Research On Mesh Generation Techniques Based On Medical Cross-Sectional Images

Advances in medical imaging technology have made it possible to obtain the geometries of the human organs and tissues in terms of medical cross-sectional images, such as Computed Tomography(CT) and Magnetic Resonance Imaging(MRI). Medical cross-sectional image based geometric modeling and mesh generation plays an important role in the field of computational biomedicine, and it also makes the basic and key precondition for the successful virtual surgery simulation.There are currently two different technical routes of medical image based geometric modeling and mesh generation for human organs and tissues, one is cross-sectional contour based, and the other is grid based. The contour-based meshing techniques demand extracting the sequence of contours of the interested objects from the 2D medical images, and then to reconstruct the 3D surface or volume meshes between contours from the adjacent cross sections. This meshing family is capable of controlling the meshing density and precision with flexibility, however, when the objects to be modeled is of complex structures as holes or branches, topology issues like contour corresponding and branching are quite thorny. As for the gird-based meshing technique family, the 2D medical cross-sectional images are enveloped as a 3D volume dataset, upon which a background grid with material tags is constructed. The isosurface representing the boundary surface is extracted from the background grid, and the cells inside the isosurface is decomposed into solid elements to construct volumetric meshes. The topology issues can be untangled smoothly with the grid-based meshing methods, but it’s difficult to generate elements with good shape quality to conform the surface boundary.Triangle and tetrahedral meshes are the most popular geometric models applied in surgery simulations due to their flexible geometric property. As for geometric modeling of the human organs and tissues for virtual surgery simulation, this dissertation focuses on the research of triangular and tetrahedral mesh generation from medical cross-sectional images, involving different techniques like medical image processing, 2D mesh generation, 3D mesh generation, and mesh post-processing, aiming to constructing quality meshes for surgery simulation purpose. The main contributions of the dissertation are as follows.Firstly, medical image pre-processing techniques for mesh generation are studied, and a novel optimal path Snake algorithm is presented for contour extraction. In the new Snake algorithm, the tranditional Snake energy is converted into a potential graph that is constructed from the image gradient. The contour is extracted by searching the global optimal path between the two endpoints in the potential graph. The initialization is simplified into specifying two endpoints for a segment of contour, so that the Snake model is less sensitive to the initial contour than the traditional model. The energy minimization procedure is replaced by searching a global optimal path in the weighted graph, so that the convergence of the algorithm is guaranteed. Experiments’ results show that the new Snake algorithm can extract contours effectively.Secondly, a 2D triangular meshing algorithm for arbitrary-shaped sectional domains is proposed. The triangular mesh generation algorithm creates the initial triangular mesh for a polygon correspongding to the planar contour by using the ear-removal methods. A triangular mesh refinement method named Delaunay Longest Edge Bisection(DLEB) is presented to refine the initial mesh. The DLEB refinement method integrates the technique of longest edge bisection and Delaunay swapping to insert new vertices into the triangular mesh. The triangular meshing algorithm can triangulate arbitrary planar domains without dealing with boundary recovery, and both the mesh density and the triangle shape quality can be controlled reasonably.Thirdly, contour-based 3D mesh generation algorithms are proposed, including the triangular surface meshing algorithm and the tetrahedral meshing algorithm for the inter-sectional surface and domain respectively. The triangular surface meshing algorithm is presented to reconstruct the side surface between two adjacent cross-sections. In order to resolve the issue of contour correspondence, a novel correspondence coefficient is designed to decided if two contours from different cross-sections belong to one topology or not. A constrained tiling criterion is also proposed to construct “optimal” triangles between the corresponding contours, aiming to guarantee the convergence of the tiling process. The medial-axis interpolation technique is applied to resolve the branching problem. As for the tetrahedral mesh generation between adjacent sections, a group operator based Advancing Front Technique(AFT) is presented. Starting from a triangular surface mesh that encloses the inter-section domain, the AFT algorithm decomposes the inside domain into tetrahedral elements progressively. Different from the traditional AFT algorithms, in the proposed AFT algorithm only the sectional triangles are included in the front, and group operators are presented to construct a group of tetrahedral elements at one time. Both the front triangle type and the element quality are considered for quality tetrahedral mesh generation. In order to deal with the untetrahedralizable polygons that appear when the tetrahedral meshing process reaches the last stage, Steiner nodes are inserted according to the geometry features of the remaining polygon.Fourthly, a grid-based meshing algorithm is proposed to generate triangular or tetrahedral meshes by using isosurface extraction and stuffing. Given a medical volum dataset constructed from 2D medical cross-sections, a uniform or adaptive background grid is constructed, and then the Dual Contouring, a boundary feature preserving technique, is applied to extract the isosurface as the triangular surface mesh. At the isosurface stuffing stage, pre-defined tetrahedralization templates are used to decompose the interior domain into tetrahedral elements. Adaptive three-dimensional meshes can be generated by constructing Octree-structured grid instead of uniform grid. The T-vertices occuring in the adaptive meshing are eliminated by an edge bisection method, ensuring the topology conformity without inserting additional vertices.Finally, a tetrahedral mesh post-processing framework based on the list-iteration strategy is presented. In order to improve the element shape quality as well as to reduce the number of the tetrahedra, the framework forms a list of the poor-shaped tetrahedral elements, and picks an element in this list to perform some operators, such as edge contract, smoothing, remeshing, and even refinement. The quality of the element’s 1-ring neighborhood is measured to determine which operator should be imposed on that element. When all the elements in the list are processed, an iteration is over, and the list is updated for the next iteration. Experiments show that the tetrahedral mesh post-processing framework could improve the generated tetrahedral mesh quality and reduce its elements number as well.