MAP Estimation of Epipolar Geometry by EM Algorithm and Local Diffusion

Finding epipolar geometry for two images is a fundamental problem in computer vision. While this typically relies on feature point correspondence, the epipolar constraint can also be used for improving the accuracy of correspondence. We propose a probabilistic framework for estimating the epiploar geometry, in which the geometry and the feature correspondence are estimated iteratively at the same time. Using the EM algorithm to maximize a posteriori, our approach updates feature correspondence with estimated epipolar geometry. The correspondence is further improved with local diffusion on a prior Markov Random Field model. In turn, more accurate epipolar geometry is recovered. Experiments show this approach produces more accurate fundamental matrix compared with typical methods and can handle some challenging situations such as view rotation and scale changes.