Correspondence-free determination of the affine fundamental matrix.

Fundamental matrix estimation is a central problem in computer vision and forms the basis of tasks such as stereo imaging and structure from motion. Existing algorithms typically analyze the relative geometries of matched feature points identified in both projected views. Automated feature matching is itself a challenging problem. Results typically have a large number of false matches. Traditional fundamental matrix estimation methods are very sensitive to matching errors, which led naturally to the application of robust statistical estimation techniques to the problem. In this work, an entirely novel approach is proposed to the fundamental matrix estimation problem. Instead of analyzing the geometry of matched feature points, the problem is recast in the frequency domain through the use of Integral Projection, showing how this is a reasonable model for orthographic cameras. The problem now reduces to one of identifying matching lines in the frequency domain which, most importantly, requires no feature matching or correspondence information. Experimental results on both real and synthetic data are presented that demonstrate the algorithm is a practical technique for fundamental matrix estimation. The behavior of the proposed algorithm is additionally characterized with respect to input noise, feature counts, and other parameters of interest.

Maximum-likelihood estimation of circle parameters via convolution.

The accurate fitting of a circle to noisy measurements of circumferential points is a much studied problem in the literature. In this paper, we present an interpretation of the maximum-likelihood estimator (MLE) and the Delogne-Kåsa estimator (DKE) for circle-center and radius estimation in terms of convolution on an image which is ideal in a certain sense. We use our convolution-based MLE approach to find good estimates for the parameters of a circle in digital images. In digital images, it is then possible to treat these estimates as preliminary estimates into various other numerical techniques which further refine them to achieve subpixel accuracy. We also investigate the relationship between the convolution of an ideal image with a "phase-coded kernel" (PCK) and the MLE. This is related to the "phase-coded annulus" which was introduced by Atherton and Kerbyson who proposed it as one of a number of new convolution kernels for estimating circle center and radius. We show that the PCK is an approximate MLE (AMLE). We compare our AMLE method to the MLE and the DKE as well as the Cramér-Rao Lower Bound in ideal images and in both real and synthetic digital images.