In the field of design, engineers are often confronted with the following problem. A prototype shaped by a designer or an existing object should be remodeled as a CAD-model to further improve the design or to provide a backup of the object. With modern optical scanners, engineers are able to obtain high quality point clouds representing the object. These point clouds need work before they can serve as good CAD-models.

Often the objects under consideration possess a symmetry which is not perfect in a mathematical sense. To fulfill modern quality requirements, this lack of symmetry needs to be removed. In this project we developed a procedure to convert an almost symmetric point cloud in the plane into a symmetric smooth contour that can then be further processed by engineers to obtain their CAD-model.

The procedure presented is new. The only similar algorithm known in the literature depends on so-called landmarks in the point clouds and uses Procrustes analysis to solve the problem.

The procedure is divided into two steps: first we estimate the axis of symmetry of the almost symmetric point cloud to find a mirror image of the original point cloud; second we smooth the union of the original point cloud and its mirror image to obtain a good estimate of the symmetric model.

Author
Prof. Dr. Marcel Steiner, IGN   (http://personenseiten.fhnw.ch/marcel.steiner/)

Publication
Symmetrisation of Almost Symmetric Point Clouds in the Plane, M. Steiner,
Projektarbeit, Weiterbildungs-Lehrgang in angewandter Statistik, ETH Zürich, 2007.