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206
Pointbased multiscale surface representation
 ACM TRANS. GRAPH
, 2001
"... In this paper we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of pointbased surface approximations at successively higher levels of smoothness, i.e., coarser scales of detail, using geometric ..."
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Cited by 40 (0 self)
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In this paper we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of pointbased surface approximations at successively higher levels of smoothness, i.e., coarser scales of detail, using geometric lowpass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Lowpass filtering and encoding are combined in an efficient multilevel projection operator using local weighted least squares fitting. Our representation is motivated by the need for higher level editing semantics, which allow surface modifications at different scales. The user is enabled to edit the surface at different approximation levels to perform coarsescale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multiscale representation provides a separation in geometric scale, which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented, that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement or bandbass filtering.
Hierarchical Splatting of Scattered Data
 In VIS ’03: Proceedings of the 14th IEEE Visualization 2003 (VIS’03
, 2003
"... Numerical particle simulations and astronomical observations create huge data sets containing uncorrelated 3D points of varying size. These data sets cannot be visualized interactively by simply rendering millions of colored points for each frame. Therefore, in many visualization applications a scal ..."
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Cited by 38 (2 self)
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Numerical particle simulations and astronomical observations create huge data sets containing uncorrelated 3D points of varying size. These data sets cannot be visualized interactively by simply rendering millions of colored points for each frame. Therefore, in many visualization applications a scalar density corresponding to the point distribution is resampled on a regular grid for direct volume rendering. However, many fine details are usually lost for voxel resolutions which still allow interactive visualization on standard workstations. Since no surface geometry is associated with our data sets, the recently introduced pointbased rendering algorithms cannot be applied as well.
Perspective Accurate Splatting
, 2004
"... We present a novel algorithm for accurate, high quality point rendering, which is based on the formulation of splatting using homogeneous coordinates. In contrast to previous methods, this leads to perspective correct splat shapes, avoiding artifacts such as holes caused by the affine approximation ..."
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Cited by 35 (3 self)
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We present a novel algorithm for accurate, high quality point rendering, which is based on the formulation of splatting using homogeneous coordinates. In contrast to previous methods, this leads to perspective correct splat shapes, avoiding artifacts such as holes caused by the affine approximation of the perspective projection. Further, our algorithm implements the EWA resampling filter, hence providing high image quality with anisotropic texture filtering. We also present an extension of our rendering primitive that facilitates the display of sharp edges and corners. Finally, we describe an efficient implementation of the entire point rendering pipeline using vertex and fragment programs of current GPUs.
Threedimensional Point Cloud Recognition via Distributions of Geometric Distances
, 2008
"... A geometric framework for the recognition of threedimensional objects represented by point clouds is introduced in this paper. The proposed approach is based on comparing distributions of intrinsic measurements on the point cloud. In particular, intrinsic distances are exploited as signatures for r ..."
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Cited by 34 (3 self)
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A geometric framework for the recognition of threedimensional objects represented by point clouds is introduced in this paper. The proposed approach is based on comparing distributions of intrinsic measurements on the point cloud. In particular, intrinsic distances are exploited as signatures for representing the point clouds. The first signature we introduce is the histogram of pairwise diffusion distances between all points on the shape surface. These distances represent the probability of traveling from one point to another in a fixed number of random steps, the average intrinsic distances of all possible paths of a given number of steps between the two points. This signature is augmented by the histogram of the actual pairwise geodesic distances in the point cloud, the distribution of the ratio between these two distances, as well as the distribution of the number of times each point lies on the shortest paths between other points. These signatures are not only geometric but also invariant to bends. We further augment these signatures by the distribution of a curvature function and the distribution of a curvature weighted distance. These
On Fast Surface Reconstruction Methods for Large and Noisy Datasets
 in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA
, 2009
"... Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For result ..."
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Cited by 34 (9 self)
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Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For resulting smooth surfaces, the data is resampled with variable densities according to previously estimated surface curvatures. Incremental scans are easily incorporated into an existing surface mesh, by determining the respective overlapping area and reconstructing only the updated part of the surface mesh. The proposed framework is flexible enough to be integrated with additional point label information, where groups of points sharing the same label are clustered together and can be reconstructed separately, thus allowing fast updates via triangular mesh decoupling. To validate our approach, we present results obtained from laser scans acquired in both indoor and outdoor environments. I.
Fast construction of kNearest Neighbor Graphs for Point Clouds
"... Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space ..."
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Cited by 28 (1 self)
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Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space usage. (3) Better cache efficiency. (4) Ability to handle large data sets. (5) Ease of parallelization and implementation. If the point set has a bounded expansion constant, our algorithm requires one comparison based parallel sort of points according to Morton order plus near linear additional steps to output the knearest neighbor graph. Index Terms—Nearest neighbor searching, point based graphics, knearest neighbor graphics, Morton Ordering, parallel algorithms. 1
Dynamic sampling and rendering of algebraic point set surfaces
 COMPUTER GRAPHICS FORUM
, 2008
"... Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving leastsquares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature ..."
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Cited by 26 (10 self)
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Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving leastsquares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel realtime rendering system of such surfaces using a dynamic upsampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive upsampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.
Optimized SubSampling of Point Sets for Surface Splatting
 Computer Graphics Forum
, 2004
"... Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for highperformance and highquality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of prim ..."
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Cited by 26 (0 self)
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Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for highperformance and highquality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for pointsampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new subsampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error tolerance #. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a holefree piecewise linear C continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.
Professor of Management and
 Vice President for University Development
, 1968
"... This work demonstrates the utility of sophisticated simulation tools in aiding agribusiness managers’ decision making. The system dynamics model developed here provides insight into the use of such models to evaluate potential adoption rates and diffusion patterns of yield mapping and monitoring tec ..."
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Cited by 25 (0 self)
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This work demonstrates the utility of sophisticated simulation tools in aiding agribusiness managers’ decision making. The system dynamics model developed here provides insight into the use of such models to evaluate potential adoption rates and diffusion patterns of yield mapping and monitoring technologies. The model allows for comparative analyses of the possible effects of different profit assumptions on adoption and diffusion. © 2001 Elsevier Science Inc. All rights reserved.
Statistical Point Geometry
, 2003
"... We propose a scheme for modeling point sample geometry with statistical analysis. In our scheme we depart from the current schemes that deterministically represent the attributes of each point sample. We show how the statistical analysis of a densely sampled point model can be used to improve the ..."
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Cited by 23 (1 self)
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We propose a scheme for modeling point sample geometry with statistical analysis. In our scheme we depart from the current schemes that deterministically represent the attributes of each point sample. We show how the statistical analysis of a densely sampled point model can be used to improve the geometry bandwidth bottleneck and to do randomized rendering without sacrificing visual realism. We first carry out a hierarchical principal component analysis (PCA) of the model. This stage partitions the model into compact local geometries by exploiting local coherence. Our scheme handles vertex coordinates, normals, and color. The input model is reconstructed and rendered using a probability distribution derived from the PCA analysis. We demonstrate the benefits of this approach in all stages of the graphics pipeline: (1) orders of magnitude improvement in the storage and transmission complexity of point geometry, (2) direct rendering from compressed data, and (3) viewdependent randomized rendering.