Image Texture and Fourier Analysis in a Polar Spatial Frequency System: methods illustration

Abstract

We illustrate the connection between image-texture and defined regions in a polar spatial frequency coordinate system. This is provided within the context of describing a non-parametric method for characterizing two-dimensional

spectra of gray scaled images, described in part previously. The spectrum is divided into concentric radial bands of fixed bandwidth. Each band is summarized, producing a set of measures characterizing the image as a function of radial spatial frequency. This set of measures has a parallel multiscale description as texture in the image domain. This approach was modified to capture texture with directional attributes. This is a data reduction technique that gives a full accounting of the image variance as function of image texture and direction indexed to regions in the polar frequency plane. Application examples include analyzing the summarized spectrum graphically, making inter/intra image spectral comparisons, and evaluating spectral models. Simulated noise images, an image of peppers, and a gray scale image with well-defined linear structure were used to illustrate the principles.