A benchmark for surface reconstruction

Abstract

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 reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original 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 comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

Implicit B-Spline Surface Reconstruction

“…IPs are defined linearly with respect to the coefficient vector, and this property makes them popular for linear fitting, as explained in the next section. Unfortunately, these monomials are not locally supported 1 and, as a consequence, any change in the 1 support of an implicit function is where it doesn't vanish. coefficients can lead to global changes in the whole shape of the zero set.…”

“…S URFACE reconstruction is one of the common fundamental problems in computer vision, graphics and CAD aiming at providing a smooth surface to describe the given point cloud [1]. Thanks to the recent development in 3D scanning technology, multi-view geometry and low cost depth sensors such as Kinect, we are provided with large data volume to be analyzed, which can be noisy or corrupted by outliers and missing data.…”

Moving particle semi-implicit method for fluid simulation with implicitly defined deforming obstacles

“…As a result, the approximate boundary point can be obtained by substituting (14) and (15) to (13). We use the approximate distance (14) for the computation of (6), (7), (10) and (12) and the approximate boundary point (13) for the computation of (11).…”

“…We use the approximate distance (14) for the computation of (6), (7), (10) and (12) and the approximate boundary point (13) for the computation of (11).…”

“…There are different approaches to shape modeling with implicit form such as surface modeling interpolating surface points [11,12,13,14], shape modeling with user manipulation [15,16,17,18] and conversion from polygonal shape models [19,20]. In the first approach, surfaces are typically generated from a set of given oriented boundary points and current techniques allow automatic generation of accurate and detailed implicit surfaces from millions of input points.…”