In 2001 Prof. 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 Prof. 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.

Statistical modelling of geometrical invariant sampled sets / Chiabert, Paolo; DE MADDIS, Manuela. - (2007), pp. 169-178. (Intervento presentato al convegno 9th CIRP International Seminar on Computer-Aided Tolerancing tenutosi a Tempe, Arizona, USA nel 10-12 April, 2005).

Statistical modelling of geometrical invariant sampled sets

CHIABERT, Paolo;DE MADDIS, MANUELA
2007

Abstract

In 2001 Prof. 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 Prof. 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1828483
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo