On the Geometry of Texture

We consider texture images as a composition of manifolds in the feature-space. This geometrical interpretation leads to a natural way for texture enhancement. A flow, based on manifold volume minimization, yields a natural enhancement procedure for texture images. The 2D Gabor-Morlet transform is first used to decompose the image into subband images, where each sub-image corresponds to a different scale. Each sub-band image may be considered as a 3D manifold in a 5D space from which the original image can be reconstructed in a numerically stable way. Following our previous results, we then invoke Polyakov action from String Theory, and develop a minimization process through a geometric flow that efficiently enhances each sub-band image in a spatial-orientation feature space. Finally, the enhanced sub-band images are composed back into an enhanced texture image.