The Experts below are selected from a list of 6918 Experts worldwide ranked by ideXlab platform
Li Kong - One of the best experts on this subject based on the ideXlab platform.
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PatchCNN: An Explicit Convolution Operator for Point Clouds Perception
2021Co-Authors: Wang F(王斐), Li Kong, Zhang Xing, Jiang Y(姜勇), Wei XiaotongAbstract:A novel convolution architecture PatchCNN is proposed for extending 2-D grid convolution to the nongrid structured data: point clouds, without any intermediate data representation. Previous studies implicitly capture local shape pattern from the meaningful subset or a local region without considering the interaction among points of the local region. The PointPatch module in our deep network, in spirit to the 8-pixels neighborhood in the 2-D image, explicitly models geometric relationship among points in the local region. We adopt a light 3-D convolution network to adaptively integrate features of the PointPatch module. The integrated features encode geometric relationship and the impact of surrounding points, which brings sufficient shape awareness and robustness for point cloud perception. Additionally, in our work, the convolution weight on each point is treated as a Lipschitz Continuous Function approximated by multilayer perceptron (MLP) and integrated features in the local region. Theoretically, the explicit learning strategy proposed in PatchCNN introduces inductive bias beneficial to the learning shape pattern in 3-D Euclidean space. Extensive experiments on ModelNet40 and ScanNet v2 data sets demonstrate that the proposed method achieves the competitive performance on par or even better than state-of-The-Art methods. © 2004-2012 IEEE.
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PatchCNN: An Explicit Convolution Operator for Point Clouds Perception
IEEE Geoscience and Remote Sensing Letters, 2026Co-Authors: Fei Wang, Xing Zhang, Yong Jiang, Li KongAbstract:A novel convolution architecture PatchCNN is proposed for extending 2-D grid convolution to the nongrid structured data: point clouds, without any intermediate data representation. Previous studies implicitly capture local shape pattern from the meaningful subset or a local region without considering the interaction among points of the local region. The PointPatch module in our deep network, in spirit to the 8-pixels neighborhood in the 2-D image, explicitly models geometric relationship among points in the local region. We adopt a light 3-D convolution network to adaptively integrate features of the PointPatch module. The integrated features encode geometric relationship and the impact of surrounding points, which brings sufficient shape awareness and robustness for point cloud perception. Additionally, in our work, the convolution weight on each point is treated as a Lipschitz Continuous Function approximated by multilayer perceptron (MLP) and integrated features in the local region. Theoretically, the explicit learning strategy proposed in PatchCNN introduces inductive bias beneficial to the learning shape pattern in 3-D Euclidean space. Extensive experiments on ModelNet40 and ScanNet v2 data sets demonstrate that the proposed method achieves the competitive performance on par or even better than state-of-the-art methods.
Fei Wang - One of the best experts on this subject based on the ideXlab platform.
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PatchCNN: An Explicit Convolution Operator for Point Clouds Perception
IEEE Geoscience and Remote Sensing Letters, 2026Co-Authors: Fei Wang, Xing Zhang, Yong Jiang, Li KongAbstract:A novel convolution architecture PatchCNN is proposed for extending 2-D grid convolution to the nongrid structured data: point clouds, without any intermediate data representation. Previous studies implicitly capture local shape pattern from the meaningful subset or a local region without considering the interaction among points of the local region. The PointPatch module in our deep network, in spirit to the 8-pixels neighborhood in the 2-D image, explicitly models geometric relationship among points in the local region. We adopt a light 3-D convolution network to adaptively integrate features of the PointPatch module. The integrated features encode geometric relationship and the impact of surrounding points, which brings sufficient shape awareness and robustness for point cloud perception. Additionally, in our work, the convolution weight on each point is treated as a Lipschitz Continuous Function approximated by multilayer perceptron (MLP) and integrated features in the local region. Theoretically, the explicit learning strategy proposed in PatchCNN introduces inductive bias beneficial to the learning shape pattern in 3-D Euclidean space. Extensive experiments on ModelNet40 and ScanNet v2 data sets demonstrate that the proposed method achieves the competitive performance on par or even better than state-of-the-art methods.
