Results 1  10
of
180
Algebraic point set surfaces
 IN PROCEEDINGS SIGGRAPH ’07
, 2007
"... 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 M ..."
Abstract

Cited by 80 (8 self)
 Add to MetaCart
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.
Reassembling fractured objects by geometric matching
 TOG
"... We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graphcuts based ..."
Abstract

Cited by 78 (10 self)
 Add to MetaCart
We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graphcuts based segmentation algorithm for identifying potential fracture surfaces, featurebased robust global registration for pairwise matching of fragments, and simultaneous constrained local registration of multiple fragments. We develop several new techniques in the area of geometry processing, including the novel integral invariants for computing multiscale surface characteristics, registration based on forward search techniques and surface consistency, and a nonpenetrating iterated closest point algorithm. We illustrate the performance of our algorithms on a number of realworld examples.
On normals and projection operators for surfaces defined by point sets
 IN EUROGRAPHICS SYMP. ON POINTBASED GRAPHICS
, 2004
"... Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated nonlinear optimization to compute a tangent frame and the (commonly overlooked) fact that the ..."
Abstract

Cited by 60 (3 self)
 Add to MetaCart
Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated nonlinear optimization to compute a tangent frame and the (commonly overlooked) fact that the normal to this tangent frame is not the surface normal. An alternative definition of Point Set Surfaces, inspired by the MLS projection, is the implicit surface version of Adamson & Alexa. We use this surface definition to show how to compute exact surface normals and present simple, efficient projection operators. The exact normal computation also allows computing orthogonal projections.
Registration of Point Cloud Data from a Geometric Optimization Perspective
, 2004
"... We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximant ..."
Abstract

Cited by 59 (13 self)
 Add to MetaCart
We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximants of the squared distance function are used to develop a linear system whose solution gives the best aligning rigid transform for the given pair of point clouds. The rigid transform is applied and the linear system corresponding to the new orientation is build. This process is iterated until it converges. The pointtopoint and the pointtoplane Iterated Closest Point (ICP) algorithms can be treated as special cases in this framework. Our algorithm can align PCDs even when they are placed far apart, and is experimentally found to be more stable than pointtoplane ICP. We analyze the convergence behavior of our algorithm and of pointtopoint and pointtoplane ICP under our proposed framework, and derive bounds on their rate of convergence. We compare the stability and convergence properties of our algorithm with other registration algorithms on a variety of scanned data.
Feature preserving point set surfaces based on nonlinear kernel regression
, 2009
"... Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we addre ..."
Abstract

Cited by 55 (3 self)
 Add to MetaCart
(Show Context)
Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [SOS04,Kol05] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other nonrobust approaches.
Consolidation of Unorganized Point Clouds for Surface Reconstruction
"... We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optim ..."
Abstract

Cited by 47 (10 self)
 Add to MetaCart
We consolidate an unorganized point cloud with noise, outliers, nonuniformities, and in particular interference between closeby surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlierfree and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a prioritydriven normal propagation scheme based on a new priority measure and an orientationaware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the closeby surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1
Curve Skeleton Extraction from Incomplete Point Cloud
, 2009
"... We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of orient ..."
Abstract

Cited by 42 (10 self)
 Add to MetaCart
We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of oriented points, we introduce a variational definition for an oriented point that is most rotationally symmetric with respect to S. Our formulation effectively utilizes normal information to compensate for the missing data and leads to robust curve skeleton computation over regions of a shape that are generally cylindrical. We present an iterative algorithm via planar cuts to compute the ROSA of a point cloud. This is complemented by special handling of noncylindrical joint regions to obtain a centered, topologically clean, and complete 1D skeleton. We demonstrate that quality curve skeletons can be extracted from a variety of shapes captured by incomplete point clouds. Finally, we show how our algorithm assists in shape completion under these challenges by developing a skeletondriven point cloud completion scheme.
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 ..."
Abstract

Cited by 40 (0 self)
 Add to MetaCart
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.
Parameterizationfree Projection for Geometry Reconstruction
"... We introduce a Locally Optimal Projection operator (LOP) for surface approximation from pointset data. The operator is parameterization free, in the sense that it does not rely on estimating a local normal, fitting a local plane, or using any other local parametric representation. Therefore, it can ..."
Abstract

Cited by 38 (7 self)
 Add to MetaCart
We introduce a Locally Optimal Projection operator (LOP) for surface approximation from pointset data. The operator is parameterization free, in the sense that it does not rely on estimating a local normal, fitting a local plane, or using any other local parametric representation. Therefore, it can deal with noisy data which clutters the orientation of the points. The method performs well in cases of ambiguous orientation, e.g., if two folds of a surface lie near each other, and other cases of complex geometry in which methods based upon local plane fitting may fail. Although defined by a global minimization problem, the method is effectively local, and it provides a second order approximation to smooth surfaces. Hence allowing good surface approximation without using any explicit or implicit approximation space. Furthermore, we show that LOP is highly robust to noise and outliers and demonstrate its effectiveness by applying it to raw scanned data of complex shapes.
Diffusion tensor visualization with glyph packing
 Visualization and Computer Graphics, IEEE Transactions on
"... Abstract—A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating largerscale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tracto ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
(Show Context)
Abstract—A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating largerscale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tractography can address the second. We adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyphbased tensor visualizations. By carefully distributing glyphs throughout the field (either on a slice, or in the volume) into a dense packing, using potential energy profiles shaped by the local tensor value, we remove undue visual emphasis of the regular sampling grid of the data, and the underlying continuous features become more apparent. The method is demonstrated on a DTMRI scan of a patient with a brain tumor. Index Terms—Diffusion tensor, glyphs, particle systems, anisotropic sampling, fiber tractography. F 1