This paper builds upon the current methods to increase their capability and automation for 3D surface construction from noisy and potentially sparse point clouds. It presents an analysis of an artificial neural network surface regression and mapping method, describing caveats, improvements and justification for the different approach.
Yumer and Kara suggest a NN regression method of surface fitting and hole stitching. The flexibility achieved by an adaptive neural network topology differs from previous attempts as the ideal topology of the network obtained (the hyperaparmeters) are not fixed @cite_11 , meaning the network can be tailored to each point cloud automatically. This method is good for removing noise as the underlying geometry of the point data and not random noise is represented in the final surface.
@cite_11
2137983211
In this paper, the problem of non-rigid shape recognition is studied from the perspective of metric geometry. In particular, we explore the applicability of diffusion distances within the Gromov-Hausdorff framework. While the traditionally used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting the points. The diffusion distance constitutes an intrinsic metric which is robust, in particular, to topological changes. Such changes in the form of shortcuts, holes, and missing data may be a result of natural non-rigid deformations as well as acquisition and representation noise due to inaccurate surface construction. The presentation of the proposed framework is complemented with examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes. We present cone carving, a novel space carving technique supporting topologically correct surface reconstruction from an incomplete scanned point cloud. The technique utilizes the point samples not only for local surface position estimation but also to obtain global visibility information under the assumption that each acquired point is visible from a point lying outside the shape. This enables associating each point with a generalized cone, called the visibility cone, that carves a portion of the outside ambient space of the shape from the inside out. These cones collectively provide a means to better approximate the signed distances to the shape specifically near regions containing large holes in the scan, allowing one to infer the correct surface topology. Combining the new distance measure with conventional RBF, we define an implicit function whose zero level set defines the surface of the shape. We demonstrate the utility of cone carving in coping with significant missing data and raw scans from a commercial 3D scanner as well as synthetic input. We propose a method for reconstructing 3D shapes from 2D sketches in the form of line drawings. Our method takes as input a single sketch, or multiple sketches, and outputs a dense point cloud representing a 3D reconstruction of the input sketch(es). The point cloud is then converted into a polygon mesh. At the heart of our method lies a deep, encoder-decoder network. The encoder converts the sketch into a compact representation encoding shape information. The decoder converts this representation into depth and normal maps capturing the underlying surface from several output viewpoints. The multi-view maps are then consolidated into a 3D point cloud by solving an optimization problem that fuses depth and normals across all viewpoints. Based on our experiments, compared to other methods, such as volumetric networks, our architecture offers several advantages, including more faithful reconstruction, higher output surface resolution, better preservation of topology and shape structure. In this paper, we develop a set of data processing algorithms for generating textured facade meshes of cities from a series of vertical 2D surface scans and camera images, obtained by a laser scanner and digital camera while driving on public roads under normal traffic conditions. These processing steps are needed to cope with imperfections and non-idealities inherent in laser scanning systems such as occlusions and reflections from glass surfaces. The data is divided into easy-to-handle quasi-linear segments corresponding to approximately straight driving direction and sequential topological order of vertical laser scans; each segment is then transformed into a depth image. Dominant building structures are detected in the depth images, and points are classified into foreground and background layers. Large holes in the background layer, caused by occlusion from foreground layer objects, are filled in by planar or horizontal interpolation. The depth image is further processed by removing isolated points and filling remaining small holes. The foreground objects also leave holes in the texture of building facades, which are filled by horizontal and vertical interpolation in low frequency regions, or by a copy-paste method otherwise. We apply the above steps to a large set of data of downtown Berkeley with several million 3D points, in order to obtain texture-mapped 3D models. We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero level-set of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laser-scanned data, image-based 3D reconstruction, and mesh repair. We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBF — previously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energy-minimisation characterisation of polyharmonic splines result in a “smoothest” interpolant. This scale-independent characterisation is well-suited to reconstructing surfaces from non-uniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a non-interpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for real-world rangefinder data. Abstract The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss–Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results. With significant data missing in a point scan, reconstructing a complete surface with sufficient geometric and topological fidelity is highly challenging. We present an interactive technique for surface reconstruction from incomplete and sparse scans of 3D objects possessing sharp features. A fundamental premise of our interaction paradigm is that directly editing data in 3D is not only counterintuitive but also ineffective, while working with 1D entities (i.e., curves) is a lot more manageable. To this end, we factor 3D editing into two "orthogonal" interactions acting on skelet al and profile curves of the underlying shape, controlling its topology and geometric features, respectively. For surface completion, we introduce a novel skeleton-driven morph-to-fit, or morfit, scheme which reconstructs the shape as an ensemble of generalized cylinders. Morfit is