Invariant geometric properties of image correspondence vectors as rigid constraints to motion estimation

Accurate motion estimation algorithms are based on a number of invariant pr operties that can be inferred from the motion. A large number of calibratio n algorithms have been proposed over the last two decades mainly based on a nalytic, perspective, or epipolar geometries. Extending Chasles' screw moti on concept to the estimation of motion parameters in computer vision, we ha ve presented an analysis of geometric properties of image correspondence ve ctors synthesized into a single coordinate frame and developed calibration algorithms using both simulated and real range image data.(15,16) In this p aper, ute extend that work by defining the relevant geometric properties of image correspondence vectors from the point of view of invariants and by d eveloping two calibration algorithms using the Monte Carlo method and media n filtering. The algorithms are applied to real and synthetic image data co rrupted by noise and outliers. Experimental results demonstrate that the me dian filter based algorithm is generally more robust and accurate than the Monte Carlo based algorithm and that the geometric analysis of invariant pr operties of correspondence vectors is a useful framework to motion paramete r estimation.