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Poisson Surface Reconstruction
, 2006
"... We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function ..."
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Cited by 369 (5 self)
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We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
The Space of Human Body Shapes: Reconstruction And Parameterization from Range Scans
 ACM TRANS. GRAPH
, 2003
"... We develop a novel method for fitting highresolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination ..."
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Cited by 290 (4 self)
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We develop a novel method for fitting highresolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination of three measures: proximity of transformed vertices to the range data, similarity between neighboring transformations, and proximity of sparse markers at corresponding locations on the template and target surface. We solve for the transformations with a nonlinear optimizer, run at two resolutions to speed convergence. We demonstrate reconstruction and consistent parameterization of 250 human body models. With this parameterized set, we explore a variety of applications for human body modeling, including: morphing, texture transfer, statistical analysis of shape, model fitting from sparse markers, feature analysis to modify multiple correlated parameters (such as the weight and height of an individual), and transfer of surface detail and animation controls from a template to fitted models.
Multilevel Partition of Unity Implicits
 ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighti ..."
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Cited by 218 (7 self)
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We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape. Our approach
Shape modeling with pointsampled geometry
 ACM Transactions on Graphics
, 2003
"... Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and ..."
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Cited by 201 (30 self)
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Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and complete freeform shape modeling framework for pointsampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, pointsampled surfaces can easily be restructured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on pointsampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.
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. ..."
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Cited by 180 (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.
Modelling with Implicit Surfaces that Interpolate
 ACM Transactions on Graphics
, 2002
"... We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction [24] and shape transformation [30], but the emphasis of our work is on model creation. These implicit surfaces are described by specify ..."
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Cited by 126 (1 self)
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We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction [24] and shape transformation [30], but the emphasis of our work is on model creation. These implicit surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach, and the isosurface of this function describes a surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength for model creation is that interpolating implicit surfaces allow the direct specification of both the location of points on the surface and the surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make this form of implicit surface particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert in [32]. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model, as well as a new way to form blends between objects.
RidgeValley Lines on Meshes via Implicit Surface Fitting
 ACM TRANS. GRAPH
, 2004
"... We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multil ..."
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Cited by 123 (8 self)
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We propose a simple and effective method for detecting view and scaleindependent ridgevalley lines defined via first and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A highquality estimation of highorder surface derivatives is achieved by combining multilevel implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.
ExampleBased 3D Scan Completion
 EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING
, 2005
"... Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete sur ..."
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Cited by 85 (23 self)
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Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete surface scans, using a database of 3D shapes to provide geometric priors for regions of missing data. Our method retrieves suitable context models from the database, warps the retrieved models to conform with the input data, and consistently blends the warped models to obtain the final consolidated 3D shape. We define a shape matching penalty function and corresponding optimization scheme for computing the nonrigid alignment of the context models with the input data. This allows a quantitative evaluation and comparison of the quality of the shape extrapolation provided by each model. Our algorithms are explicitly designed to accommodate uncertain data and can thus be applied directly to raw scanner output. We show on a variety of real data sets how consistent models can be obtained from highly incomplete input. The information gained during the shape completion process can be utilized for future scans, thus continuously simplifying the creation of complex 3D models.
Spectral Surface Reconstruction from Noisy Point Clouds
, 2004
"... We introduce a noiseresistant algorithm for reconstructing a watertight surface from point cloud data. It forms a
..."
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Cited by 81 (1 self)
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We introduce a noiseresistant algorithm for reconstructing a watertight surface from point cloud data. It forms a
ShapeShop: SketchBased Solid Modeling with BlobTrees
, 2005
"... Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume M ..."
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Cited by 81 (18 self)
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Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume Models (BlobTrees) as an underlying shape representation. The BlobTree framework supports interactive creation of complex, detailed solid models with arbitrary topology. A new technique is described for inflating 2D contours into rounded threedimensional implicit volumes. Sketchbased modeling operations are defined that combine these basic shapes using standard blending and CSG operators. Since the underlying volume hierarchy is by definition a construction history, individual sketched components can be nonlinearly edited and removed. For example, holes can be interactively dragged through a shape. ShapeShop also provides 2D drawing assistance using a new curvesketching system based on variational contours. A wide range of models can be sketched with ShapeShop, from cartoonlike characters to detailed mechanical parts. Examples are shown which demonstrate significantly higher model complexity than existing systems.