Surface Reconstruction And Smoothing Based On Elastic Deformation

With the development of Computer Aided Geometric Design, the research focus of curve and surface modeling methods has changed from representation to controllable de-formation, and then to simulation deformation. The classic elastic deformation methods become the bridge of communication between geometric deformation and physical defor-mation, and illuminate extensive applications in various fields, due to their advantages in simplicity, effective simulation, intuition and speed. According to different applica-tion conditions, elastic deformation methods require distinct representations, processing schemes and interactions with respect to exterior data, and hence they need to be im-proved contrapuntally. In this dissertation, elastic deformation methods are employed as the base of studying space curve/surface stereo reconstruction and mesh smoothing together with enhancement. In addition, a fast approach dealing with industrial prob-lems of labeling in complex irregular regions is proposed as well. The main work can be summarized as follows:1. The idea of elastic deformation methods is first used to handle space curve/surface stereo reconstruction problem. In the step of stereo reconstruction, based on deformation method and perspective invariant NURBS representation, we evolute the curve/surface from the view of inverse optimization to finish reconstruction. This manner can obtain more effective use of local properties from projected curve/surface, reduce the need of matching curve/surface data in multiview images, meanwhile improve the reconstruction precision. Considering the 2D data reconstruction inevitably exists error, a discussion on its influence to stereo reconstruction is given next. Finally, the proposed approach is ex-perimented with ideal and real data, and gains a satisfying reconstruction effect. Besides, in the step of image data reconstruction, a variational level set segmentation approach which integrates the image information from both boundary gradient and region is pre-sented. It effectively utilizes the image information and does not need re-initialization. Experiments illustrate its abilities in segmenting different kinds of images.2. Surface fundamental forms which are used to define elastic deformation describe the local differential features of surface. From the perspective of mesh signal processing, high quality mesh with real modeling effect can be obtained by processing this type of features. Based on the description of local differential features given by elastic deformation methods, we modify the fundamental form features of mesh surface. The new mesh is reconstructed in the least square sense with proper constraints added. With the help of fast linear system solver, the algorithm can achieve real-time smoothing and enhancement effect. Experimental results demonstrate that the proposed method is simple, fast and able to prevent volume shrinkage and shape distortion to some extent.3. Labeling in complex irregular regions is studied and a fast code-based labeler (FCBL) is proposed to accomplish this objective. The region is discretized by specified labeling character size, and then encoded by the Freeman encoding technique for decreas-ing the storage. We enhance the encoding scheme to make it more suitable for our complex problem. Based on the codes, searching algorithms are designed and can be extended with customized constraints. In addition, by introducing a smart optimal direction estimation, the labeling speed and accuracy of FCBL are significantly improved. Experiments with a large range of real data gained from industrial factories demonstrate the feasibility and stability of FCBL.