*David H. Marimont*

A representation for image curves and an algorithm for its computation are introduced. The representation is designed to facilitate matching of image curves to completely specified model plane curves and estimation of their orientation in space, despite the presence of noise. variable resolution, or partial occlusion. This is an important subproblem of model-based vision. A curve may be represented at a variety of scales, and a strategy for selecting natural scales is proposed. At each scale, the representaion is simply a list of positions in the plane, with tangent directions and curvatures specified at each position; each curvature is either a zero or an extremum (hereafter critical points). The algorithm for computing the representation involves smoothing with gaussians at different scales: extracting tile critical points from the smoothed curves. and using dynamic programming to construct a list of critical points which best approximate the curve for each length of list possible. We propose to examine the tradeoff between the error of the approximation and length of the lists to find natural scales.

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