Arbitrary Topology Shape Reconstruction from Planar Cross Sections

ments are usually obtained one slice at a time, where each slice is a 2D array of scalar values corresponding to meaIn computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the surements distributed over a plane passing through the 2D scalar-valued slices obtained by the imaging system is diffiobject. The set of planes generating the slices are usually cult because of the large spacings between the 2D slices. The parallel to each other and equispaced along some axis aliasing that results from this undersampling in the direction through the object. orthogonal to the slices leads to two problems, known as the Once these measurement slices have been obtained, the correspondence problem and the tiling problem. A third probgoal is to enable a human to easily visualize, in 3D, this lem, known as the branching problem, arises because of the large collection of data. Many algorithms have been develstructure of the objects being imaged in these applications. oped for this purpose, but they can all be classified into Existing reconstruction algorithms typically address only one two categories [8]: volume rendering methods and surface or two of these problems. In this paper, we approach all three reconstruction methods. of these problems simultaneously. This is accomplished by imposing a set of three constraints on the reconstructed surface This paper concentrates on surface reconstruction methand then deriving precise correspondence and tiling rules from ods, all of which proceed by extracting the isosurfaces these constraints. The constraints ensure that the regions tiled corresponding to a specified image intensity. Each isosurby these rules obey physical constructs and have a natural face is represented as an assembly of simple surface primiappearance. Regions which cannot be tiled by these rules withtives, such as triangles or other polygons. Once these surout breaking one or more constraints are tiled with their medial face primitives are calculated, they can be quickly rendered axis (edge Voronoi diagram). Our implementation of the above from different viewpoints using widely available graphics approach generates triangles of 3D isosurfaces from input hardware. This allows the user to quickly examine many which is either a set of contour data or a volume of image different viewing spaces. slices. Results obtained with synthetic and actual medical data This paper presents a surface-based algorithm which are presented. There are still specific cases in which our new achieves both faster rendering and lower likelihood of reapproach can generate distorted results, but these cases are much less likely to occur than those which cause distortions construction error than previous surface reconstruction alin other tiling approaches.  1996 Academic Press, Inc. gorithms. These improvements are obtained by taking a unified approach to the three problems inherent in all surface-based approaches [20]: the correspondence prob