Quadratic Programming Vs. Concurrent Correlation Matching under Non-Uniform Image Contrast and Offset G. Gimel’farb, P. Delmas, A. Shorin, J. Morris Computer Science, University of Auckland, New Zealand. Email: {ggim001,pdel016,al,jmor159}@cs.auckland.ac.nz Abstract Recognition of objects-of-interest by similarity of prototypes (templates) to sensed images of natural scenes is important in computer vision, digital photogrammetry and multimedia data retrieval. However, accurate template matching in the presence of non-uniform nuisance contrast and offset deviations remains a challenging problem. Uniform deviations leading to cross-correlation matching scores have been studied for decades, but non-uniform ones have been little explored - mostly, only computationally intensive gradient- based matching for low order polynomial deviation model. This paper presents two computationally simpler alternative approaches: (i) an analytical least-squares template matching for polynomial deviation models of an arbitrary order using abank of concurrent cross-correlation scores and (ii) a fast numerical quadratic programming based matching for a new general model of loosely constrained non-uniform contrast and offset deviations. Experiments confirm that these approaches hold great promise in practice. Keywords: Template matching, polynomial contrast, non-uniform contrast, concurrent correlation, quadratic programming 1 Introduction Robust template matching is a basic part of any image processing, computer vision, photogrammet- ric and multimedia system that has to detect, clas- sify or retrieve objects on the basis of sensed 1D signals or 2D images of natural scenes. Typical matching frameworks assume that the sensed data mostly follow probability models that account for varying environments and sensing or imaging con- ditions. The most popular cross-correlation match- ing assumes uniform contrast deviations of a tem- plate in the presence of an additive, independent, central-symmetric and random noise [1, 2]. How- ever, in practice, these assumptions frequently do not hold and non-uniform contrast deviations that exist even in a controlled real world environment (e.g. due to changing illumination) often make the correlation rather useless. A polynomial model of non-uniform contrast in- troduced by Lai [3] stimulated a number of sub- sequent efforts [4, 5, 6]. Instead of the more con- ventional but not robust least squares estimator, Lai’s matching uses the robust M-estimator [7] and thus a computationally complex numerical gradi- ent search for the best match in the parameter space of both geometric transformation and poly- nomial coefficients. This high dimensional space is 978-1-4244-2582-2/08/$25.00 c 2008 IEEE difficult to explore extensively, so various simplifi- cations were made such as a heuristic feature sam- pling with manual changes of selection parameters for different recognition tasks [6] or matching only contour images after edge detection [5]. Thus the approach was practical with only a small number of polynomial coefficients and failed with non-smooth contrast changes and even shadows [3]. Low or- der polynomial contrast deviations tend to have a rather unnatural visual appearance (Fig. 1(c)): even small movements of light sources lead to large jumps in intensity (due to shadows and reflections) which cannot be adequately modelled with sim- ple polynomial functions. Fig. 2(c) shows contrast deviations for a small (15 ◦ ) rotation of the light source. We show that the least-squares framework allows us to reduce matching based on an arbitrary order (a) Template (b) Polynomial (c) Deviation Figure 1: (a) Template from the MIT database [8], (b) (synthetic) example of scaled parabolic contrast factors, and (c) contrast deviations using this model. Authorized licensed use limited to: The University of Auckland. Downloaded on February 9, 2009 at 23:41 from IEEE Xplore. Restrictions apply.