Recently, several content-based image retrieval (CBIR) systems that make use of segmented images have been proposed. In these systems, images are segmented and represented as a set of regions, and the distance between images is computed according to the visual features of their regions. A major problem of existing distance functions used to compare segmented images is that they are not metrics. Hence, it is not possible to exploit filtering techniques and/or access methods to speedup query processing, as both techniques make extensive use of the triangular inequality property - one of the metric axioms. In this work, we propose MiCRoM (Minimum-Cost Region Matching), an effective metric distance which models the comparison of segmented images as a minimum-cost network flow problem. To our knowledge, this is the first time a true metric distance function is proposed to evaluate the distance between segmented images. Our experiments show that MiCRoM is at least as effective as existing non-metric distances. Moreover, we have been able to use the recently proposed Omni-sequential filtering technique, and have achieved nearly 2/3 savings in retrieval/query processing time.