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Essential representation and calibration of rigid body transformations

Liu Y., Rodrigues M. A.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

123-138

In [20], we extended Chasles' screw motion concept to computer vision calibration tasks by investigating geometric properties of image correspondence vectors. In this paper, we analyse geometric properties of reflected correspondence vectors synthesised into a single coordinate frame leading to the development of two representation theorems of rigid transformations. The theorems and their corollaries provide a novel method to identify the original transformation and an insight into the relationships between the representation of rigid transformation, rigid constraints, and the transformation parameters. The analysis provides a framework for the development of novel calibration algorithms as demonstrated by two new proposed algoriths. For a comparative study of performance, we also implemented another well known calibration procedure based on the constraint least squares (CLS) ( [4] ) method. The experimental results have shown that the proposed algorithms are more accurate that the CLS algorithm when the image data are corrupted by both noise and outliers.