Industrial Geometry

This subproject focuses on active contour methods for curves and surfaces. In particular, we studied the interaction between different possible representations of geometric objects. The main results have been obtained in a close cooperation between the groups in Linz and Innsbruck. The activities can roughly be organized in four groups.

First, we studied evolution processes of T-spline level sets and applications to geometry reconstruction and image segmentation. Second, we explored the framework of coupled evolution and used it for dealing with geometric constraints and image segmentation. Third, we studied the relation between Gauß-Newton-type methods for orthogonal distance regression and evolution processes. Fourth, in a cooperation with subproject 3, we worked on the modeling, analysis and implementation of variational techniques on M-reps shape manifolds.

In addition to these core activities, we cooperated intensively with the Computational Geometry group (subproject 5) on questions related the use of higher order geometric primitives, in particular addressing the computation of the medial axis of planar domains which are bounded by general free-form curves. We also cooperated with subproject 1 on rational surfaces with special offsetting-related properties.

• Evolution of T-spline Level sets, 3D Geometry Reconstruction
• Coupled evolution
• Gauß-Newton-type methods for orthogonal distance regression
• Image Analysis

(a) (b)
Fig. 1: (a) The data and reconstructed mesh with sharp features. (b) 3D Geometry reconstructions.

Fig. 2: Approximation with area constraint. The area equal 0.4, 0.5 and 0.6.

Fig. 3: Medial axis computation using spiral biarc approximation (Cooperation with subproject 5). The computation time was 13.25 seconds, where 13830 arcs have been used to describe the shape.