In 2001 Mario Costa proposed a methodology for the statistical identification of three dimensional shapes based on the synthesis of two mathematical tools: the classification of geometrical shapes according to their invariant properties under the action of rigid motions and the Parzen's method for the non-parametric estimation of Probability Density Functions from a finite number of sampled points. This paper provides an extensive experimental test on the original algorithms developed by Mario Costa by analyzing a number of cases which differ on size and surface classes. From a conceptual point of view, the non-parametric, model-independent estimation of the Probability Density Function of a set of points closes the loop composed of design, manufacturing and inspection activities along the product development process. It seems therefore possible to adopt the proposed methodology to provide an unambiguous description of product morphology.
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Chiabert, P., De Maddis, M. (2007). Statistical Modelling of Geometrical Invariant Sampled Sets. In: Davidson, J.K. (eds) Models for Computer Aided Tolerancing in Design and Manufacturing. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5438-6_18
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DOI: https://doi.org/10.1007/1-4020-5438-6_18
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