Research On Medical Model Reconstruction And Volumetric Mesh Generation And Deformation

How to realistically simulate the human living tissue behavior in an anatomically correct way, is one of the most active and challenging research topic in the fields of computer graphics, visualization, medicine and biomechanics. The essential techniques are model construction, and model modification and deformation in various tasks.The purpose of this thesis is to deal with some existing problems of current geometrical modeling, physical modeling, and model deformation techniques related to human biomechanical tissues. The main research contents include following topics:(1) Design special and effective methods for some biomechanical tissues with complicated shape and structure (such as the mandible with teeth), based on their characteristics, to reconstruct the geometrical model from medical images.This research involves the tasks of medial image segmentation, and surface reconstruction from planar contours. For the first task, unnecessary holes inside of the model should be avoided, and non-interest front regions should be excluded. For the second one, three fundamental problems of reconstruction: the correspondence problem, branching problem, and tiling problem should be handled properly.(2) Investigate various volumetric mesh generation tools and methods for biomechanical tissues with anisotropic material properties.The validity of the simulation result of physical model is mainly dependent upon the geometrical similarity, as well as the material similarity of the model to the real structure of the object to be analyzed. Although it is well known that most of the human biomechanical tissues have obvious orthotropic material properties, there is no published study that develops a meshing tool integrated with orthotropic material characteristics assignment function in the fields of general meshing or biomechanics modeling.The basic idea of this thesis is taking advantage of the fact that the long axis direction indicated by the shape configuration of most anisotropic tissues is compatible with the trajectory of maximum material stiffness, to guide the construction of volumetric mesh of high quality, as well as the three trajectory vector fields of the orthotropic material.(3) Study volumetric mesh deformation techniques which can preserve shape and volume details.It is helpful to obtain a new meshing of complicated object from standardized mesh model by deformation technique which can preserve the quality of the mesh cells. Beside, volumetric mesh deformation can be used to simulate various difficult deformation tasks, such as soft tissue simulation in surgery. But compare to a significant body of work on surface mesh deformation, there are very few research works related to the volumetric mesh deformation.This study of the thesis is inspired by the state-of-the-art surface mesh deformation techniques --- differential domain methods, such as the Laplacian coordinate based deformation and gradient field based deformation, which can preserve geometrical details, and have only linear computations. To extend the differential domain methods to the volumetric mesh deformation, one important issue is how to extract the geometrical differential properties of the volumetric mesh by local shape descriptor. In other words, volumetric mesh Laplacian operator, volumetric gradient operator and divergence operator are needed. Another issue is how to cope with the local transformation of the volumetric differential properties.By investigate the above problems, this thesis achieves several important research results, the main contributions are listed below:(1) A series of new methods specially designed for human mandible surface reconstruction based on the characteristics of mandible. The non-seed region segmentation method, and the dimension reduction idea of using reference curve to solve the reconstruction correspondence and branching problem, and method of tiling surface by mating points at multi-order convex hulls, could be easily expanded to other medical image based reconstruction problems.(2) An ad hoc volumetric meshing tool for biomechanical tissues with anisotropic material properties. By employing pairs of B-Spline curves which capture of the inherent shape of the model as auxiliary baselines, a sequence of Spline surfaces were interpolated adaptively as curve cross-sections to cut the original geometry, to construct volumetric meshes as well as the inherent trajectory vector fields of the orthotropic material.(3) An automatic biomechanical volumetric meshing methodology based on harmonic field, whose scalar distribution pattern tends to conform very well to the shape of the model. Our choice of harmonic fields to drive the meshing process has a number of important advantages. Of primary importance is that it guarantees a high degree of smoothness. The iso-contours extracted from surface harmonic field and gradient vectors of volumetric harmonic fields, which are used directly as vector fields of the orthotropic material, all have high quality. In addition, the whole process is automatic except only a few extreme constraint points input for the construction of surface harmonic field at the beginning. (4) Two novel linear differential domain volumetric mesh deformation techniques which can preserve the intrinsic geometrical qualities: the volumetric mesh Laplacian coordinate based deformation and volumetric gradient field based deformation. Compared to using surface mesh, employing volumetric mesh deformation can preserve the shape and volume details much better during deformation and avoid local self-intersections, and can achieve better local transformation propagation because of the internal mesh connections between distant points on the surface. And by employing the volumetric harmonic field to propagate local transformations to manipulate the volumetric mesh Laplacian coordinate or volumetric gradient field, quite satisfied deformation result are obtained.Although designed for biomechanical tissues and computer surgery simulation, these model construction and model deformation techniques could be used directly in othe virtual and simulation tasks in computer graphics.