Image Space I3 and Eigen Curvature for Illumination Insensitive Face Detection

Generally, the performance of present day computer vision systems is still very much affected by varying brightness and light source conditions. Recently, Koenderink suggested that this weakness is due to methodical flaws in low level image processing. As a remedy, he develops a new theory of image modeling. This paper reports on applying his ideas to the problem of illumination insensitive face detection. Experimental results will underline that even a simple and conventional method like principal component analysis can accomplish robust and reliable face detection in the presence of illumination variation if applied to curvature features computed in Koenderink’s image space. 1 Motivation and Related Work In a recent paper on image processing methodology [1], Koenderink fiercely criticized the common practice to understand digital greyscale images as entities embedded in R3. He observes that if an image was indeed a set of points (xi, yi, zi)i=1...M ∈ R3 where the intensity values zi = f(xi, yi) define a surface above the X,Y plane, the geometry ofR3 would allow to rotate this surface about an arbitrary axis. However, such a rotation might cause intensity values to lie in the image coordinate plane and image coordinates to be parallel to the intensity direction. Koenderink argues that a structure that allows for operations leading to physically senseless configurations is not the most reasonable choice for image modeling. As a more appropriate approach to mathematical image modeling he proposes a structure which he calls image space I3. The basic idea is to define I3 as a fiber bundle that locally looks like P2 × L where the base manifold P2 corresponds to the picture plane and the fibers L are logarithmic scales of the intensity. An analysis of the (differential) geometry of this image space reveals that images in I3 are (by construction) invariant under different brightness transformations. In this contribution, we explore the merits this model offers for computer vision. The application domain for our investigation will be illumination insensitive face detection. Face detection and recognition are arguably among the most popular topics in computer vision and respective publications are almost innumerable. In fact, the field is so active, it already produced its meta literature (cf. e.g. [2,3,4]). A complete survey of face detection techniques therfore is far beyond the prospects of this report but we shall single out a few contributions which are relevant for our discussion. Since they were first considered by Sirovich and Kirby [5] and popularized by Turk and Pentland [6], Principal Component Analysis (PCA) based approaches have become M. Kamel and A. Campilho (Eds.): ICIAR 2005, LNCS 3656, pp. 456–463, 2005. c © Springer-Verlag Berlin Heidelberg 2005 Image Space I and Eigen Curvature for Illumination Insensitive Face Detection 457 a widespread tool in face detection. Although there are other subspace techniques like Linear Discriminant Analysis, Independent Component Analysis, or kernelized PCA, simple PCA is still among the most reliable methods [7,8]. However, its performance is known to depend on light source conditions. Recent contributions aiming at illumination invariance hence measure the gradient similarity statistics [9] or combine edge phase congruency information with local intensity normalization [10]. Others render eigen-harmonics to recover a standard illumination [11] or use eigen light-fields [12].