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Research Papers

Reverse Engineering: Statistical Threshold for New Selective Sampling Morphological Descriptor

[+] Author and Article Information
E. Vezzetti

Dipartimento di Sistemi di Produzione Ed Economia dell’Azienda, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyenrico.vezzetti@polito.it

J. Comput. Inf. Sci. Eng 10(1), 011008 (Mar 10, 2010) (10 pages) doi:10.1115/1.3330423 History: Received August 08, 2007; Revised November 29, 2009; Published March 10, 2010; Online March 10, 2010

During the digitization process of a physical object, the operator has to choose an acquisition pitch. Currently, 3D scanners employ constant pitches. For this reason the grid dimension choice normally represents a compromise between the scanner performances and specific applications, and the resolution and accuracy of the specific application. This is a critical problem because, normally, the object shape is assumed as a combination of different geometries with different morphological complexities. As a consequence of this, while some basic geometries (i.e., planes, cylinders, and cones) require only few points to describe their behavior, others need much more information. Normally, this problem is solved with a significant operator involvement. Starting from the object morphology and from the 3D scanner performances, the author finds the optimal acquisition strategy with an iterative and refining process made of many attempts. This approach does not guarantee an efficient acquisition of the object, because it depends strongly on the subjective ability of the operator involved in the acquisition. Many approaches propose points cloud management methodologies that introduce or erase punctual information, working with statistical hypothesis after the acquisition phase. This research work proposes an operative strategy, which starts from, first, a raw point acquisition, then it partitions the object surface, identifying different morphological zone boundaries (shape changes). As a consequence, some of the identified regions will be redigitized with deeper scansions in order to reach a more precise morphological information. The proposed partitioning methodology has been developed to directly interact with the 3D scanner. It integrates the use of a global morphological descriptor (Gaussian curvature), managed in order to be applicable in a discrete context (points cloud), with the concept of the 3D scanner measuring uncertainty. This integration has been proposed in order to provide an automatic procedure and a “curvature variation threshold,” able to identify real significant shape changes. The proposed methodology will neglect those regions where the shape changes are only correlated with the uncontrolled noise introduced by the specific 3D scanner performances.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Measured points indexing methodology

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Figure 2

Increased number of planar curvature variation analysis directions strategy

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Figure 3

Normal vector variation idea

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Figure 4

Gauss–Weingarten’s application and Gauss curvature correlation

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Figure 5

Gauss map: (a) for a conic and (b) pyramidal vertex. The Gauss map for P(t) represents the curve enclosing the finite neighborhood of P0 on the Σ surface.

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Figure 6

Elements for geodetic curvature definition

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Figure 7

Characteristic angles of the boundary curve P(t)

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Elements of triangulated surfaces not containing curvature information

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Figure 9

Jump angles: (a) explicated on continuous and (b) unfolded triangulated surfaces

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Figure 10

Gaussian curvature configurations: (a) positive, (b) null, and (c) negative

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Figure 11

Gaussian curvature configurations reachable with a surrounding region boundary with four vertexes

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Figure 12

Four vertexes configuration: (a) possible curvature values reachable, and (b) an example of saddle shape with many orientations (monkey saddle)

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Figure 13

Surface for the sensitivity test: (a) points cloud obtained in a simulated acquisition on an ideal noised surface, and (b) (red points) zones that need a deeper scansion

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Figure 14

Surface for the sensitivity test: (a) real surface and (b) (red points) zones that need a deeper scansion

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Figure 15

Area definition

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Figure 16

Sensibility evaluation: (a) increased instrument uncertainty and (b) decreased instrument uncertainty values

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Figure 17

Nonstructured grid example: (a) real surface and (b) (red points) zones that need a deeper scansion

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