor too curvy, through which the brightness flux is maximal. We prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions. We also prove that the discrete minimizers provided by our graph-based algorithm converge, as the resolution increases, to continuous minimizers. In contrast to most existing segmentation methods with computable and meaningful, i.e., nondegenerate, global optima, the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes. Numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations. Furthermore, our results allow drawing conclusions about global optima of a parameterization-independent version of the snakes functional: the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution.

Resumo Limpo

present first ratiobas imag segment method allow impos curvatur regular region boundari approach general ratio framework pioneer jermyn ishikawa allow penalti function take account local curvatur curv key idea cast segment problem one find cyclic path minim ratio graph graph node repres line segment among ratio whose discret counterpart can global minim approach focus particular elast ratio formula see text depend given imag orient boundari c segment region candid minim ratio amount find curv neither small curvi bright flux maxim prove exist minim criterion among continu curv mild regular assumpt also prove discret minim provid graphbas algorithm converg resolut increas continu minim contrast exist segment method comput meaning ie nondegener global optima propos approach fulli unsupervis sens requir kind user input seed node numer experi demonstr curvatur regular allow substanti improv qualiti segment furthermor result allow draw conclus global optima parameterizationindepend version snake function propos algorithm allow determin paramet valu function meaning solut simultan provid correspond global solut

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