Learning to Match: Deriving Optimal Template-Matching Algorithms from Probabilistic Image Models

摘要

Finding correspondences between images by template matching is a common problem in image understanding. Although a variety of solutions have been proposed, most of them rely on the arbitrary choice of a template and a matching function. Often, different cost functions lead to different results, and the choice of a good cost for a specific application remains an art. Statistical models on the other hand, allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles. The key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples. We present a family of statistical models for grayscale images, which allow us to derive optimal template-matching algorithms. The intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template. Firstly, we assume the intensity distribution to be Gaussian and derive an intensity-matching algorithm, which is a generalization of the classical sum-of-squared differences. Then, we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation-matching algorithm that can handle photometric variations. Both models are exemplified on the automatic detection of anatomical landmarks in brain Magnetic Resonance Images.