A new robust geometrical algorithm for motion estimation from range images

We present a geometric analysis of reflected correspondence vectors synthesised into a single coordinate frame. The analysis provides an extension to Chasles' work for machine vision tasks (R.S. Ball, 1900), by providing an explicit representation of motion parameters based on the use of distance between feature points and angle information and also by providing a clear insight into the number of solutions to motion parameters. We demonstrate that robust motion estimation algorithms can be developed from the analysis by proposing and implementing a calibration algorithm making full use of the geometric properties of reflected correspondence vectors. A fuzzy reasoning step has been included in the algorithm in order to counteract the adverse effects of noise and outliers. Accuracy and robustness are assessed and compared with a constraint least squares algorithm using both synthetic and real range image data.