EUROGRAPHICS 2008 / G. Drettakis and R. Scopigno (Guest Editors) Volume 27 (2008), Number 2 Surface Reconstruction From Non-parallel Curve Networks L. Liu 1 , C. Bajaj 2 , J. O. Deasy 1 , D. A. Low 1 and T. Ju 1 1 Washington University in St. Louis, USA 2 University of Texas at Austin, USA Abstract Building surfaces from cross-section curves has wide applications including bio-medical modeling. Previous work in this area has mostly focused on connecting simple closed curves on parallel cross-sections. Here we consider the more general problem where input data may lie on non-parallel cross-sections and consist of curve networks that represent the segmentation of the underlying object by different material or tissue types (e.g., skin, muscle, bone, etc.) on each cross-section. The desired output is a surface network that models both the exterior surface and the internal partitioning of the object. We introduce an algorithm that is capable of handling curve networks of arbitrary shape and topology on cross-section planes with arbitrary orientations. Our algorithm is simple to implement and is guaranteed to produce a closed surface network that interpolates the curve network on each cross-section. Our method is demonstrated on both synthetic and bio-medical examples. 1. Introduction Reconstructing a complete surface from incomplete data is a topic of wide interest in geometry processing. A common case of this is planar curves that represent cross-sections of a complete surface. In bio-medical modeling, for instance, contours of an anatomical structure are drawn by physicians on 2D images (such as in freehand ultrasound) or on slices of a 3D volume (such as MRI and CT scans), and a sur- face connecting these contours is sought which represents the structure in 3D. An example is shown in Figure 1 (a) for a human Parotid gland obtained from a CT volume. Surface reconstruction from cross-section curves has been extensively studied for the past three decades. Previous work mostly considers connecting curves on parallel cross- sections (e.g., Figure 1 (a)), where many solutions exist (see a brief review in Section 2). Here we are interested in the more difficult problem of surface reconstruction from non- parallel cross-sections (e.g., Figure 1 (b)). The need for han- dling curves on non-parallel planes arises in multiple appli- cations. In freehand 2D ultrasound, for example, both the location and orientation of each individual image plane can be freely changed through an input device that has 6 degrees of freedom. Additionally, when selecting planar slices of a 3D MRI or CT scan to specify contours, a physician often wishes to customize the orientation of each slice to better align to the imaged object. For example, the contours in Fig- Figure 1: Types of cross-section curves we consider in this paper: simple closed curves on parallel (a) and non-parallel (b) planes, and curve networks (c,d). ure 1 (b) delineate the same subject as in (a) but are drawn on a set of non-parallel slices chosen by a physician to more accurately capture anatomically meaningful features. c  2007 The Author(s) Journal compilation c 2007 The Eurographics Association and Blackwell Publishing Ltd. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.