Geometric Transformations

Abstract

Most people have tried to do a geometric transformation of an image when preparing a presentation or when manipulating an image. The two most well-known are perhaps rotation and scaling, but others exist. In this chapter it is described how such transformations operate and the issues that need to be considered when doing such transformations are discussed. The term “geometric” transformation refers to the class of image transformation where the geometry of the image is changed but the actual pixel values remain unchanged. The chapter first focusses on the class of affine transformations, including translation, scaling, rotation, and shearing. Next, some of the practical issues that need to be considered when implementing such transformations are discussed. Lastly the chapter introduces the more advanced transformation known as homography and relates this to the well-known problems of keystoning and camera calibration.