Image elementary manifold and its application in image analysis

Abstract

Image basis function plays a key role in image information analysis. Due to the complex geometric structure in image, a better image basis or frame often have a very large family with a large number of basis functions lying in a lower dimen-sionality manifold, such as 2D Gabor functions and Contourlets used in image texture analysis, the corresponding image transform and analysis will be very time consuming. In this article, we propose a novel image representation method called “image elementary manifold”, here, an image elementary manifold can rep-resent all the basis functions lying in the same manifold. A fast elementary mani-fold based image decomposition and reconstruction algorithm are given. Compar-ing to traditional image representation methods, elementary manifold based image analysis reduce time consumption, discovers the latent intrinsic structure of imag-es more efficiently and provides the possibility of empirical prediction. Finally, many experiments show the feasibility of image elementary manifold in image analysis.