University of Macau Abstract THE GENERATION AND SIMPLIFICATION OFISOSURFACE IN VISC by Bao Yu Wu Thesis Supervisor:Professor of Computer Science, En-Hua Wu Faculty of Science and Technology Master of Science in Software Engineering The study of this thesis is conducted under the research project “The generation and simplification of Isosurface in ViSC”, It aims to analyze and visualize complex scientific data, called the Visualization in Scientific Computing, briefly as ViSC. The development of this subject may be retraced to the first ViSC Report in 1987, when the computer graphics development was principally driven by scientific and technical applications. Nowadays, Scientific Visualization (SV)has become a hot research topic and is playing a very important role in computer science, especially in the area of Medical Imaging. This thesis will first present the key issues and the fundamentals in SV. Visualization techniques are in general divided into two categories, surface rendering techniques, and (direct) volume rendering techniques. In the generation of isosurfaces, Marching cube algorithm is one of the most important techniques. It creates triangle models of constant density surfaces from 3D data, in particular the medical data. Here, we take the CT data as samples to test the algorithm. However, this algorithm is by far the most popularly implemented algorithm for iso-intensity surface extraction, efficiently generating isosurfaces with low memory requirements. The number of surfaces, constructed from multiple 2D slices of computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) are very large, and these models usually are tessellated into huge amount of polygonal approximated-meshes after the processing like the isosurface generation by the Marching cube algorithm, therefore, it is difficult to handle them directly. The next goal is to simplify these models, to display a 3D polygonal mesh with fewer triangles while retaining the same shape. In this thesis, the edge collapse and vertex split these two methods are used to implement the polygonal simplification. The edge collapse operator collapses an edge to a single vertex. This causes the removal of the edge as well as the triangles spanning the edge. The inverse operator of an edge collapse is a vertex split, which adds edges and triangles in an inverse way. Thus, the edge collapse operator simplifies a mesh and the vertex split operator adds detail to the mesh. Since the CT data represents the real human/animal body organization slice by slice, in a discrete format, produced by the measurement of physical instruments, therefore the noise inevitably exists in the data, As a result, quite often it is not effective to generate nice isosurfaces, and in particular if the selection of the isosurface function value is not in a proper range, large holes would be produced. Thus, we need to preprocess the polygonal mesh before simplification. Scheme is proposed in our work to restore the original bad mesh to become a good one. Two methods are proposed to restore the original mesh; one is to delete the bad polygons directly. However, if there are too much bad polygons in the original mesh, a full deletion will cause shape distortion. Another method is to restore the mesh and try to well maintain its shape. In the latter one, firstly, the bad polygons are necessary to be separated from the original mesh and the connectivity relationship is important to be found among its neighboring triangles, and then the bad polygons could be transferred into good ones on the basis of connectivity relationship. At last, the coloring method is adopted to extract the biggest and completed parts to present the original mesh. With the completion of the restoration and simplification to the polygonal mesh, the new polygonal mesh simplified and compact is easier and more efficient to make any further operations. In this thesis, the principle and the general methods on ViSC will be introduced. Then the emphasis will be focused on the isosurface generation by using Marching cube algorithm. The simplification and restoration to the isosurface meshes will be introduced in detail, and test examples are presented to show the validity of the work. Key word: Visualization in ScientificComputing(ViSC), Scientific Visualization(SV), Isosurface, Marching cube(MC), PLY, Level of Detail(LOD),Mesh Simplification, Edge Collapse, Vertex Split, Mesh Optimization.