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Intelligent 3D geometry reconstruction using dynamic and evolution-based techniques

Final Activity Report Summary - ISIS (Intelligent 3D geometry reconstruction using dynamic and evolution-based techniques)

We firstly studied the evolution of T-spline level sets, i.e. curves or surfaces implicitly defined by T-spline functions, for geometry reconstruction and image segmentation. Our method produced piecewise algebraic curves or surfaces to represent the shape of the given data with complex topology.

In order to represent and reconstruct sharp features by an implicitly defined curve, we incorporated the so-called corner detector functions into T-spline level sets so that sharp corners could be correctly constructed.

We moreover proposed an effective method for constructing a triangular mesh from a set of unorganised data points, which could be non-uniformly sampled, noisy or even contain holes. Our method was quite general and applicable to three-dimensional models with complex topology and sharp features.

We also formulated the framework of dual evolution by simultaneously considering evolution processes for B-spline curves and T-spline level sets. The main advantage of this framework was that it combined the advantages of both representations.

Furthermore, we investigated how to formulate additional constraints, such as range constraints, volume constraints and convexity constraints, and combined them into our framework of shape evolution. In this way, we were able to conveniently utilise a priori knowledge about the shape of the object to be reconstructed.

We additionally developed an evolution-based algorithm for approximate parameterisation of implicitly defined curves by parametric spline curves. Our method did not use any a priori information about the topology of the curves.

We also proposed a new method for three-dimensional shape morphing, where the in-between objects were represented by T-spline level sets. We developed a fully automated algorithm to produce morphing sequences between shapes of any topology.

In order to efficiently discretise the evolution equation we used particles on the evolving surface. In particular, we defined criteria for local and global resampling, which were necessary to maintain a sufficiently uniform distribution of the particles on the surface.

The B-snake model (active B-spline contour) was combined with a Mumford-Shah type segmentation of the level set function to overcome the difficulties of how to choose the optimal stopping time and the correct level of the evolving function for image segmentation.

Finally, we proposed to use a shape metric based on the small displacement theory of elasticity for shape morphing and elastic deformation. Some promising results were achieved by using this approach.