The fundamental matrix (FM) describes the geometric relations that exist between two images of the same scene. Different error criteria are used for estimating FMs from an input set of correspondences. In this paper, the accuracy and efficiency aspects of the different error criteria were studied. We mathematically and experimentally proved that the most popular error criterion, the symmetric e...

In this paper, we present the use of two evolutionary algorithms to estimate fundamental matrices. We first propose a modification of the Hybrid Taguchi Genetic Algorithm (HTGA) that employs a single objective function, either geometric or algebraic distance, for optimization. We then propose to use a multi-objective optimization algorithm, Intelligent Multi-Objective Evolutionary Algorithm (IM...

Matching a pair of affine invariant regions between images results in estimation of the affine transformation between the regions. However, the parameters of the affine transformations are rarely used directly for matching images, mainly due to the lack of an appropriate error metric of the distance between them. In this paper we derive a novel metric for measuring the distance between affine t...

The optical flow observed by a moving camera satisfies, in the absence of noise, a special equation analogous to the epipolar constraint arising in stereo vision. Computing the ‘‘flow fundamental matrix’’ of this equation is an essential prerequisite to undertaking three-dimensional analysis of the flow. This article presents an optimal formulation of the problem of estimating this matrix under...

This paper addresses the problem of robustly estimating correspondences between stereo images, together with the computation of the Fundamental Matrix-F. The fundamental matrix describes the epipolar geometry of a pair of stereo images, and a number of algorithms have been described in the literature to estimate this matrix. However, most of these algorithms assume that a number of correct poin...

Computer vision plays an important role in many automatic applications, such as surface measurement, industrial inspection, reverse engineering and even mobile robot navigation. All these applications might be solved by means of a stereovision system formed by at least two cameras if the geometry of such stereo rig is previously known. So, camera calibration is based on computing the intrinsic ...

In common motion segmentation and estimation applications where the exact nature of objects’ motions and the camera parameters are not known a priori, the most general motion model (the fundamental matrix) is applied. Although the estimation of a fundamental matrix and its use for motion segmentation are well understood, the conditions governing the feasibility of segmentation for different typ...

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with exp...

The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper addresses the important problem of its robust determination given a number of image point correspondences. We rst de ne precisely this matrix, and sh...

We present a novel method for estimating the fundamental matrix, a key problem arising in stereo vision. The method aims to minimise a cost function that is derived from maximum likelihood considerations. The respective minimiser turns out to be significantly more accurate than the familiar algebraic least squares technique. Furthermore, the method is identical in accuracy to a Levenberg-Marqua...