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21
Bayesian Point Cloud Reconstruction
- EUROGRAPHICS 2006
, 2006
"... In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key id ..."
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Cited by 21 (5 self)
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In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a well-sampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewise-smooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and real-world data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations
Gaussian process implicit surfaces for shape estimation and grasping
- in IEEE Int. Conf. Robotics and Automation
, 2011
"... Abstract — The choice of an adequate object shape representation is critical for efficient grasping and robot manipulation. A good representation has to account for two requirements: it should allow uncertain sensory fusion in a probabilistic way and it should serve as a basis for efficient grasp an ..."
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Cited by 18 (0 self)
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Abstract — The choice of an adequate object shape representation is critical for efficient grasping and robot manipulation. A good representation has to account for two requirements: it should allow uncertain sensory fusion in a probabilistic way and it should serve as a basis for efficient grasp and motion generation. We consider Gaussian process implicit surface potentials as object shape representations. Sensory observations condition the Gaussian process such that its posterior mean defines an implicit surface which becomes an estimate of the object shape. Uncertain visual, haptic and laser data can equally be fused in the same Gaussian process shape estimate. The resulting implicit surface potential can then be used directly as a basis for a reach and grasp controller, serving as an attractor for the grasp end-effectors and steering the orientation of contact points. Our proposed controller results in a smooth reach and grasp trajectory without strict separation of phases. We validate the shape estimation using Gaussian processes in a simulation on randomly sampled shapes and the grasp controller on a real robot with 7DoF arm and 7DoF hand. I.
Object correspondence as a machine learning problem
- In Proceedings of the 22nd International Conference on Machine Learning (ICML 05
, 2005
"... We propose machine learning methods for the estimation of deformation fields that transform two given objects into each other, thereby establishing a dense point to point correspondence. The fields are computed using a modified support vector machine containing a penalty enforcing that points of one ..."
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Cited by 15 (5 self)
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We propose machine learning methods for the estimation of deformation fields that transform two given objects into each other, thereby establishing a dense point to point correspondence. The fields are computed using a modified support vector machine containing a penalty enforcing that points of one object will be mapped to “similar ” points on the other one. Our system, which contains little engineering or domain knowledge, delivers state of the art performance. We present application results including close to photorealistic morphs of 3D head models. 1.
Adaptive Fourier-based surface reconstruction
- In Geometric Modeling and Processing (GMP 2006), Springer Lecture Notes in Computer Science (LNCS
, 2007
"... Abstract. In this paper, we combine Kazhdan’s FFT-based approach to surface reconstruction from oriented points with adaptive subdivision and partition of unity blending techniques. The advantages of our surface reconstruction method include a more robust surface restoration in regions where the sur ..."
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Cited by 6 (0 self)
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Abstract. In this paper, we combine Kazhdan’s FFT-based approach to surface reconstruction from oriented points with adaptive subdivision and partition of unity blending techniques. The advantages of our surface reconstruction method include a more robust surface restoration in regions where the surface bends close to itself and a lower memory consumption. The latter allows us to achieve a higher reconstruction accuracy than the original global approach. Furthermore, our reconstruction process is guided by a global error control achieved by computing the Hausdorff distance of selected input samples to intermediate reconstructions. 1
Nonparametric regression between general riemannian manifolds
- SIAM J. Imaging Sciences
"... Abstract. We study nonparametric regression between Riemannian manifolds based on regularized empirical risk minimization. Regularization functionals for mappings between manifolds should respect the geometry of input and output manifold and be independent of the chosen parametrization of the manifo ..."
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Cited by 3 (0 self)
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Abstract. We study nonparametric regression between Riemannian manifolds based on regularized empirical risk minimization. Regularization functionals for mappings between manifolds should respect the geometry of input and output manifold and be independent of the chosen parametrization of the manifolds. We define and analyze the three most simple regularization functionals with these prop-erties and present a rather general scheme for solving the resulting optimization problem. As appli-cation examples we discuss interpolation on the sphere, fingerprint processing, and correspondence computations between three-dimensional surfaces. We conclude with characterizing interesting and sometimes counterintuitive implications and new open problems that are specific to learning between Riemannian manifolds and are not encountered in multivariate regression in Euclidean space.
A multi-scale Tikhonov regularization scheme for implicit surface modelling
- In Proc. of Conference on Computer Vision and Pattern Recognition (CVPR). IEEE
, 2007
"... Kernel machines have recently been considered as a promising solution for implicit surface modelling. A key challenge of machine learning solutions is how to fit implicit shape models from large-scale sets of point cloud samples efficiently. In this paper, we propose a fast solution for approximatin ..."
