Densities and maximum likelihood estimation of matching constraints

In this paper we present a theory for obtaining densities that are important for computer vision. As a result of the theory we compute the exact and novel density of the slope of a line fitted to image points. This density makes it possible to obtain confidence intervals for the slope or to make hypothesis testing about if two intersecting lines form a corner or not. The theory also lets us derive a novel technique for maximum likelihood estimation, that can be used for computing the fundamental matrix, conics, or any other constraint that can be expressed by polynomials of degree 2. We present exact and novel densities for the fundamental matrix and conic constraints, that are needed for the estimation. Experiments show how the results can be used in practise to compute maximum likelihood estimates of the fundamental matrix.