5.1 Spatial filtering

5.1.1 Introduction

The term “spatial” refers to the set of pixels of the image. Any spatial processing can be expressed as


where I is the original image, J the processed one and T an operator acting on I, defined on a neighborhood of (x,y). If this neighborhood is of size 1, T acts pixel by pixel, and we related this filtering to point to point analysis (Chapter 3).

We consider in the following a neighborhood of size strictly greater than 1, centered in (x,y). We are then interested in spatial filtering (as opposed to frequency filtering, which we will discuss in the next section), and we detail here linear and non-linear filters.

Linear filters are based on the linearity assumption of the ...

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