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 that the normalised algorithm acts to minimise. The cost function is then shown to be statistically better founded than the cost function associated with the non-normalised algorithm. This augments the original argument that improved performance is due to the better conditioning of a pivotal matrix. Experimental results are given that support the adopted approach. This work continues a wider effort to place a variety of estimation techniques within a coherent framework.

• Type: Conference
• Year: 2003
• Where: ICIAP
• Authors: Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, Darren Gawley
• Keywords: Cost Function, ICIAP 2003, Image Processing, Iterative Estimation Methods, Normalised Algorithm Acts