Abstract
We examine image understanding from the classical source-channel point of view of statistical communications. The space of images corresponding to the source is a Grenander deformable template, an orbit under the group action of diffeomorphisms of a prototype. The prior distribution on the source is induced through a distribution on the group.The channel corresponding to the remote sensor generates the observable images reflecting projection and noise which is statistically modeled via a conditional probability density, the likelihood function. Minimum-risk estimation, rate-distortion, and compression are examined by introducing a distance between images via a distance on the group. Three examples are examined, both for finite and infinite dimensional groups associated with geometric and signature variation in image understanding (1,2) and anatomical shape representation (3).1. U. Grenander, M. I. Miller and A. Srivastava, “Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR,” IEEE Trans. on Pattern Analysis and Machine Intelligence, November 1998.2. E. Shusterman, M. I. Miller and B. Rimoldi, “Rate-Distortion Theoretic Design of Dictionaries for Object Recognition,” Research Monograph Center for Imaging Sciences, 1997.3. U. Grenander and M. I. Miller, “Computational Anatomy: An Emerging Discipline,” Quarterly of Applied Mathematics, pp. 617-694, 1998.(*) This work was supported by Grant ARO DAAH-04-95-1-0494, ONR-MURI N00014-98-1-0606.