Learning OpenCV

Stretch, Shrink, Warp, and Rotate

In this section we turn to geometric manipulations of images. ^[74] Such manipulations include stretching in various ways, which includes both uniform and nonuniform resizing (the latter is known as warping). There are many reasons to perform these operations: for example, warping and rotating an image so that it can be superimposed on a wall in an existing scene, or artificially enlarging a set of training images used for object recognition. ^[75] The functions that can stretch, shrink, warp, and/or rotate an image are called geometric transforms (for an early exposition, see [Semple79]). For planar areas, there are two flavors of geometric transforms: transforms that use a 2-by-3 matrix, which are called affine transforms; and transforms based on a 3-by-3 matrix, which are called perspective transforms or homographies. You can think of the latter transformation as a method for computing the way in which a plane in three dimensions is perceived by a particular observer, who might not be looking straight on at that plane.

An affine transformation is any transformation that can be expressed in the form of a matrix multiplication followed by a vector addition. In OpenCV the standard style of representing such a transformation is as a 2-by-3 matrix. We define:

It is easily seen that the effect of the affine transformation A · X + B is exactly equivalent ...