Some Methods Of Constrained Surface Parameterization And Skeleton Extraction And Their Applications

With the development of data acquisition equipment, computer software/hardware, and computer network, digital geometry processing has become the advanced research field and popular topic in Computer Graphics. The texture mapping and skeleton extrac-tion of 3D models are two basic and important problems both in academia and industry. In this dissertation, we are concerned with the triangular mesh and point cloud models, which are both main representations of digital medium, and do some research on con-strained parameterization and skeleton extraction. We also apply them in digital plant field successfully, which brings satisfying results. The main work can be summarized as follows:1. We present an adaptive method for constrained texture mapping of triangular meshes. It balances the conformal term and constraint term of the objective function by induc-ing a series of weights, and the parameterization results are computed by iterative op-timization. During the iterative process, the weights in each step are chosen adaptively by the results in the previous step, and finally converge to a series of optimal weights. The parameterization results by applying this method indicate that the conformality can be well preserved while the constrained conditions are satisfied. Experimental re-sults on amount of mesh models in texture mapping and mesh morphing applications show its simplicity of implementation and its efficiency.2. We present a texture mapping method for leaf triangular meshes, based on feature extraction. In order to deal with the problem that the traditional methods can not handle leaf models, we first analyze the shapes of leaves. Then we extract, sift and match the feature points of the boundary and midvein curves, based on the symmetric and geometric information. We obtain the texture mapping results by constrained parameterization method, after the computation of boundary mapping. Experimental results reveal that 3D leaf models with a strong sense of reality can be produced by the proposed method.3. We present an effective skeleton extraction method for tree point cloud models. We are concerned with the unique characteristics of trees, and improve the algorithm pro-posed by others. It mainly includes:the main crotches identification based on minimal spanning tree, which is generated from contracted point cloud, and the global scalar field of sampling radii. Meanwhile, the adaptive sampling strategy well captures the geometric and topological information of original point cloud, and the skeleton curve with high quality can be extracted by constructing and refining the graph. Experi-mental results on different kinds of trees indicate that the robustness and effectiveness of the proposed method. 4. We present a novel curve reconstruction method for complicated stripe-shaped point cloud data. The first step is anisotropic and adaptive sampling of original data. Ac-cording to the differences of sampling radii, we identify each non-linear region auto-matically based on clustering algorithm. Then we refine the graph that constructed by sampling nodes, by applying the contraction and merging operators, and finally improve the geometric approximation of reconstructed curve by Least-Square curve fitting. Experimental results on amount of complicated point clouds reveal that the proposed method can not only deal with the non-uniform and multi-scales data, but also reconstruct the curves that have self-intersecting regions or multiple parts.