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Accurate motion estimation algorithms are based on a number of invariant properties that can be inferred from the motion. A large number of calibration algorithms have been proposed over the last two decades mainly based on analytic, perspective, or epipolar geometries. Extending Chasles' screw motion concept to the estimation of motion parameters in computer vision, we have presented an analysis of geometric properties of image correspondence vectors synthesized into a single coordinate frame and developed calibration algorithms using both simulated and real range image data.^15,16 In this paper, we extend that work by defining the relevant geometric properties of image correspondence vectors from the point of view of invariants and by developing two calibration algorithms using the Monte Carlo method and median filtering. The algorithms are applied to real and synthetic image data corrupted by noise and outliers. Experimental results demonstrate that the median filter based algorithm is generally more robust and accurate than the Monte Carlo based algorithm and that the geometric analysis of invariant properties of correspondence vectors is a useful framework to motion parameter estimation.

In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.