Abstract
This chapter discusses polynomial and rational operators for image processing and analysis. A wide class of nonlinear operators can be devised for image processing applications, based on polynomial and rational functions of the pixels of an image. This chapter shows that this approach can be exploited successfully for image enhancement, image analysis, and image format conversion. The chapter also presents the properties of polynomial-based functions. It deals with the formalisms of polynomial and rational filters and provides an overview of the theoretical properties of operators that are based on the Volterra series and of their extensions to two dimensions. The chapter then discusses the applications of polynomial filters for contrast enhancement, texture segmentation, and edge extraction. Finally, it takes a look at rational operators with a number of applications such as noise smoothing, image interpolation and contrast enhancement.
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