Computing the Uncertainty of Geometric Primitives and Transformations

In this work we present the uncertainty transformation and its properties and apply these in a frequently encountered problem in computer vision: the alignment problem. A convex polytope is used to captivate the uncertainty of transformations that arises when the position of image points is not exactly known. The uncertainty polytope is used to compute the correspondences between points on the source and the image object. The computation can be made faster when rectangular uncertainty regions are used by splitting up the problem. We show how to efficiently compute the minimal size of an uncertainty region for a given set of point correspondences as a similarity measure in the alignment procedure. Our alignment method is illustrated by an application involving the recognition of plant leaves in digital images. Finally, we present a new method for the computation of the transformation parameters: these are obtained through fitting planes. Keywords—Geometric uncertainty, image transformation