Image segmentation with minimum mean cut

We introduce a new graph-theoretic approach to image segmentation based on minimizing a novel class of 'mean cut' cost functions. Minimizing these cost functions corresponds to finding a cut with minimum mean edge weight in a connected planar graph. This approach has several advantages over prior approaches to image segmentation. First, it allows cuts with both open and closed boundaries. Second, it guarantees that the partitions are connected. Third, the cost function does not introduce an explicit bias, such as a preference for large-area foregrounds, smooth or short boundaries, or similar-weight partitions. This lack of bias allows it to produce segmentations that are better aligned with image edges, even in the presence of long thin regions. Finally, the global minimum of this cost function is largely insensitive to the precise choice of edge-weight function. In particular, we show that the global minimum is invariant under a linear transformation of the edge weights and thus insensitive to image contrast. Building on algorithms by Ahuja et al. (1993), we present a polynomial-time algorithm for finding a global minimum of the mean-cut cost function and illustrate the results of applying that algorithm to several synthetic and real images.