Quantitative Assessment of Image Segmentation Quality by Random Walk Relaxation Times

The purpose of image segmentation is to partition the pixel grid of an image into connected components termed segments such that (i) each segment is homogenous and (ii) for any pair of adjacent segments, their union is not homogenous. (If it were homogenous the segments should be merged). We propose a rigorous definition of segment homogeneity which is scale-free and adaptive to the geometry of segments. We motivate this definition using random walk theory and show how segment homogeneity facilitates the quantification of violations of the conditions (i) and (ii) which are referred to as under-segmentation and over-segmentation, respectively. We describe the theoretical foundations of our approach and present a proof of concept on a few natural images.