Research Internships at Microsoft provide a dynamic environment for research careers with a network of world-class research labs led by globally-recognized scientists and engineers, who pursue innovation in a range of scientific and technical disciplines to help solve complex challenges in diverse fields, including computing, healthcare, economics, and the environment. Feature matching is a fundamental step for the solution of many geometric computer vision problems, such as SLAM, 3D registration, and image stitching. However, in each of these problems the ultimate goal is the estimation of geometric parameters related to the scene: the camera motion, the transformation between the 3D objects, the homography relating the images. A Bayesian approach should therefore treat the matches as nuisance parameters, and dispense with them accordingly. In this project we'll attack this problem through a unified framework, using fundamental methods for randomized algorithms, and validate the Bayesian solution against RANSAC and other matching algorithms. Two lines of work will be pursued: Development of match-free algorithm for the class of geometric computer vision problems discussed above. Careful implementation of the algorithm and its benchmarking against competing methods.