Covariance Propagation for Guided Matching

We present a general approach and analytical method for determining a search region for use in guided matching under projective mappings. Our approach is based on the propagation of covariance through a first-order approximation of the error model to define the boundary of the search region for a specified probability and we provide an analytical expression for the Jacobian matrix used in the covariance propagation calculation. The resulting closed-form expression is easy to implement and generalizes to n dimensions. We apply our method to point-to-point mapping under a planar homography, point-to-line mapping under a fundamental matrix, and mosaic construction from video in the case of the video looping back on itself.