A Total Variation Spectral Framework for Scale and Texture Analysis

A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, such as disks, approach impulses. A reconstruction formula from the spectral to the spatial domain is given, allowing the design of new filters. The framework formulates a new representation of images which can enhance the understanding of scales in the L¹ sense and improve the analysis and processing of textures. An example of a texture processing application illustrates possible benefits of this new framework.