Measuring similarity between pixel signatures

We address the problem of finding specific types of structure in medical images, such as mammograms. We use scale-orientation signatures to provide a rich description of local structure but observe that, when they are treated as vectors for statistical analysis, obvious measures of similarity such as Euclidean distance are not robust to small changes in structure. We describe three robust methods for measuring similarity, based on the transportation (earth mover's) distance. The most sophisticated of these - the best partial matching (BPM) distance - detects common structure between signatures, even when potentially confounding structure is also present. We compare the three new similarity measures and Euclidean distance experimentally. BPM distance is shown to give the best results for both synthetic and real mammogram data. © 2002 Published by Elsevier Science B.V.