Abstract Inspired by recent developments in contraction‐based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area‐minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call “mean curvature skeletons”. To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non‐manifold edge collapses. With topology simplified throughout the flow, minimal post‐processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso‐skeletons ; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture.

Abstract Objects with many concavities are difficult to acquire using laser scanners. The highly concave areas are hard to access by a scanner due to occlusions by other components of the object. The resulting point scan typically suffers from large amounts of missing data. Methods that use surface‐based priors rely on local surface estimates and perform well only when filling small holes. When the holes become large, the reconstruction problem becomes severely under‐constrained, which necessitates the use of additional reconstruction priors. In this paper, we introduce weak volumetric priors which assume that the volume of a shape varies smoothly and that each point cloud sample is visible from outside the shape. Specifically, the union of view‐rays given by the scanner implicitly carves the exterior volume, while volumetric smoothness regularizes the internal volume. We incorporate these priors into a surface evolution framework where a new energy term defined by volumetric smoothness is introduced to handle large amount of missing data. We demonstrate the effectiveness of our method on objects exhibiting deep concavities, and show its general applicability over a broader spectrum of geometric scenario.

We present an algorithm for curve skeleton extraction via Laplacian-based contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeleton-based manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeleton-driven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easy-to-manipulate structure for effective topology modification, leading to more faithful surface reconstruction.

Trees, bushes, and other plants are ubiquitous in urban environments, and realistic models of trees can add a great deal of realism to a digital urban scene. There has been much research on modeling tree structures, but limited work on reconstructing the geometry of real-world trees -- even then, most works have focused on reconstruction from photographs aided by significant user interaction. In this paper, we perform active laser scanning of real-world vegetation and present an automatic approach that robustly reconstructs skeletal structures of trees, from which full geometry can be generated. The core of our method is a series of global optimizations that fit skeletal structures to the often sparse, incomplete, and noisy point data. A significant benefit of our approach is its ability to reconstruct multiple overlapping trees simultaneously without segmentation. We demonstrate the effectiveness and robustness of our approach on many raw scans of different tree varieties.

Aabstract We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a ‘tangential distance field’ (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi‐origin silhouette extraction in Hough space, silhouette‐based view point selection, camera path planning and light source placement.

Abstract Object‐space silhouette extraction is an important problem in fields ranging from non‐photorealistic computer graphics to medical robotics. We present an efficient silhouette extractor for triangle meshes under perspective projection and make three contributions. First, we describe a novel application of 3D Hough transforms, which allows us to organize mesh data more effectively for silhouette computations than the traditional dual transform. Next, we introduce an incremental silhouette update algorithm which operates on an octree augmented with neighbour information and optimized for efficient low‐level traversal. Finally, we present a method for initial extraction of silhouette, using the same data structure, whose performance is linear in the size of the extracted silhouette. We demonstrate significant performance improvements given by our approach over the current state of the art. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Three‐Dimensional Graphics and Realism]: Visible line/surface algorithms