a hybrid operator which optimally interpolates between adjacent curve profiles (the "morph") and snaps the surface to input points (the "fit"). The interactive reconstruction iterates between user edits and morfit to converge to a desired final surface. We demonstrate various interactive reconstructions from point scans with sharp features and significant missing data. We present a new technique for extracting line-type features on point-sampled geometry. Given an unstructured point cloud as input, our method first applies principal component analysis on local neighborhoods to classify points according to the likelihood that they belong to a feature. Using hysteresis thresholding, we then compute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the features while maintaining a close connection to the underlying surface, we use an adaptation of active contour models. Central to our method is a multi-scale classification operator that allows feature analysis at multiple scales, using the size of the local neighborhoods as a discrete scale parameter. This significantly improves the reliability of the detection phase and makes our method more robust in the presence of noise. To illustrate the usefulness of our method, we have implemented a non-photorealistic point renderer to visualize point-sampled surfaces as line drawings of their extracted feature curves. In this paper we present an automatic algorithm to detect basic shapes in unorganized point clouds. The algorithm decomposes the point cloud into a concise, hybrid structure of inherent shapes and a set of remaining points. Each detected shape serves as a proxy for a set of corresponding points. Our method is based on random sampling and detects planes, spheres, cylinders, cones and tori. For models with surfaces composed of these basic shapes only, for example, CAD models, we automatically obtain a representation solely consisting of shape proxies. We demonstrate that the algorithm is robust even in the presence of many outliers and a high degree of noise. The proposed method scales well with respect to the size of the input point cloud and the number and size of the shapes within the data. Even point sets with several millions of samples are robustly decomposed within less than a minute. Moreover, the algorithm is conceptually simple and easy to implement. Application areas include measurement of physical parameters, scan registration, surface compression, hybrid rendering, shape classification, meshing, simplification, approximation and reverse engineering. We present a novel shape completion technique for creating temporally coherent watertight surfaces from real-time captured dynamic performances. Because of occlusions and low surface albedo, scanned mesh sequences typically exhibit large holes that persist over extended periods of time. Most conventional dynamic shape reconstruction techniques rely on template models or assume slow deformations in the input data. Our framework sidesteps these requirements and directly initializes shape completion with topology derived from the visual hull. To seal the holes with patches that are consistent with the subject's motion, we first minimize surface bending energies in each frame to ensure smooth transitions across hole boundaries. Temporally coherent dynamics of surface patches are obtained by unwarping all frames within a time window using accurate interframe correspondences. Aggregated surface samples are then filtered with a temporal visibility kernel that maximizes the use of nonoccluded surfaces. A key benefit of our shape completion strategy is that it does not rely on long-range correspondences or a template model. Consequently, our method does not suffer error accumulation typically introduced by noise, large deformations, and drastic topological changes. We illustrate the effectiveness of our method on several high-resolution scans of human performances captured with a state-of-the-art multiview 3D acquisition system. We propose a novel framework for reconstructing lightweight polygonal surfaces from point clouds. Unlike traditional methods that focus on either extracting good geometric primitives or obtaining proper arrangements of primitives, the emphasis of this work lies in intersecting the primitives (planes only) and seeking for an appropriate combination of them to obtain a manifold polygonal surface model without boundary.,,We show that reconstruction from point clouds can be cast as a binary labeling problem. Our method is based on a hypothesizing and selection strategy. We first generate a reasonably large set of face candidates by intersecting the extracted planar primitives. Then an optimal subset of the candidate faces is selected through optimization. Our optimization is based on a binary linear programming formulation under hard constraints that enforce the final polygonal surface model to be manifold and watertight. Experiments on point clouds from various sources demonstrate that our method can generate lightweight polygonal surface models of arbitrary piecewise planar objects. Besides, our method is capable of recovering sharp features and is robust to noise, outliers, and missing data. We introduce an algorithm for constructing a high-quality triangulation directly from Point Set Surfaces. Our algorithm requires no intermediate representation and no post-processing of the output, and naturally handles noisy input data, typically in the form of a set of registered range scans. It creates a triangulation where triangle size respects the geometry of the surface rather than the sampling density of the range scans. Our technique does not require normal information, but still produces a consistent orientation of the triangles, assuming the sampled surface is an orientable two-manifold. Our work is based on using Moving Least-Squares (MLS) surfaces as the underlying representation. Our technique is a novel advancing front algorithm, that bounds the Hausdorff distance to within a user-specified limit. Specifically, we introduce a way of augmenting advancing front algorithms with global information, so that triangle size adapts gracefully even when there are large changes in surface curvature. Our results show that our technique generates high-quality triangulations where other techniques fail to reconstruct the correct surface due to irregular sampling on the point cloud, noise, registration artifacts, and underlying geometric features, such as regions with high curvature gradients. We present a novel explicit surface tracking method. Its main advantage over existing approaches is the fact that it is both completely grid-free and fast which makes it ideal for the