Research On Mesh Morphing And Editing With Feature Preservation

Today, the rapid advance of 3D scanning techniques has made the acquisition of 3D data of the objects from real world getting easier and easier. Users can reconstruct the geometric models of complex objects by these high-precision data. These geometric models not only reflect the actual shape of the objects but also provide designers a starting point of creating new models. Thus, to create mesh models with new appearances by processing and reusing the existing models is becoming an extremely important way to ease the efficiency problem of geometric design in computer graphics. The core techniques of the reuse of existing 3D mesh models are mesh editing and mesh morphing and the key property of mesh editing and morphing is to preserve the features during the processing. Based on 3D triangular meshes, we did some researches on mesh editing, morphing and some related techniques with feature preservation and proposed a series of mesh processing algorithms including mesh segmentation, mesh parameterization, mesh editing and morphing. These algorithms have greatly pushed the development of mesh processing with feature preservation.Targeting the problem of feature preservation, this thesis proposes different approaches. The main contributions include:1. A novel mesh segmentation algorithm based on 3D Delaunay triangulation was presented to partition meshes meaningfully. A volume-based distance (VD) for each face was first computed using 3D Delaunay triangulation. After a smoothing process, clustering of the mesh faces was performed to extract k clusters based on their VD values: a Gaussian Mixture Model (GMM) fitting k Gaussians to the histogram of VD values of the faces, this was achieved using the Expectation-Maximization (EM) algorithm. Finally, by considering the quality of clustering, the smoothness of the partition boundary and the minima rule proposed in human cognitive vision the- ory, our method employed a graph-cut algorithm to get the meaningful partitioning. Experiment indicates that the method is fast and can partition a mesh into meaningful parts.2. A novel interactive system was presented for establishing compatible meshes for articulated shapes. Given two mesh surfaces, our system automatically generates both the global level component correspondence and the local level feature correspondence. Users can use some sketch-based tools to specify the correspondence in an intuitive and easy way. Then all the other vertex correspondences could be generated automatically. The cross parameterization preserves both high level and low level features of the shapes. The technique showed in the system benefits various applications in graphics including mesh interpolation, deformation transfer, and texture transfer.3. Recently, animations with deforming objects have been frequently used in various computer graphics applications. Morphing of objects is one of the techniques which realize shape transformation between two or more existing objects. In this thesis, we present a novel morphing approach for 3D triangular meshes with the same topology. The basic idea of our method is to interpolate the mean curvature flow of the input meshes as the curvature flow Laplacian operator encodes the intrinsic local information of the mesh. The in-between meshes are recovered from the interpolated mean curvature flow in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Our approach can generate visual pleasing and physical plausible morphing sequences and avoid the shrinkage and kinks appeared in the linear interpolation method. Experimental results are presented to show the applicability and flexibility of our approach.4. In computer graphics, some regions on a 3D model are often required to precisely preserve the features during editing. A new feature preserving mesh editing method was proposed. First we use one of the existing mesh editing methods to estimate the final editing result. Then we get the deformation function between this result and the input mesh. Using singular value decomposition on the deformation function of each faces in the feature region which specified by user, we extract the rigid component of the function. Our method keeps the global shape of the feature region, and avoids the scale and distortion that cause the visual unpleasing. We also propose a refined algorithm which makes the resulting mesh more reasonable. The framework produces visually pleasing editing results with simple user interaction.