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12
A Bayesian method for probable surface reconstruction and decimation
 ACM TRANS. GRAPH
, 2006
"... We present a Bayesian technique for the reconstruction and subsequent decimation of 3D surface models from noisy sensor data. The method uses oriented probabilistic models of the measurement noise, and combines them with featureenhancing prior probabilities over 3D surfaces. When applied to surface ..."
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Cited by 47 (5 self)
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We present a Bayesian technique for the reconstruction and subsequent decimation of 3D surface models from noisy sensor data. The method uses oriented probabilistic models of the measurement noise, and combines them with featureenhancing prior probabilities over 3D surfaces. When applied to surface reconstruction, the method simultaneously smooths noisy regions while enhancing features, such as corners. When applied to surface decimation, it finds models that closely approximate the original mesh when rendered. The method is applied in the context of computer animation, where it finds decimations that minimize the visual error even under nonrigid deformations.
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 21 (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.
Design and Analysis of Optimization Methods for Subdivision Surface Fitting
"... Abstract—We present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically motivated optimization schemes and reveal their intrinsic rel ..."
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Cited by 6 (1 self)
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Abstract—We present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically motivated optimization schemes and reveal their intrinsic relations with standard methods for constrained nonlinear optimization. A commonly used method in graphics, called point distance minimization, is shown to use a variant of the gradient descent step and thus has only linear convergence. The second method, called tangent distance minimization, which is well known in computer vision, is shown to use the GaussNewton step and, thus, demonstrates nearquadratic convergence for zero residual problems but may not converge otherwise. Finally, we show that an optimization scheme called squared distance minimization, recently proposed by Pottmann et al., can be derived from the Newton method. Hence, with proper regularization, tangent distance minimization and squared distance minimization are more efficient than point distance minimization. We also investigate the effects of two stepsize control methods—LevenbergMarquardt regularization and the Armijo rule—on the convergence stability and efficiency of the above optimization schemes. Index Terms—Subdivision surface, fitting, optimization, squared distance. Ç 1
Neural mesh ensembles
 In Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium, 3DPVT ’04
, 2004
"... This paper proposes the use of neural network ensembles to boost the performance of a neural network based surface reconstruction algorithm. Ensemble is a very popular and powerful statistical technique based on the idea of averaging several outputs of a probabilistic algorithm. In the context of ..."
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Cited by 5 (1 self)
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This paper proposes the use of neural network ensembles to boost the performance of a neural network based surface reconstruction algorithm. Ensemble is a very popular and powerful statistical technique based on the idea of averaging several outputs of a probabilistic algorithm. In the context of surface reconstruction, two main problems arise. The first is finding an efficient way to average meshes with different connectivity, and the second is tuning the parameters for surface reconstruction to maximize the performance of the ensemble. We solve the first problem by voxelizing all the meshes on the same regular grid and taking majority vote on each voxel. We tune the parameters experimentally, borrowing ideas from weak learning methods. 1.
On Stochastic Methods for Surface Reconstruction
 THE VISUAL COMPUTER
"... In this article, we present and discuss three statistical methods for Surface Reconstruction. A typical input to a Surface Reconstruction technique consists of a large set of points that has been sampled from a smooth surface and contains uncertain data in the form of noise and outliers. We first p ..."
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Cited by 3 (0 self)
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In this article, we present and discuss three statistical methods for Surface Reconstruction. A typical input to a Surface Reconstruction technique consists of a large set of points that has been sampled from a smooth surface and contains uncertain data in the form of noise and outliers. We first present a method that filters out uncertain and redundant information yielding a more accurate and economical surface representation. Then we present two methods, each of which converts the input point data to a standard shape representation; the first produces an implicit representation while the second yields a triangle mesh.
NUMERICAL CONTROL OF KOHONEN NEURAL NETWORK FOR SCATTERED DATA APPROXIMATION
"... Abstract. Surface reconstruction from scattered data using Kohonen neural network is presented in this paper. The network produces a topologically predefined grid from the unordered data which can be applied as a rough approximation of the input set or as a base surface for further process. The qual ..."
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Cited by 2 (0 self)
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Abstract. Surface reconstruction from scattered data using Kohonen neural network is presented in this paper. The network produces a topologically predefined grid from the unordered data which can be applied as a rough approximation of the input set or as a base surface for further process. The quality and computing time of the approximation can be controlled by numerical parameters. As a further application, ruled surface is produced from a set of unordered lines by the network. 1.
www.disi.unige.it/person/OdoneF
"... www.mpisb.mpg.de/˜schall We consider applications of clustering techniques, Mean Shift and SelfOrganizing Maps, to surface reconstruction (meshing) from scattered point data and review a novel kernelbased clustering method. ..."
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www.mpisb.mpg.de/˜schall We consider applications of clustering techniques, Mean Shift and SelfOrganizing Maps, to surface reconstruction (meshing) from scattered point data and review a novel kernelbased clustering method.
Statistical Learning for Shape Applications
"... Statistical methods are well suited to the large amounts of data typically involved in digital shape applications. In this paper, we look at two statistical learning methods related to digital shape processing. The first, neural meshes, learns the shape of a given point cloud – the surface reconstr ..."
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Statistical methods are well suited to the large amounts of data typically involved in digital shape applications. In this paper, we look at two statistical learning methods related to digital shape processing. The first, neural meshes, learns the shape of a given point cloud – the surface reconstruction problem – in O(n²) time. We present an alternate implementation of the algorithm that takes O(n log n) time. Secondly, we present a simple method to automatically learn the correct orientation of a shape in an image from a database of images with correctly oriented shapes.
Authors ’ Addresses
, 2003
"... We propose a new surface reconstruction algorithm based on an incrementally expanding neural network known as Growing Cell Structure. The neural network learns a probability space, which represents the surface for reconstruction, through a competitive learning process. The topology is learned throug ..."
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We propose a new surface reconstruction algorithm based on an incrementally expanding neural network known as Growing Cell Structure. The neural network learns a probability space, which represents the surface for reconstruction, through a competitive learning process. The topology is learned through statistics based operations which create boundaries and merge them to create handles. We study the algorithm theoretically, calculating its complexity, using probabilistic arguments to find relationships between the parameters, and finally, running statistical experiments to optimize the parameters.