8 March 2002 Fitting geometric models in image processing using Grassmann manifolds
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This paper presents a new method of fitting geometric objects to measurement data. The coefficients of the implicit equations describing the object to be fitted are used as the Grassmann coordinates. The design matrix is then formed as the dual space to the Grassmann coordinates. The analysis of the null space of the design matrix yields the solution being sought. Degenerate data or models can be identified by analyzing the Grassmann manifolds in the null space. The method can also be applied to fitting coupled geometric objects, such as concentric circles. A solution has been found which enables the linear fitting of rational polynomials a problem which was considered to be non-linear. The method is demonstrated for conic sections, quartics, rational Bezier curves and for some examples in image processing.
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Paul O'Leary, Paul O'Leary, "Fitting geometric models in image processing using Grassmann manifolds", Proc. SPIE 4664, Machine Vision Applications in Industrial Inspection X, (8 March 2002); doi: 10.1117/12.460198; https://doi.org/10.1117/12.460198

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