Smooth surface reconstruction from noisy range data (original) (raw)
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Solid Model Reconstruction of Large-Scale Outdoor Scenes from 3D Lidar Data
Springer Tracts in Advanced Robotics, 2013
Globally consistent 3D maps are commonly used for robot mission planning, navigation, and teleoperation in unstructured and uncontrolled environments. These maps are typically represented as 3D point clouds; however other representations, such as surface or solid models, are often required for humans to perform scientific analyses, infrastructure planning, or for general visualization purposes. Robust large-scale solid model reconstruction from point clouds of outdoor scenes can be challenging due to the presence of dynamic objects, the ambiguitiy between non-returns and sky-points, and scalability requirements. Volume-based methods are able to remove spurious points arising from moving objects in the scene by considering the entire ray of each measurement, rather than simply the end point. Scalability can be addressed by decomposing the overall space into multiple tiles, from which the resulting surfaces can later be merged. We propose an approach that applies a weighted signed distance function along each measurement ray, where the weight indicates the confidence of the calculated distance. Due to the unenclosed nature of outdoor environments, we introduce a technique to automatically generate a thickened structure in order to model surfaces seen from only one side. The final solid models are thus suitable to be physically printed by a rapid prototyping machine. The approach is evaluated on 3D laser point cloud data collected from a mobile lidar in unstructured and uncontrolled environments, including outdoors and inside caves. The accuracy of the solid model reconstruction is compared to a previously developed binary voxel carving method. The results show that the weighted signed distance approach produces a more accurate reconstruction of the surface, and since higher accuracy models can be produced at lower resolutions, this additionally results in significant improvements in processing time.
3D scattered data approximation with adaptive compactly supported radial basis functions
Proceedings Shape Modeling Applications, 2004.
In this paper, we develop an adaptive RBF fitting procedure for a high quality approximation of a set of points scattered over a piecewise smooth surface. We use compactly supported RBFs whose centers are randomly chosen from the points. The randomness is controlled by the point density and surface geometry. For each RBF, its support size is chosen adaptively according to surface geometry at a vicinity of the RBF center. All these lead to a noise-robust high quality approximation of the set. We also adapt our basic technique for shape reconstruction from registered range scans by taking into account measurement confidences. Finally, an interesting link between our RBF fitting procedure and partition of unity approximations is established and discussed.
Fast surface reconstruction and hole filling using positive definite radial basis functions
2005
Surface reconstruction from large unorganized data sets is very challenging, especially if the data present undesired holes. This is usually the case when the data come from laser scanner 3D acquisitions or if they represent damaged objects to be restored. An attractive field of research focuses on situations in which these holes are too geometrically and topologically complex to fill using triangulation algorithms. In this work a local approach to surface reconstruction from point-clouds based on positive definite Radial Basis Functions (RBF) is presented that progressively fills the holes by expanding the neighbouring information. The method is based on the algorithm introduced in [7] which has been successfully tested for the smooth multivariate interpolation of large scattered data sets. The local nature of the algorithm allows for real time handling of large amounts of data, since the computation is limited to suitable small areas, thus avoiding the critical efficiency problem involved in RBF multivariate interpolation. Several tests on simulated and real data sets demonstrate the efficiency and the quality of the reconstructions obtained using the proposed algorithm.
Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Computer Aided Geometric Design, 2012
Radial Basis Function (RBF) has been used in surface reconstruction methods to interpolate or approximate scattered data points, which involves solving a large linear system. The linear systems for determining coefficients of RBF may be ill-conditioned when processing a large point set, which leads to unstable numerical results. We introduce a quasiinterpolation framework based on compactly supported RBF to solve this problem. In this framework, implicit surfaces can be reconstructed without solving a large linear system. With the help of an adaptive space partitioning technique, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is localized, it can be easily parallelized on multi-core CPUs.
Reconstruction of Smoothed Polyhedral Surfaces from Multiple Range Images
In order to digitize the whole surface of a threedimensional object by means of an optical range sensor, usually multiple range images are acquired from different viewpoints. We demonstrate how the range images can be accurately merged into a single triangular mesh with curvature dependent density by the use of local topological mesh operations. A new filter, that is specially adapted to the requirements of geometrical data, has been designed. This enables smoothing of measuring errors like noise, aliasing, outliers, and registration errors with minimum interference of real object features like edges. Curvature variations are minimized and surface undulations are avoided in order to produce high quality surfaces for rendering and NC milling. 1
Proceedings Shape Modeling Applications, 2004.
Implicit surfaces can be constructed from scattered surface points using radial basis functions (RBFs) to interpolate the surface's embedding function. Many researchers have used thin-plate spline RBFs for this because of their desirable smoothness properties. Others have used compactly supported RBFs, leading to a sparse matrix solution with lower computational complexity and better conditioning. However, the limited radius of support introduces a free parameter that leads to varying solutions as well as varying computational requirements: a larger radius of support leads to smoother and more accurate solutions but requires more computation. This paper presents an empirical analysis of this radius of support. The results using compactly supported RBFs are compared for varying model sizes and radii of support, exploring the relationship between data density and the accuracy of the interpolated surface.
Decomposing sensory measurements into relevant parts is a fundamental prerequisite for solving complex tasks, e.g., in the field of mobile manipulation in domestic environments. In this paper, we present a fast approach to surface reconstruction in range images by means of approximate polygonal meshing. The obtained local surface information and neighborhoods are then used to 1) smooth the underlying measurements, and 2) segment the image into planar regions and other geometric primitives. An evaluation using publicly available data sets shows that our approach does not rank behind state-of-the-art algorithms while allowing to process range images at high frame rates.
A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions
2003 Shape Modeling International.
In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarse-to-fine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point cloud distributed along a surface, we first use spatial down sampling to construct a coarse-to-fine hierarchy of point sets. Then we interpolate the sets starting from the coarsest level. We interpolate a point set of the hierarchy, as an offsetting of the interpolating function computed at the previous level. Fig. 1 shows an original point set (the leftmost image) and its coarse-to-fine hierarchy of interpolated sets. According to our numerical experiments, the method is essentially faster than the state-of-art scattered data approximation with globally supported RBFs [9] and much simpler to implement.
Compact Representation of Range Imaging Surfaces
2006
Range images of complex geometry presented by large point data sets almost always yield surface reconstruction imperfections. We propose a novel compact and complete mesh representation for non-uniformly sampled noisy range image data using an adaptive Radial Basis Function network. The network is established using a heuristic learning strategy. Neurons can be inserted, removed or updated iteratively, adapting to the complexity and distribution of the underlying data. This flexibility is particularly suited to highly variable spatial frequencies, and is conducive to data compression with network representations. Experiments confirm the performance advantages of the network when applied to 3D point-cloud surface reconstruction.
Multi-Scale 3-D Free-Form Surface Smoothing
1998
A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed (through fusion of range images) and are then described at multiple scales. This is achieved by convolving local parametrizations of the surface with 2-D Gaussian filters iteratively. Our method for local parametrization makes use of semigeodesic or goedesic polar coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates surface noise and small surface detail gradually. Our technique for 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion.