Study On The Theory And Methodology Of Reverse CAD Modeling From Medical Cross Sections

To fulfill the need of the application of RP technique in medical domain, reverse CAD modeling from medical cross sections is systematically studied in this dissertation. Firstly, Some algorithms related to the research of this dissertation are studied. New algorithms for orientation and inclusion test for simple polygon, an error constrained automatic faring algorithm for B-spline curve and a theorem regarding the termination criterion for subdivision of triangular Bezier patch are proposed. Then based on similarity between contours of adjacent sections, a methodology for surface reconstruction from cross sections is presented. Finally, a virtual measuring method is proposed. Based on theoretical study, a prototype reverse CAD system is developed. Six chapters are included in this dissertation.In Chapter 1, the study background of reverse CAD modeling from medical cross sections is analyzed firstly. Then, the progress of medical computerized tomography techniques and scientific visualization of medical cross sections is summarized. On this base, the problem of reverse CAD modeling from medical cross sections is presented. Finally, the significance of this research is pointed out and the main contents of this dissertation are summarized.Some algorithms related to the research of this dissertation are presented in Chapter 2. Cross section is a set of polygons and for this reason some relative algorithms for polygon are studied firstly. New algorithms for orientation and inclusion test for simple polygon are proposed. And Ghosh's convex hull algorithms for simple polygon and convex polygons, Subramanian's triangulation algorithm for arbitrary planar domain and O'Rourke's intersection algorithm for convex polygons are modified to make them more robust. Normally measured data are flawed by noise and should be processed before surface reconstruction. Fairing method is studied and an error constrained automatic faring algorithm for B-spline curve is presented. As the purpose of this research is the application of RP technique in medical domain, a theorem regarding the termination criterion for subdivision of triangular Bezier patch is presented. All algorithms except the termination criterion for subdivision of triangular Bezier patch are applied in the prototype reverse CAD system. Applications show that the algorithms are stable, reliable and simple.Surface reconstruction from complicated cross sections is a main topic in the research of visualization. Reverse CAD modeling from complicated cross sections is systematically studied in Chapter 3 on the base of analyzing and summarizing the relative research in visualization domain. Firstly a qualitative criterion for determining the space betweenadjacent sections in the sampling process and Gaussian smoothing algorithm is proposed. Then a topological reconstruction method is given. At last a new reconstruction method based on the similarity between adjacent sections is proposed. By matching overall corresponding points, Divide and Conquer method is adopted in determination of local corresponding points between adjacent sections. The determination of overall corresponding points also provided a method of modifying the correspondence between adjacent sections. On the base of determination of corresponding points between adjacent sections, dissimilar segments are separated to construct spatial dissimilar polygons. Then triangular mesh interpolating the cross sections are obtained by tiling the dissimilar polygons and similar segments. The problems of multiple contours to multiple contours and connected bifurcation are considered in this algorithm. The vertices of the mesh are interpolated with triangular Bezier patch.Quality of composite triangular Bezier patch reconstructed from cross sections is usually not good enough to apply in engineering. A virtual measuring method is proposed in Chapter 4 to solve this problem. Firstly surface region with bad quality is extracted and vertices of the surface region are approximated with B-spline surface. Then the...