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47
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 ..."
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Cited by 41 (10 self)
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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.
Concurrent number cruncher: a gpu implementation of a general sparse linear solver
 Int. J. Parallel Emerg. Distrib. Syst
"... A wide class of numerical methods needs to solve a linear system, where the matrix pattern of nonzero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on GPUs, especially since dedicated general purp ..."
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Cited by 40 (0 self)
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A wide class of numerical methods needs to solve a linear system, where the matrix pattern of nonzero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on GPUs, especially since dedicated general purpose APIs such as CTM (AMDATI) and CUDA (NVIDIA) have appeared. CUDA even provides a BLAS implementation, but only for dense matrices (CuBLAS). Other existing linear solvers for the GPU are also limited by their internal matrix representation. This paper describes how to combine recent GPU programming techniques and new GPU dedicated APIs with high performance computing strategies (namely block compressed row storage, register blocking and vectorization), to implement a sparse generalpurpose linear solver. Our implementation of the Jacobipreconditioned Conjugate Gradient algorithm outperforms by up to a factor of 6.0x leadingedge CPU counterparts, making it attractive for applications which content with single precision.
Variational Harmonic Maps for Space Deformation
 IN ACM TRANS. ON GRAPHICS VOL.28, NO. 3 (SIGGRAPH
, 2009
"... A space deformation is a mapping from a source region to a target region within Euclidean space, which best satisfies some userspecified constraints. It can be used to deform shapes embedded in the ambient space and represented in various forms – polygon meshes, point clouds or volumetric data. For ..."
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Cited by 37 (6 self)
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A space deformation is a mapping from a source region to a target region within Euclidean space, which best satisfies some userspecified constraints. It can be used to deform shapes embedded in the ambient space and represented in various forms – polygon meshes, point clouds or volumetric data. For a space deformation method to be useful, it should possess some natural properties: e.g. detail preservation, smoothness and intuitive control. A harmonic map from a domain Ω ⊂ R d to R d is a mapping whose d components are harmonic functions. Harmonic mappings are smooth and regular, and if their components are coupled in some special way, the mapping can be detailpreserving, making it a natural choice for space deformation applications. The challenge is to find a harmonic mapping of the domain, which will satisfy constraints specified by the user, yet also be detailpreserving, and intuitive to control. We generate harmonic mappings as a linear combination of a set of harmonic basis functions, which have a closedform expression when the source region boundary is piecewise linear. This is done by defining an energy functional of the mapping, and minimizing it within the linear span of these basis functions. The resulting mapping is harmonic, and a natural "AsRigidAsPossible " deformation of the source region. Unlike other space deformation methods, our approach does not require an explicit discretization of the domain. It is shown to be much more efficient, yet generate comparable deformations to stateoftheart methods. We describe an optimization algorithm to minimize the deformation energy, which is robust, provably convergent, and easy to implement.
Laplacian Mesh Processing
 EUROGRAPHICS ’05 STAR – STATE OF THE ART REPORT
, 2005
"... Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and dif ..."
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Cited by 27 (0 self)
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Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.
Cone Carving for Surface Reconstruction
"... We present cone carving, a novel space carving technique supporting topologically correct surface reconstruction from an incomplete scanned point cloud. The technique utilizes the point samples not only for local surface position estimation but also to obtain global visibility information under th ..."
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Cited by 14 (2 self)
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We present cone carving, a novel space carving technique supporting topologically correct surface reconstruction from an incomplete scanned point cloud. The technique utilizes the point samples not only for local surface position estimation but also to obtain global visibility information under the assumption that each acquired point is visible from a point lying outside the shape. This enables associating each point with a generalized cone, called the visibility cone, that carves a portion of the outside ambient space of the shape from the inside out. These cones collectively provide a means to better approximate the signed distances to the shape specifically near regions containing large holes in the scan, allowing one to infer the correct surface topology. Combining the new distance measure with conventional RBF, we define an implicit function whose zero level set defines the surface of the shape. We demonstrate the utility of cone carving in coping with significant missing data and raw scans from a commercial 3D scanner as well as synthetic input.
