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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Measuring the distances is an important problem in many image-segmentation algorithms. The distance should tell whether two image points belong to a single or, respectively, to two different image segments. The paper deals with the problem of measuring the distance along the manifold that is defined by image. We start from the discussion of difficulties that arise if the geodesic distance, diffusion distance, and some other known metrics are used. Coming from the diffusion equation and inspired by the diffusion distance, we propose to measure the proximity of points as an amount of substance that is transferred in diffusion process. The analogy between the images and electrical circuits is used in the paper, i.e., we measure the proximity as an amount of electrical charge that is transported, during a certain time interval, between two nodes of a resistor-capacitor network. We show how the quantity we introduce can be used in the algorithms for supervised (seeded) and unsupervised image segmentation. We also show that the distance between the areas consisting of more than one point (pixel) can also be easily introduced in a meaningful way. Experimental results are also presented.