Stephen M. Pizer, Andrew Thall

Medical Image Display & Analysis Group, University of North Carolina, Chapel Hill

Viewing 3D objects from a medial point of view allows one to focus on the object’s decomposition into figures. Viewing figures from a first order medial point of view, i.e., adding to the medial surface and the radius function their first derivatives, leads to a medial-centric view of both the object surface and of 3-space that allows not only global but local shape information to be accessed, as a result of local magnification equivariance. The result for a single figure object is an object intrinsic coordinate system in which distance is decomposed into distance along the medial surface and distance along boundary normals from the medial locus up to any external focal surface. Moreover, both distances are measured proportional to medial radius. This leads to a frame fitted to the medial surface according to this geometry, as well as to frames fitted to each point in space. The way in which this yields correspondences in position, local frame (orientation), and local ruler under figural deformation and thus to possibilities for shape statistics will be discussed. A discussion of figurally based coordinates for objects made from multiple attached figures will follow. Finally, the issues of defining these object-intrinsic for the interstitial space between multiple objects will be briefly introduced.