@MISC{Hew_geometricoperations, author = {Patrick Hew}, title = {Geometric Operations}, year = {} }

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Abstract

This paper describes the geometric operations of translation, scaling and rotation, when applied to images. 1 Introduction This paper describes the geometric operations of translation, scaling and rotation, when applied to images. The goal is to precisely define these in the context of [1]. 2 Translation Definition 1. Let f be an image and (a; b) 2 R 2 . Define a coordinate transformation x 0 = x + a y 0 = y + b We shall say that f 0 is the result of translating f by (a; b) if f 0 (x 0 ; y 0 ) = f(x; y) for every (x; y) 2 R 2 . 3 Scaling Definition 2. Let f be an image and ff ? 0. Define a coordinate transformation x 0 = ffx y 0 = ffy We shall say that f 0 is the result of scaling f by ff if f 0 (x 0 ; y 0 ) = f(x; y) for every (x; y) 2 R 2 . The value ff is called the scale factor from f to f 0 . We shall say that an image f 0 is a scaled version of f if there exists a scale factor from f to f 0 . It is worth noting that scaling a raster...