Guided Multi-Dimensional Reconstruction from Cross-Sections

Given parallel (n?1)-dimensional cross-sections of an n-dimensional body, one would like to reconstruct the body. The method based upon distance eld interpolation gives a robust solution to this problem in its ability to deal with any topology in any dimension. Still this method may give undesired solutions to the problem if the changes from one cross-section to the next are big relative to the size of the details in the cross-sections. In the present work we suggest a way to improve the distance eld interpolation method. For this we rst assume that the data to the problem are the cross-sections and some speciied points on them, prescribing geometric links between the diierent cross-sections. These links may be manually user-deened, or automatically deened by matching features in the cross-sections. The distance eld interpolation method is modiied so that the interpolation is guided by those links. We describe some rules for deening a smooth least-distorting mapping which realizes the desired links, and present the corresponding guided interpolation. x1. Introduction The problem of reconstructing an n-dimensional body from its cross-sections appears in many applications, from biomedical imaging to 2D and 3D animation. In 3D animation the problem can also be viewed as a surface blending problem. Namely, the continuous evolution of a surface from a source surface, through intermediate surfaces, into a target surface. This is an object-space problem of generating intermediate 3D models 5], to be distinguished from image-space transformations 10]. This paper describes a method that allows the user to create a series of models which form a smooth transition of a given set of general keyframe models. The method deals explicitly with surfaces and its principles are naturally extended from 2D space (contours) to 3D (surfaces) and to hyper-surfaces in higher dimensions.