Reconstructing images from their most singular fractal manifold

Abstract

Real-world images are complex objects, difficult to describe but at the same time possessing a high degree of redundancy. A very recent study [1] on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature. One particular fractal component, related to the most singular (sharpest) transitions in the image, seems to be highly informative about the whole scene. In this paper we will show how to decompose the image into their fractal components.We will see that the most singular component is related to (but not coincident with) the edges of the objects present in the scenes. We will propose a new, simple method to reconstruct the image with information contained in that most informative component.We will see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set.We will discuss the results from the perspective of coding, proposing this method as a starting point for future developments.