The Effect of Illuminant Rotation on Texture Filters: Lissajous’s Ellipses M. Chantler 1 , M. Schmidt 2 , M. Petrou 3 , and G. McGunnigle 1 1 Texture Lab., Heriot-Watt University, Edinburgh,Scotland, mjc@cee.hw.ac.uk http://www.cee.hw.ac.uk/texturelab/ 2 Darmstadt University of Technology, Germany, 3 Department of Electronic and Electrical Engineering, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom M.Petrou@ee.surrey.ac.uk http://www.ee.surrey.ac.uk/Personal/M.Petrou Abstract. Changes in the angle of illumination incident upon a 3D surface texture can significantly change its appearance. These changes can affect the output of texture features to such an extent that they cause complete misclassification. We present new theory and experi- mental results that show that changes in illumination tilt angle cause texture clusters to describe Lissajous’s ellipses in feature space. We focusontexturefeaturesthatmaybemodelledasalinearfilterfollowed by an energy estimation process e.g. Laws filters, Gabor filters, ring and wedge filters. This general texture filter model is combined with a linear approximation of Lambert’s cosine law to predict that the outputs of these filters are sinusoidal functions of illuminant tilt. Experimentation with 30 real textures verifies this proposal. Furthermore we use these resultstoshowthattheclustersofdistincttexturesdescribedifferentel- lipticalpathsinfeaturespaceasilluminanttiltvaries.Theseresultshave significantimplicationsforilluminanttiltinvarianttextureclassification. Keywords: Texture, illumination, texture features 1 Introduction It has been shown that changes in the angle of illumination incident upon a 3D surface texture can change its appearance significantly as illustrated in Fig. 1. Such changes in image texture can cause complete misclassification of surface textures [1]. Essentially the problem is that side-lighting, as used for instance in Brodatz’s texture album [2], enhances the appearance of surface texture but produces an image which is a directionally filtered version of the surface height function. Furthermore as the theory developed by Kube and Pentland [3] pre- dicts, the axis of this filter is a function of the illumination’s tilt angle 1 . This is 1 Intheaxissystemweuse,thecameraaxisisparalleltothe z-axis, illuminant tilt is the angle the illuminant vector makes with the x-axis when it is projected into the A. Heyden et al. (Eds.): ECCV 2002, LNCS 2352, pp. 289–303, 2002. c  Springer-Verlag Berlin Heidelberg 2002