Statistical region-based active contours with exponential family observations

TL;DR

This paper develops a general framework for statistical region-based active contours using exponential family distributions, providing explicit evolution equations and demonstrating effectiveness on synthetic and real images.

Contribution

It introduces a unified approach for active contours with exponential family models, deriving explicit evolution formulas and extending beyond Gaussian assumptions.

Findings

Closed-form evolution speed with Maximum Likelihood estimators

Applicability demonstrated on synthetic images

Effective on real image segmentation tasks

Abstract

In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to the special Gaussian case. Using shape derivation tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain) and derive the corresponding evolution speed. A general result is stated within the framework of multi-parameter exponential family. More particularly, when using Maximum Likelihood estimators, the evolution speed has a closed-form expression that depends simply on the probability density function, while complicating additive terms appear when using other estimators, e.g. moments method. Experimental results on both synthesized and real images demonstrate the applicability of our approach.