"Ratio regions": a technique for image segmentation

We develop a image segmentation algorithm in which the segmented region has both an exterior boundary cost and an interior benefit associated with it. Our segmentation method proceeds by minimizing the ratio between the exterior boundary cost and the enclosed interior benefit using a computationally efficient graph partitioning algorithm. Our interest is motivated by very efficient algorithms for finding the globally optimum solution, and a desire to investigate how weak smoothness constraints may be globally imposed without disallowing very high local curvature. We analyze the performance of the approach, indicating both strengths and weaknesses, and discuss its connections with prior image partitioning algorithms. The relationship with snakes is discussed in detail and it is shown how to efficiently compute an approximation to common snakes under the additional constraint that it enclose a given point. When user interaction is available, there is a clear advantage to minimizing user interaction for purposes of improved speed and ease of use and for robustness. "Ratio regions" can accommodate several levels of user interaction and it is empirically shown that very coarse initializations can be tolerated. User interaction not only guides the algorithm to perceptually salient regions but can also be exploited to significantly reduce the computational cost.