A Benchmark for Surface Reconstruction MATTHEW BERGER University of Utah and Air Force Research Laboratory JOSHUA A. LEVINE Scientific Computing and Imaging Institute, University of Utah LUIS GUSTAVO NONATO Universidade de S˜ ao Paulo GABRIEL TAUBIN Brown University and CLAUDIO T. SILVA Polytechnic Institute of New York University We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruc- tion, a comprehensive means of evaluating this class of algorithms is no- ticeably absent. We propose a simple pipeline for measuring surface re- construction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We employ implicit surfaces for modeling shapes which are expressive enough to contain details of varying size, in addi- tion to preserving sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realis- tic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced via a commercial optical laser scanner, wherein we scan a 3D-printed version of the original implicit surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly-distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for the comparison of surface reconstruction algorithms, they lack a fine-grain analysis. Hence to comple- ment this, the second set of experiments are designed to measure specific properties of surface reconstruction, both from a sampling and surface mod- eling viewpoint. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Compu- tational Geometry and Object Modeling—Curve, surface, solid, and object representations; G.1.2 [Mathematics of Computing]: Approximation— Approximation of surfaces and contours 1. INTRODUCTION Over the past two decades there has been an immense amount of effort dedicated to the problem of surface reconstruction. The prob- lem of surface reconstruction may be formulated as follows: given a sampling of points measured on a surface, recover the original surface from which those points came. This problem is motivated by a large number of applications. For instance, surface reconstruc- tion is a crucial first step in the recovery of non-rigid motion of time-varying geometry [Sharf et al. 2008; Li et al. 2009], and used as “ground-truth” data for multi-view stereo reconstruction evalua- tion [Seitz et al. 2006]. The generality of the problem has given rise to a wide variety of surface reconstruction algorithms. The distinctions in the various reconstruction algorithms hinge on the expected form of the input point data and output reconstructed surface. The input may be a single depth image, a registered point cloud, or a registered point cloud equipped with normals. Moreover, the modality of the point data plays a major role in reconstruction, where various modalities from the 3D vision literature include optical laser scanners, struc- tured lighting, structure from motion, and photometric stereo. The form of the output can be broken down into two main com- ponents: surface representation and the dependency on the input data. The surface representation may be a parametric surface, an implicit surface, or a triangulated surface mesh. The dependency on the input data can range from interpolating all of the input data, interpolating only a subset of the input, or simply approximating the input. The focus of this work is on the evaluation and comparison of surface reconstruction algorithms which take as input a registered point cloud equipped with normals and output a triangulated sur- face mesh which approximates the input data. More specifically, we focus on input data acquired via triangulation-based scanning, wherein normals are absent and must be computed from the points themselves. This class of input is extremely broad, and quite com- mon in point cloud data due to the rising ubiquity of triangulation- based scanners such as optical laser scanners. This class of output is very flexible for surface reconstruction, in that triangle meshes are capable of representing surfaces of arbitrary detail, while the approximation requirement allows for much freedom in reconstruc- tion from point clouds containing large imperfections. Despite the vast amount of work in this class of algorithms, to date there has been an insufficient means of evaluation. These al- gorithms typically operate on acquired scan data, where there does not exist a computational representation of the surface from which the scanned points were measured. Hence it is not possible to com- pare the reconstructed surface to the original surface, and it is quite common for such approaches to instead provide a visual compar- ison. Quantitative measures are typically done using synthetically generated data, but existing quantitative evaluation approaches con- tain a number of shortcomings, ranging from the representation of the reference shape, to how sampling is performed. ACM Transactions on Graphics, Vol. VV, No. N, Article XXX, Publication date: Month YYYY.