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63
Defining pointset surfaces
 ACM Trans. Graph. (Proceedings of ACM SIGGRAPH
, 2004
"... The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. ..."
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Cited by 177 (2 self)
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The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. This definition reveals connections to research in computer vision and computational topology. Variants of the MLS surface can be created by varying the vector field and the energy function. As an example, we define a similar surface determined by a cloud of surfels (points equipped with normals), rather than points. We also observe that some procedures described in the literature to take points in space onto the MLS surface fail to do so, and we describe a simple iterative procedure which does. the relationship of extremal surfaces and implicit surfaces. As we discuss in Section 5, there is an implicit surface containing every extremal surface, including the MLS surface. This can be quite useful, particularly for defining normals precisely. 1
Robust Global Registration
, 2005
"... We present an algorithm for the automatic alignment of two 3D shapes (data and model), without any assumptions about their initial positions. The algorithm computes for each surface point a descriptor based on local geometry that is robust to noise. A small number of feature points are automatically ..."
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Cited by 126 (11 self)
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We present an algorithm for the automatic alignment of two 3D shapes (data and model), without any assumptions about their initial positions. The algorithm computes for each surface point a descriptor based on local geometry that is robust to noise. A small number of feature points are automatically picked from the data shape according to the uniqueness of the descriptor value at the point. For each feature point on the data, we use the descriptor values of the model to find potential corresponding points. We then develop a fast branchandbound algorithm based on distance matrix comparisons to select the optimal correspondence set and bring the two shapes into a coarse alignment. The result of our alignment algorithm is used as the initialization to ICP (iterative closest point) and its variants for fine registration of the data to the model. Our algorithm can be used for matching shapes that overlap only over parts of their extent, for building models from partial range scans, as well as for simple symmetry detection, and for matching shapes undergoing articulated motion.
Algebraic point set surfaces
 In Proceedings SIGGRAPH ’07
, 2007
"... Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Samp ..."
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Cited by 74 (7 self)
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Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Sample positions are partly highlighted. In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.
Approximating and Intersecting Surfaces from Points
, 2003
"... Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each poin ..."
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Cited by 74 (3 self)
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Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted covariances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zeroset is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted covariances are well defined in a tubular neighborhood of the surface. For certain, wellchosen weight functions we can show that wellsampled surfaces lead to smooth distance fields with nonzero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute raysurface intersections for fast ray casting and ray tracing of the surface.
Integral Invariants for Robust Geometry Processing
 IN: ICCV ’95: PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON COMPUTER VISION. IEEE COMPUTER SOCIETY
, 2005
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Approximating Bounded, Nonorientable Surfaces from Points
 In Shape Modeling International
, 2004
"... We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally nonorientable surfaces. The surface is defined implicitly using directions of weighted covariances and weighted averages of the points. Specifically, a point belongs ..."
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Cited by 23 (3 self)
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We present an approach to surface approximation from points that allows reconstructing surfaces with boundaries, including globally nonorientable surfaces. The surface is defined implicitly using directions of weighted covariances and weighted averages of the points. Specifically, a point belongs to the surface, if its direction to the weighted average has no component into the direction of smallest covariance. For bounded surfaces, we require in addition that any point on the surface is close to the weighted average of the input points. We compare this definition to alternatives and discuss the details and parameter choices. Points on the surface can be determined by intersection computations. We show that the computation is local and, therefore, no globally consistent orientation of normals is needed. Continuity of the surfaces is not affected by the particular choice of local orientation. We demonstrate our approach by rendering several bounded (and nonorientable) surfaces using ray casting.
A Barcode Shape Descriptor for Curve Point Cloud Data
, 2004
"... In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD). Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. We also provide a metric over the space ..."
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Cited by 22 (12 self)
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In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD). Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology. We also provide a metric over the space of barcodes, enabling fast comparison of PCDs for shape recognition and clustering. To demonstrate the feasibility of our approach, we implement our pipeline and provide experimental evidence in shape classification and parametrization.
Efficient raytracing of deforming pointsampled surfaces
 Computer Graphics Forum
, 2005
"... We present efficient data structures and caching schemes to accelerate raysurface intersections for deforming pointsampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compar ..."
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Cited by 14 (3 self)
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We present efficient data structures and caching schemes to accelerate raysurface intersections for deforming pointsampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compared to existing techniques. Starting from a tight bounding sphere hierarchy for the undeformed object, we use a lazy updating scheme to adapt the hierarchy to the deformed surface in each animation step. In addition, we achieve a significant speedup for raysurface intersections by caching perray intersection points. We also present a technique for rendering sharp edges and corners in pointsampled models by introducing a novel surface clipping algorithm.
P.: Splatbased ray tracing of point clouds
 Journal of WSCG
, 2008
"... Pointbased surface representations have gained increasing interest in the computer graphics community within the last decade. Surface splatting established as one of the main rendering techniques for point clouds. We present a raytracing approach for objects whose surfaces are represented by point ..."
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Cited by 12 (7 self)
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Pointbased surface representations have gained increasing interest in the computer graphics community within the last decade. Surface splatting established as one of the main rendering techniques for point clouds. We present a raytracing approach for objects whose surfaces are represented by point clouds. Our approach is based on casting rays and intersecting them with splats. Since raytracing methods require smoothly changing surface normals for producing the desired photorealistic results, splat generation must include the derivation of such normals. We determine a neighborhood around each point of the point cloud, estimate the surface normal at each of the points, compute splats with varying radii that cover the surface, and use the normals of all points that are covered by each splat to generate a smoothly varying normal field for each splat. This part of the computation is viewindependent and, thus, can be precomputed. During the rendering step, raysplat intersections are performed, where the normal at the intersection point is interpolated using local coordinates of the splat’s normal field. Care has to be taken where splats overlap. We speed up the computations of the raysplat intersections using an octree data structure.
MultiResolution PointSample Raytracing
, 2003
"... We propose a new strategy for raytracing complex scenes without aliasing artifacts. The algorithm intersects anisotropic ray cones with prefiltered surface sample points from a multiresolution point hierarchy. The algorithm can be extended to capture effects of distributed raytracing [7] such as bl ..."
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Cited by 8 (0 self)
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We propose a new strategy for raytracing complex scenes without aliasing artifacts. The algorithm intersects anisotropic ray cones with prefiltered surface sample points from a multiresolution point hierarchy. The algorithm can be extended to capture effects of distributed raytracing [7] such as blurry reflections, depth of field, or soft shadows. In contrast to former antialiasing techniques based on cone tracing, the multiresolution algorithm can be applied efficiently to scenes of high complexity. The running time does not depend on the variance in the image as this is the case for the prevalent stochastic raytracing techniques. Thus, the new technique is faster than stochastic raytracing for images with many high frequency details.