Feature Matching with Affine-Function Transformation Models

Feature matching is an important problem and has extensive uses in computer vision. However, existing feature matching methods support either a specific or a small set of transformation models. In this paper, we propose a unified feature matching framework which supports a large family of transformation models. We call the family of transformation models the affine-function family, in which all transformations can be expressed by affine functions with convex constraints. In this framework, the goal is to recover transformation parameters for every feature point in a template point set to calculate their optimal matching positions in an input image. Given pairwise feature dissimilarity values between all points in the template set and the input image, we create a convex dissimilarity function for each template point. Composition of such convex functions with any transformation model in the affine-function family is shown to have an equivalent convex optimization form that can be optimized efficiently. Four example transformation models in the affine-function family are introduced to show the flexibility of our proposed framework. Our framework achieves 0.0 percent matching errors for both CMU House and Hotel sequences following the experimental setup in [6].