Computing Exact Aspect Graphs of Curved Objects: Parametric Surfaces

Jean Ponce, David J. Kriegman

This paper introduces a new approach for computing the exact aspect graph of curved objects observed under orthographic projection. Curves corresponding to various visual events partition the Gaussian sphere into regions where the image structure is stable. A catalogue of these events for piecewise-smooth objects is available from singularity theory. For a solid bounded by rational parametric patches and their intersection curves, it is shown that each visual event is characterized by a system of n polynomials in n + 1 variables whose solutions can be found by numerical curve tracing methods. Combining these methods with ray tracing, it is possible to characterize the stable image structure within each region. Results from a preliminary implementation are presented.

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