Freeform Vector Graphics with Controlled ThinPlate Splines
"... Figure 1: We build on thinplate splines to enrich vector graphics with a variety of powerful and intuitive controls. Recent work defines vector graphics using diffusion between colored curves. We explore higherorder fairing to enable more natural interpolation and greater expressive control. Speci ..."
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Cited by 13 (1 self)
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Figure 1: We build on thinplate splines to enrich vector graphics with a variety of powerful and intuitive controls. Recent work defines vector graphics using diffusion between colored curves. We explore higherorder fairing to enable more natural interpolation and greater expressive control. Specifically, we build on thinplate splines which provide smoothness everywhere except at userspecified tears and creases (discontinuities in value and derivative respectively). Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines. We refine the representation with novel contour and slope curves, which anisotropically constrain interpolation derivatives. Compound curves further increase editing power by expanding a single curve into multiple offsets of various basic types (value, tear, crease, slope, and contour). The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.
Point cloud skeletons via laplacianbased contraction
 In Proc. Conf. on Shape Modeling and Appl
, 2010
"... Abstract—We present an algorithm for curve skeleton extraction via Laplacianbased contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly p ..."
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Cited by 13 (3 self)
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Abstract—We present an algorithm for curve skeleton extraction via Laplacianbased contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeletonbased manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeletondriven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easytomanipulate structure for effective topology modification, leading to more faithful surface reconstruction. Keywordscurve skeleton; point cloud; Laplacian; contraction; topology repair; surface reconstruction I.
Practical Least Squares for Computer Graphics
"... Abstract. The course presents an overview of the leastsquares technique and its variants. A wide range of problems in computer graphics can be solved using the leastsquares technique (LS). Many graphics problems can be seen as finding the best set of parameters for a model given some data. For inst ..."
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Cited by 10 (0 self)
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Abstract. The course presents an overview of the leastsquares technique and its variants. A wide range of problems in computer graphics can be solved using the leastsquares technique (LS). Many graphics problems can be seen as finding the best set of parameters for a model given some data. For instance, a surface can be determined using data and smoothness penalties, a trajectory can be predicted using previous information, joint angles can be determined from end effector positions, etc. All these problems and many others can be formulated as minimizing the sum of squares of the residuals between some features in the model and the data. Despite this apparent versatility, solving problems in the leastsquares sense can produce poor results. This occurs when the nature of the problem error does not match the assumptions of the leastsquares method. The course explains these assumptions and show how to circumvent some of them to apply LS to a wider range of problem. The focus of the course is to provide a practical understanding of the techniques. Each technique will be explained using the simple example of fitting a line through data, and then illustrated through its use in one or more computer graphics papers. Prerequisites. The attendee is expected to have had an introductory course to computer graphics and some basic knowledge in linear algebra at the level of OpenGL transforms. Updates and Slides. The latest version of these notes and the associated slides are located at
Noniterative approach for global mesh optimization
, 2007
"... This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The ..."
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Cited by 5 (4 self)
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This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Our global mesh optimization approach can be effectively used in at least three applications: smoothing the noisy mesh, improving the simplified mesh, and geometric modeling with subdivisionconnectivity. Many experimental results are presented to show the applicability and flexibility of the approach.
Weighted averages on surfaces
 ACM Trans. Graph
, 2013
"... Figure 1: Interactive control for various geometry processing and modeling applications made possible with weighted averages on surfaces. From left to right: texture transfer, decal placement, semiregular remeshing and Laplacian smoothing, splines on surfaces. We consider the problem of generalizing ..."
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Cited by 5 (1 self)
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Figure 1: Interactive control for various geometry processing and modeling applications made possible with weighted averages on surfaces. From left to right: texture transfer, decal placement, semiregular remeshing and Laplacian smoothing, splines on surfaces. We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem, namely computing an average of given anchor points on the mesh with given weights, and the inverse problem, which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.