M.Sc Student | Lipshitz Boris |
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Subject | Discrete Curvature Estimation of Scanned Noisy Objects for Verification of Scanned Engineering Parts with CAD Models |

Department | Department of Mechanical Engineering |

Supervisor | Professor Anath Fischer |

In recent years advances in 3D scanning technology have enabled highly accurate measurements with relatively low noise. Nevertheless, derivative computations are unstable for real data, and the estimated curvature is thus very sensitive to noise. Curvature is an invariant surface property that is not affected by the choice of the coordinate system, the position of the viewer, or the particular parameterization of the surface. A large range of problems in 3D computer vision and computational geometry can be solved by means of surface curvature properties.

A
common geometric surface representation in reverse engineering is a triangular
mesh, which is constructed from sampled points. The curvature for triangular
meshes is not defined. The faces are flat and thus have zero curvature, and
only continuity
at the vertices as edges. However, triangle faces are piecewise linear
approximations of the sampled object. Thus, the curvature of unknown surfaces
can be estimated by extracting information from the triangular mesh. Available
curvature estimation methods are as follows: *angle-based* curvature
estimation method, linear approximation method by analytic surface (Hamann),
curvature extraction method from curve fitting (Taubin). Most algorithms can
approximate the curvature of synthetic meshes quite accurately, but they fail
with real noisy data. In the current research several curvature estimation
algorithms are implemented, analyzed and extended for triangular meshes with
noise.

One important use of discrete curvature that is investigated in this research is in the field of verification. The manufacturing industry constantly needs to verify machined objects against their original CAD models. Given a prototype design of a solid model, a manufacturing engineer should be able to determine whether the part was manufactured well, that is, whether it fits the CAD model exactly. But in many cases, spatial fitting of corresponding points is not sufficient. The current work attempts to check the possibility of comparing the curvatures of corresponding objects.