The effect of Illuminant rotation on texture filters: Lissajous’s ellipses

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 experimental results that show that changes in illumination tilt angle cause texture clusters to describe Lissajous’s ellipses in feature space. We focus on texture features that may be modelled as a linear filter followed 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 results to show that the clusters of distinct textures describe different elliptical paths in feature space as illuminant tilt varies. These results have significant implications for illuminant tilt invariant texture classification.