5.1 Introduction

Most useful image processing operators are region-based. Region-based operations calculate a new pixel value based on the values in a local, typically small, neighborhood. This is usually implemented through a linear or nonlinear filtering operation with a finite-sized operator (i.e., a filter). Without loss of generality, we consider a centered and symmetric 3 × 3 neighborhood of the image pixel at position n, m, namely f [n,m ]. A general area-based transformation may be expressed as

where g is the output image resulting from applying transformation T to the 3 × 3 centered neighborhood of input image f. It should be noted that the spatial dimensions and geometry of the neighborhood are generally determined by the needs of the application. Furthermore, the transformation may be applied at every point in the image, or just at some selected number of points. Examples of image processing region-based operations include noise reduction, edge detection, edge sharpening, image enhancement, segmentation, and more.

Section 5.2 presents convolution and correlation, the fundamental linear operators of signal and system theory. These all-important operators are a particular form of Equation (5.1.1). The basic 1D and 2D formulations of convolution and correlation are reviewed, and their various relevant forms are discussed. Section 5.3 continues with examples of the use of some predefined linear filters found in the package. Subsequent sections are devoted to special functions that are particular implementations of the transformation in Equation (5.1.1). These are BlockProcessing in Section 5.4 and RegionProcessing in Section 5.6. In Section 5.5, a number of nonlinear noise reducing operators are defined. The chapter concludes with Section 5.7 describing two list plotting functions that display sampled signals in a format common in the signal processing literature.

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