An Improved Metric Space for Pixel Signatures

Our previous work in computer-aided mammography has used scale orientation pixel signatures to provide a rich description of local structure. However, when treated as vectors for statistical classification, the Euclidean space they define has unsatisfactory metric properties. We have also described a novel measure of signature similarity known as best-partial-match (BPM) distance that recognises similar structures whilst remaining robust to background variability and the presence of other structures. In this paper we describe a scheme that makes use of the BPM similarity measure to define a non-linear transformation of pixel signatures into a space with improved metric properties. Using BPM distance we select a set of prototype signatures. We apply multidimensional scaling to these prototypes to construct a new space in which a Euclidean metric behaves in the same way as the BPM distance measure. Support vector regression is then used to learn the non-linear transformation between the new and original spaces permitting a run-time method of transforming any signature into an improved metric space. We use mammographic data to test the performance of our transformed signatures and compare the results with those produced by the raw signatures. Our initial results indicate that our scheme provides an efficient run-time method of transforming signatures into a space suitable for statistical analysis.