Higher-Order Statistics in Visual Object Recognition
Thomas M. Breuel
IDIAP, C.P. 609, CH-1920 Martigny, Switzerland
tmb@idiap.ch
In this paper, I develop a higher-order statistical theory of
matching models against images. The basic idea is not only to take
into account {\em how much} of an object can be seen in the image, but
also {\em what parts} of it are jointly present. I show that this
additional information can improve the specificity (i.e., reduce the
probability of false positive matches) of a recognition algorithm.
I demonstrate formally that most commonly used quality of match
measures employed by recognition algorithms are based on an
independence assumption. Using the Minimum Description Length (MDL)
principle and a simple scene-description language as a guide, I show
that this independence assumption is not satisfied for common scenes,
and propose several important higher-order statistical properties of
matches that approximate some aspects of these statistical
dependencies. I have implemented a recognition system that takes
advantage of this additional statistical information and demonstrate
its efficacy in comparisons with a standard recognition system based
on bounded error matching.
We also observe that the existing use of grouping and segmentation
methods has significant effects on the performance of recognition
systems that are similar to those resulting from the use of
higher-order statistical information. Our analysis provides a
statistical framework in which to understand the effects of grouping
and segmentation on recognition and suggests ways to take better
advantage of such information.
Keywords: higher-order statistics, object recognition, minimum
description length, Bayesian decision theory, grouping, segmentation,
error rate.