00023 c2 cylindrical surface the test on the

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Unformatted text preview: d on the residual axial surface, but it would require criteria which are not available in the classification of invariant surfaces. The relevance of the proposed methodology relies in its objectivity: the measured points are partitioned among the invariant surfaces identifiable on the object. This partitioning does not require any human support, even if any a-priori information can be used to speed up the cognitive process. In addition, the process becomes faster and faster as it recognizes and extracts new invariant surfaces. Statistical Modelling 3. THE STATISTICAL APPROACH 173 In a nutshell the proposed approach consists of the statistical modelling of the seven classes of symmetry. For each class Ci i=1,…7, a semi-parametric model Mi and a set of reference parameters Ωi are created in order to produce a PDF which is invariant under the action of the group of symmetry Gi. Furthermore, the invariance is enforced by replacing the set of measured points D={(x1,y1,z1),(x2,y2,z2),...,(xn,yn,zn)} with his projection on the quotient set ℜ3/Ei being Ei the set of equivalent points with respect to the rigid motions g∈Gi. This projection is performed by a suitable parametric function Vi(·;Ωi). ~ ( x, y...
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