Revisiting Hartley's Normalized Eight-Point Algorithm

A statistical rationalisation of Hartley's normalised eight-point algorithm

The eight-point algorithm of Hartley occupies an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eightpoint algorithm that results from using normalised data. A first step is singling out a cost function tha...

Revisiting Hartley’s Normalised Eight-Point Algorithm

The eight-point algorithm of Hartley has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalised data. It is first established that the normalis...

Three-dimensional structure calculation: achieving accuracy without calibration

This paper addresses the problem of computing the camera motion and the three-dimensional structure of a scene using two uncalibrated images as inputs. The camera motion is calculated by estimating the essential matrix and using approximate values, easily available, for the intrinsic parameters. The classical eight-point algorithm to calculate the essential matrix is known to be very sensitive ...

Singular Vector Methods for Fundamental Matrix Computation

The normalized eight-point algorithm is broadly used for the computation of the fundamental matrix between two images given a set of correspondences. However, it performs poorly for low-size datasets due to the way in which the rank-two constraint is imposed on the fundamental matrix. We propose two new algorithms to enforce the rank-two constraint on the fundamental matrix in closed form. The ...

Finding the Essential: A Phenomenological Look at Hal Hartley's "No Such Thing"