use in large unbounded domains. A further advantage is that its running time is less sensitive to temporal variations of the input mesh than existing approaches. In terms of performance, the method provides a good trade-off point between speed and quality. The main idea behind our approach to handle topological changes is to delete all overlapping triangles and to fill or join the resulting holes in a robust and efficient way while guaranteeing that the output mesh is both manifold and without boundary. We demonstrate the flexibility, speed and quality of our method in various applications such as Eulerian and Lagrangian liquid simulations and the simulation of solids under large plastic deformations. This paper tackles the problem of computing topological invariants of geometric objects in a robust manner, using only point cloud data sampled from the object. It is now widely recognised that this kind of topological analysis can give qualitative information about data sets which is not readily available by other means. In particular, it can be an aid to visualisation of high dimensional data. Standard simplicial complexes for approximating the topological type of the underlying space (such as Cech, Rips, or a-shape) produce simplicial complexes whose vertex set has the same size as the underlying set of point cloud data. Such constructions are sometimes still tractable, but are wasteful (of computing resources) since the homotopy types of the underlying objects are generally realisable on much smaller vertex sets. We obtain smaller complexes by choosing a set of 'landmark' points from our data set, and then constructing a "witness complex" on this set using ideas motivated by the usual Delaunay complex in Euclidean space. The key idea is that the remaining (non-landmark) data points are used as witnesses to the existence of edges or simplices spanned by combinations of landmark points. Our construction generalises the topology-preserving graphs of Martinetz and Schulten [MS94] in two directions. First, it produces a simplicial complex rather than a graph. Secondly it actually produces a nested family of simplicial complexes, which represent the data at different feature scales, suitable for calculating persistent homology [ELZ00, ZC04]. We find that in addition to the complexes being smaller, they also provide (in a precise sense) a better picture of the homology, with less noise, than the full scale constructions using all the data points. We illustrate the use of these complexes in qualitatively analyzing a data set of 3 × 3 pixel patches studied by David [LPM03]. This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces. We present an efficient algorithm to obtain a triangulated graph surface for scattered points (xiyi)T, i=1,…,n, with associated function values fi. The maximal distance between the triangulated graph surface and the function values is measured in z-direction (z=f(x,y)) and lies within a user-defined tolerance. The number of triangles is minimized locally by adapting their shapes to different second-degree least squares approximations of the underlying data. The method consists of three major steps: 1. subdividing the given discrete data set into clusters such that each cluster can be approximated by a quadratic polynomial within a prescribed tolerance; 2. optimally triangulating the graph surface of each quadratic polynomial; and 3. “stitching” the triangulations of all graph surfaces together. We also discuss modifications of the algorithm that are necessary to deal with discrete data points, without connectivity information, originating from a general two-manifold surface, i.e., a surface in three-dimensional space that is not necessarily a graph surface. We introduce a robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud. We use techniques from robust statistics to guide the creation of the neighborhoods used by the moving least squares (MLS) computation. This leads to a conceptually simple approach that provides a unified framework for not only dealing with noise, but also for enabling the modeling of surfaces with sharp features.Our technique is based on a new robust statistics method for outlier detection: the forward-search paradigm. Using this powerful technique, we locally classify regions of a point-set to multiple outlier-free smooth regions. This classification allows us to project points on a locally smooth region rather than a surface that is smooth everywhere, thus defining a piecewise smooth surface and increasing the numerical stability of the projection operator. Furthermore, by treating the points across the discontinuities as outliers, we are able to define sharp features. One of the nice features of our approach is that it automatically disregards outliers during the surface-fitting phase. In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent real-time range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondences, holes due to occlusion are filled in from other frames. Our reconstruction technique is based on a statistical framework: The reconstruction should both match the measured data points and maximize prior probability densities that prefer smoothness, rigid deformation and smooth movements over time. The optimization procedure consists of an inner loop that optimizes the 4D shape using continuous numerical optimization and an outer loop that infers the discrete 4D topology of the data set using an iterative model assembly algorithm. We apply the technique to a variety of data sets, demonstrating that the new approach is capable of robustly retrieving animated models with correspondences from data sets suffering from significant noise, outliers and acquisition holes. Symmetry detection aims at discovering redundancy in the form of reoccurring structures in geometric objects. In this paper, we present a new symmetry detection algorithm for geometry represented as point clouds that is based on analyzing a graph of surface features. We combine a general feature detection scheme with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect reoccurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing variant of the ICP algorithm is applied to verify that the actual point cloud data supports the pattern detected in the feature graphs. We apply our algorithm to synthetic and real-world 3D scanner data sets, demonstrating robust symmetry detection results in the presence of scanning artifacts and noise. The modular and flexible nature of the graph-based detection scheme allows for easy generalizations of the algorithm, which we demonstrate by applying the same technique to other data modalities such as images or triangle meshes.