Date of Original Version
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.acha.2012.07.005
Abstract or Description
The local histogram transform of an image is a data cube that consists of the histograms of the pixel values that lie within a fixed neighborhood of any given pixel location. Such transforms are useful in image processing applications such as classification and segmentation, especially when dealing with textures that can be distinguished by the distributions of their pixel intensities and colors. We, in particular, use them to identify and delineate biological tissues found in histology images obtained via digital microscopy. In this paper, we introduce a mathematical formalism that rigorously justifies the use of local histograms for such purposes. We begin by discussing how local histograms can be computed as systems of convolutions. We then introduce probabilistic image models that can emulate textures one routinely encounters in histology images. These models are rooted in the concept of image occlusion. A simple model may, for example, generate textures by randomly speckling opaque blobs of one color on top of blobs of another. Under certain conditions, we show that, on average, the local histograms of such model-generated-textures are convex combinations of more basic distributions. We further provide several methods for creating models that meet these conditions; the textures generated by some of these models resemble those found in histology images. Taken together, these results suggest that histology textures can be analyzed by decomposing their local histograms into more basic components. We conclude with a proof-of-concept segmentation-and-classification algorithm based on these ideas, supported by numerical experimentation.
Applied and Computational Harmonic Analysis, 34, 3, 469-487.