A View-Point Invariant Texture Descriptor

A new texture descriptor based on fractal geometry, called the multi fractal spectrum (MFS) is introduced. The key quantity in the study of fractal geometry is the fractal dimension, which is a measure of how an object changes over scale. Consider the intensity of an image as a 3D surface and slice it at regular intervals at the dimension of height. For each interval we obtain a point set, for which we compute the fractal dimension. The vector composed of the fractal dimensions of all point sets is called the MFS of intensity. Replacing the intensity with other quantities, such as the density function, or the output of various filters (e.g. Laplacian, Gradient filters), different MFS descriptors are obtained. The MFS is shown mathematically to be invariant under any smooth mapping (bi-Lipschitz maps), which includes view-point changes and non-rigid deformations of the surface as well as local affine illumination changes. Computational experiments on unstructured textures, such as landscapes and shelves in a supermarket, demonstrate the robustness of the MFS to environmental changes. On standard data sets the MFS performs comparable to the top texture descriptors in the task of classification. However, in contrast to other descriptors, it has extremely low dimension and can be computed very efficiently and robustly. Psychophysical demonstrate that humans can differentiate black and white textures on the basis of the fractal dimension.