Region Competition

 

S. C. Zhu and A. L. Yuille, "Region  competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation",
    IEEE Trans. on PAMI vol.18, no.9, pp884-900, 1996.  A  short version of this paper appeared in Proc. 5th Int'l Conf of Computer 
    Vision, Cambridge, MA, 1995. (With T.S. Lee)
 A main contribution of this work is the derivation of a diffusion equation from a general MDL/Bayesian energy function (posterior probability).
 This equation shows that region growing and SNAKE/Balloon type algoithms are different ways for minimizing an energy. Later, the region
 competition equation was embraced by PDE lovers.

 A remaining problem is that the split-merge steps are not reversible, therefore, the whole algorithm is greedy, and is not guaranteed to find 
global optima. This problem is then resolved by the DDMCMC framework and the Swendson-Wang Cut algorithm

Energy formulation for image segmentation: An image contains n regions and each region is fitted to a model. The contours of the regions are assumed to be smooth (short length).

The region competition equation specifies the movement of a point v=(x,y) on the contour. It consists of two terms: 
    1).    A log-likelihood ratio test between two adjacent models. The region has better fit pushes /defeats the rival region.
    2).    A curvature flow for contour smothness. 
Both terms act in the normal direction of the contour.

input image
t=0
t=10
t=20
t=60
t=100
t=130