3D Texture Analysis

This chapter deals with the analysis of 3D surface texture. A model of the surface-to-image function is developed. This theory shows that sidelighting acts as a directional filter of the surface height function. Thus the directionality and power of image texture is a function of the illuminant's slant and tilt angles.

The theory is extended to common texture features such as those of Gabor and Laws to show that their behaviours follow that of simple harmonic motion. Variation of illuminant's tilt causes class centres to describe a trajectory on a hyper-ellipse, while changes in slant cause the hyper-ellipse to grow or shrink. Thus it is not surprising that classifiers trained under one set of illumination conditions will fail under another.

Finally we develop a classifier that exploits a simplified version of this theory. Given a single image of a surface texture taken under unknown illumination conditions our classifier will return both the estimated illumination direction and the class assignment.