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43
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 140 (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
Point Based Animation of Elastic, Plastic and Melting Objects
, 2004
"... We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original sha ..."
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Cited by 93 (12 self)
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We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio. In each step
A Survey of PointBased Techniques in Computer Graphics
 Computers & Graphics
, 2004
"... In recent years pointbased geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of highly complex 3Dmodels. Point sampled objects do neither have to store nor to maintain globally consistent topological ..."
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Cited by 65 (4 self)
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In recent years pointbased geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of highly complex 3Dmodels. Point sampled objects do neither have to store nor to maintain globally consistent topological information. Therefore they are more flexible compared to triangle meshes when it comes to handling highly complex or dynamically changing shapes. In this paper, we make an attempt to give an overview of the various pointbased methods that have been proposed over the last years. In particular we review and evaluate different shape representations, geometric algorithms, and rendering methods which use points as a universal graphics primitive.
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 ..."
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Cited by 48 (3 self)
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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.
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 43 (4 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.
Feature preserving point set surfaces based on nonlinear kernel regression, Computer Graphics Forum 28 (2
, 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 ..."
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Cited by 32 (1 self)
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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. 1.
A statistical method for robust 3D surface reconstruction from sparse data
 In Int. Symp. on 3D Data Processing, Visualization and Transmission
, 2004
"... General information about a class of objects, such as human faces or teeth, can help to solve the otherwise illposed problem of reconstructing a complete surface from sparse 3D feature points or 2D projections of points. We present a technique that uses a vector space representation of shape (3D Mo ..."
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Cited by 26 (5 self)
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General information about a class of objects, such as human faces or teeth, can help to solve the otherwise illposed problem of reconstructing a complete surface from sparse 3D feature points or 2D projections of points. We present a technique that uses a vector space representation of shape (3D Morphable Model) to infer missing vertex coordinates. Regularization derived from a statistical approach makes the system stable and robust with respect to noise by computing the optimal tradeoff between fitting quality and plausibility. We present a direct, noniterative algorithm to calculate this optimum efficiently, and a method for simultaneously compensating unknown rigid transformations. The system is applied and evaluated in two different fields: (1) reconstruction of 3D faces at unknown orientations from 2D feature points at interactive rates, and (2) restoration of missing surface regions of teeth for CADCAM production of dental inlays and other medical applications. I.
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.
Pointbased multiscale surface representation
 ACM TRANS. GRAPH
, 2006
"... In this article 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, that is, coarser scales of detail, using geomet ..."
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Cited by 21 (0 self)
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In this article 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, that is, 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 higherlevel editing semantics which allow surface modifications at different scales. The user would be able 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.
Fitting Subdivision Surfaces to Unorganized Point Data Using SDM
, 2004
"... We study the reconstruction of smooth surfaces from point clouds. We use a new squared distance error term in optimization to fit a subdivision surface to a set of unorganized points, which defines a closed target surface of arbitrary topology. The resulting method is based on the framework of squar ..."
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Cited by 20 (5 self)
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We study the reconstruction of smooth surfaces from point clouds. We use a new squared distance error term in optimization to fit a subdivision surface to a set of unorganized points, which defines a closed target surface of arbitrary topology. The resulting method is based on the framework of squared distance minimization (SDM) proposed by Pottmann et al. Specifically, with an initial subdivision surface having a coarse control mesh as input, we adjust the control points by optimizing an objective function through iterative minimization of a quadratic approximant of the squared distance function of the target shape. Our experiments show that the new method (SDM) converges much faster than the commonly used optimization method using the point distance error function, which is known to have only linear convergence. This observation is further supported by our recent result that SDM can be derived from the Newton method with necessary modifications to make the Hessian positive definite and the fact that the Newton method has quadratic convergence.