Results 1  10
of
73
Defining PointSet Surfaces
, 2005
"... 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. ..."
Abstract

Cited by 180 (2 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 120 (12 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 84 (4 self)
 Add to MetaCart
(Show Context)
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.
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.
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.
EnergyMinimizing Splines in Manifolds
, 2004
"... Variational interpolation in curved geometries has many applications, so there has always been demand for geometrically meaningful and efficiently computable splines in manifolds. We extend the definition of the familiar cubic spline curves and splines in tension, and we show how to compute these on ..."
Abstract

Cited by 57 (11 self)
 Add to MetaCart
Variational interpolation in curved geometries has many applications, so there has always been demand for geometrically meaningful and efficiently computable splines in manifolds. We extend the definition of the familiar cubic spline curves and splines in tension, and we show how to compute these on parametric surfaces, level sets, triangle meshes, and point samples of surfaces. This list is more comprehensive than it looks, because it includes variational motion design for animation, and allows the treatment of obstacles via barrier surfaces. All these instances of the general concept are handled by the same geometric optimization algorithm, which minimizes an energy of curves on surfaces of arbitrary dimension and codimension.
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.
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.
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 ..."
Abstract

Cited by 39 (5 self)
 Add to MetaCart
(Show Context)
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.