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Cited by 3 (0 self)
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Kernel machines have recently been considered as a promising solution for implicit surface modelling. A key challenge of machine learning solutions is how to fit implicit shape models from large-scale sets of point cloud samples efficiently. In this paper, we propose a fast solution for approximating implicit surfaces based on a multi-scale Tikhonov regularization scheme. The optimization of our scheme is formulated into a sparse linear equation system, which can be efficiently solved by factorization methods. Different from traditional approaches, our scheme does not employ auxiliary off-surface points, which not only saves the computational cost but also avoids the problem of injected noise. To further speedup our solution, we present a multi-scale surface fitting algorithm of coarse to fine modelling. We conduct comprehensive experiments to evaluate the performance of our solution on a number of datasets of different scales. The promising results show that our suggested scheme is considerably more efficient than the stateof-the-art approach. 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.
A curvature sensitive demons algorithm for surface registration
, 2006
"... Registration, the problem of establishing correspondence between points of two objects, is one of the central problems in Computer Vision, Computer Graphics and Medical Imaging. In this paper we present a new appraoch for establishing point-to-point corre-spondence between two objects given as two-d ..."
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Cited by 1 (1 self)
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Registration, the problem of establishing correspondence between points of two objects, is one of the central problems in Computer Vision, Computer Graphics and Medical Imaging. In this paper we present a new appraoch for establishing point-to-point corre-spondence between two objects given as two-dimensional surfaces in three-dimensional space. In contrast to traditional approaches for surface registration, we do not register the surfaces directly. Rather, we represent the surfaces as the zero level-set of a signed distance function in three-dimensional space. Correspondence is then established for the distance function, and thus in particular for the zero-level set that represents the surface. Using this representation, the registration algorithm becomes independent of the surfaces topology and even topological changes can be dealt with. As the basis for our registration algorithm we use the well known Thirion's Demons algorithm. Our experiments showed that using this method, the surfaces are accurately matched. However, due to the lack of information on the surface, the correspondences do not always correspond to those a human expert would identify. Therefore we extend the algorithm, such that it consid-ers the curvature information on the surface. We show that the new term fits naturally into the original formulation of Thirion's Demons. Moreover, we provide an additional interpretation of our extension in the variational framework. We performed experiments on various synthetic and medical structures. Using the here presented representation, we were able to register extremely complex structures, such as the human skull, accurately. Our experiments show that for our data the extension yields considerably improvements compared to Thirion's original formulation. 1
Watermark embedder optimization for 3D mesh objects using classication based approach
- In Proceedings of IEEE International Conference on Signal Acquisition and Processing
, 2010
"... This paper presents a novel 3D mesh watermarking scheme that utilizes a support vector machine(SVM) based classifier for watermark insertion. Artificial intelligence(AI) based approaches have been employed by watermarking algorithms for various host mediums such as images, audio, and video. However, ..."
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Cited by 1 (1 self)
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This paper presents a novel 3D mesh watermarking scheme that utilizes a support vector machine(SVM) based classifier for watermark insertion. Artificial intelligence(AI) based approaches have been employed by watermarking algorithms for various host mediums such as images, audio, and video. However, AI based techniques are yet to be explored by researchers in the 3D domain for watermark insertion and extraction processes. Contributing towards this end, the proposed approach employs a binary SVM to classify vertices as appropriate or inappropriate candidates for watermark insertion. The SVM is trained with feature vectors derived from the curvature estimates of a 1-ring neighborhood of vertices taken from normalized 3D meshes. A geometry-based non-blind approach is used by the water-marking algorithm. The robustness of proposed technique is evaluated experimentally by simulating attacks such as mesh smoothing, cropping and noise addition. 1.
Efficient Configuration Space Construction and Optimization
, 2013
"... The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this dissertation, we address three main computational ..."
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The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this dissertation, we address three main computational challenges related to configuration spaces: 1) how to efficiently compute an approximate representation of high-dimensional configuration spaces; 2) how to efficiently perform geometric, proximity, and motion planning queries in high-dimensional configuration spaces; and 3) how to model uncertainty in configuration spaces represented by noisy sensor data. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We highlight the efficiency of our algorithms for penetration depth computation and instance-based motion planning. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k-nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning. In order to extend configuration space algorithms to handle noisy sensor data arising from real-world robotics applications, we model the uncertainty in the configuration space by formulating the collision probabilities for noisy data. We use these algorithms to perform reliable motion planning for the PR2 robot.
