Statistical Object Recognition

M. Betke, E. Naftali and N. C. Makris, "Necessary Conditions to Attain Performance Bounds on Structure and Motion Estimates of Rigid Objects," Proceedings of the IEEE Computer Vision and Pattern Recognition Conference CVPR 2001, Kauai, Hawaii, December 2001.

Analytic conditions that are necessary for the maximum likelihood estimate to become asymptotically unbiased and attain minimum variance are derived for estimation problems in computer vision. In particular, problems of estimating the parameters that describe the 3D structure of rigid objects or their motion are investigated. It is common practice to compute Cramer-Rao lower bounds (CRLB) to approximate the mean-square error in parameter estimation problems, but the CRLB is not guaranteed to be a tight bound and typically underestimates the true mean-square error. The necessary conditions for the Cramer-Rao lower bound to be a good approximation of the mean-square error are derived. The tightness of the bound depends on the noise level, the number of pixels on the surface of the object, and the texture of the surface. We examine our analytical results experimentally using polyhedral objects that consist of planar surface patches with various textures that move in 3D space. We provide necessary conditions for the CRLB to be attained that depend on the size, texture, and noise level of the surface patch.

M. Betke and N. Makris, "Recognition, Resolution and Complexity of Objects Subject to Affine Transformation." International Journal of Computer Vision, 44:1, pp. 5-40, August 2001. Abstract

The problem of recognizing objects subject to affine transformation in images is examined from a physical perspective using the theory of statistical estimation. Focusing first on objects that occlude zero-mean scenes with additive noise, we derive the Cramer-Rao lower bound on the mean-square error in an estimate of the six-dimensional parameter vector that describes an object subject to affine transformation and so generalize the bound on one-dimensional position error previously obtained in radar and sonar pattern recognition. We then derive two useful descriptors from the object?s Fisher information that are independent of noise level. The first is a generalized coherence scale that has great practical value because it corresponds to the width of the object?s autocorrelation peak under affine transformation and so provides a physical measure of the extent to which an object can be resolved under affine parameterization. The second is a scalar measure of an object?s complexity that is invariant under affine transformation and can be used to quantitatively describe the ambiguity level of a general 6-dimensional affine recognition problem. This measure of complexity has a strong inverse relationship to the level of recognition ambiguity. We then develop a method for recognizing objects subject to affine transformation imaged in thousands of complex real-world scenes. Our method exploits the resolution gain made available by the brightness contrast between the object perimeter and the scene it partially occludes. The level of recognition ambiguity is shown to decrease exponentially with increasing object and scene complexity. Ambiguity is then avoided by conditioning the permissible range of template complexity above a priori thresholds. Our method is statistically optimal for recognizing objects that occlude scenes with zero-mean background.

M. Betke and N. Makris, "Information-Conserving Object Recognition." Proceedings of the Sixth International Conference on Computer Vision, pp. 145-152, Bombay, India, January 1998.

M. Betke and N. Makris, "Fast Object Recognition in Noisy Images Using Simulated Annealing." Proceedings of the Fifth International Conference on Computer Vision, pp. 523-530, June 1995.