Resolution Selection Using Generalized Entropies of Multiresolution Histograms

The performances of many image analysis tasks depend on the image resolution at which they are applied. Traditionally, resolution selection methods rely on spatial derivatives of image intensities. Differential measurements, however, are sensitive to noise and are local. They cannot characterize patterns, such as textures, which are defined over extensive image regions. In this work, we present a novel tool for resolution selection that considers sufficiently large image regions and is robust to noise. It is based on the generalized entropies of the histograms of an image at multiple resolutions. We first examine, in general, the variation of histogram entropies with image resolution. Then, we examine the sensitivity of this variation for shapes and textures in an image. Finally, we discuss the significance of resolutions of maximum histogram entropy. It is shown that computing features at these resolutions increases the discriminability between images. It is also shown that maximum histogram entropy values can be used to improve optical flow estimates for block based algorithms in image sequences with a changing zoom factor.