Active contours without edges

TLDR

The authors introduce a novel active contour model that uses curve evolution, the Mumford–Shah functional, and level sets to detect objects in images. The model minimizes an energy equivalent to a minimal partition problem, evolving via a mean‑curvature–flow–like level‑set scheme whose stopping term depends on image segmentation rather than gradients, and is implemented with a finite‑difference algorithm. Experiments demonstrate that the method can locate object boundaries without relying on image gradients, correctly handling cases where classical snakes fail, and automatically detecting interior contours from arbitrary initial curves.

Abstract

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.