Topology-Controlled Reconstruction from Partial Cross-Sections

Abstract

The problem of 3-dimensional reconstruction from planar cross-sections arises in many fields, such as biomedical image analysis and geographical information systems. The problem has been studied extensively in the past 40 years. Each cross-section in the input contains multiple contours, where each contour divides the plane into different material types. The reconstructed object is a valid volume (surrounded by a closed surface) that interpolates the input slices. Some previous works utilize prior information about the reconstructed object, such as its topology, for recovering the original shape of the object. These works assume that the input cross-sections are complete and do not contain areas of missing information. In many real-life cases, this assumption does not hold. Other existing works handle such inputs; however, the methods they suggest do not have topological guarantees for the reconstructed object. In this work, we provide the first technique that provides topology control for 3-dimensional reconstruction from partial planar cross-sections. The input to our algorithm consists of an arbitrarily-oriented set of 2-dimensional cross-sections that may contain areas of missing information (''unknown'' regions) and user-specified topology constraints on the reconstructed object. During the reconstruction process, we explore a set of distinct topologies for relabeling the ''unknown'' regions. We define a scoring function for calculating the likelihood of each topology. We then examine a set of representative topologies and choose the reconstruction that simultaneously satisfies the global topology and optimizes the scoring function.