Matching occluded and noisy shapes is a frequently encountered problem in vision and medical image analysis and more generally in computer vision. To keep track of changes inside breast, it is important for a computer aided diagnosis system (CAD) to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants and geodesic distance yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants are used on 2D planar shapes to describe the shape boundary. However, they provide no information about where a particular feature on the boundary lies with regard to overall shape structure. On the other hand, eccentricity transforms can be used to match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines both the boundary signature of shape obtained from integral invariants and structural information from the eccentricity transform to yield improved results.