David Kempe - One of the best experts on this subject based on the ideXlab platform.
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estimating the average of a Lipschitz Continuous Function from one sample
arXiv: Data Structures and Algorithms, 2011Co-Authors: Abhimanyu Das, David KempeAbstract:We study the problem of estimating the average of a Lipschitz Continuous Function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal is to find a distribution minimizing the expected estimation error against an adversarially chosen Lipschitz Continuous Function. Our work falls into the broad class of estimating aggregate statistics of a Function from a small number of carefully chosen samples. The general problem has a wide range of practical applications in areas as diverse as sensor networks, social sciences and numerical analysis. However, traditional work in numerical analysis has focused on asymptotic bounds, whereas we are interested in the \emph{best} algorithm. For arbitrary discrete metric spaces of bounded doubling dimension, we obtain a PTAS for this problem. In the special case when the points lie on a line, the running time improves to an FPTAS. Both algorithms are based on approximately solving a linear program with an infinite set of constraints, by using an approximate separation oracle. For Lipschitz-Continuous Functions over $[0,1]$, we calculate the precise achievable error as $1-\frac{\sqrt{3}}{2} \approx 0.134$, which improves upon the \quarter which is best possible for deterministic algorithms.
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estimating the average of a Lipschitz Continuous Function from one sample
European Symposium on Algorithms, 2010Co-Authors: Abhimanyu Das, David KempeAbstract:We study the problem of estimating the average of a Lipschitz Continuous Function f defined over a metric space, by querying f at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal is to find a distribution minimizing the expected estimation error against an adversarially chosen Lipschitz Continuous Function. Our work falls into the broad class of estimating aggregate statistics of a Function from a small number of carefully chosen samples. The general problem has a wide range of practical applications in areas such as sensor networks, social sciences and numerical analysis. However, traditional work in numerical analysis has focused on asymptotic bounds, whereas we are interested in the best algorithm. For arbitrary discrete metric spaces of bounded doubling dimension, we obtain a PTAS for this problem. In the special case when the points lie on a line, the running time improves to an FPTAS. For Lipschitz-Continuous Functions over [0, 1], we calculate the precise achievable error as 1 - √3-2, which improves upon the 1/4 which is best possible for deterministic algorithms.
Kwiatkowska M - One of the best experts on this subject based on the ideXlab platform.
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Reachability analysis of deep neural networks with provable guarantees
'International Joint Conferences on Artificial Intelligence', 2020Co-Authors: Ruan W, Huang X, Kwiatkowska MAbstract:This is the final version. Available from IJCAI via the DOI in this recordVerifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-Continuous Function over its outputs, computes the lower and upper bound on the Function values. Because the network and the Function are Lipschitz Continuous, all values in the interval between the lower and upper bound are reachable. We show how to obtain the safety verification problem, the output range analysis problem and a robustness measure by instantiating the reachability problem. We present a novel algorithm based on adaptive nested optimisation to solve the reachability problem. The technique has been implemented and evaluated on a range of DNNs, demonstrating its efficiency, scalability and ability to handle a broader class of networks than state-of-the-art verification approaches.Engineering and Physical Sciences Research Council (EPSRC)NSF
P Viswanathan - One of the best experts on this subject based on the ideXlab platform.
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Countable zipper fractal interpolation and some elementary aspects of the associated nonlinear zipper fractal operator
Aequationes mathematicae, 2021Co-Authors: K. K. Pandey, P ViswanathanAbstract:This note aims to extend the notion of affine zipper fractal interpolation Function from the case of a finite data set to an infinite sequence of data points. We work with a slightly more general setting wherein the assumption of affinity on the Functions involved in the construction of the zipper fractal interpolant is dropped. Invoking the iterative Functional equation for the countable zipper fractal interpolant, its stability with a perturbation of data points and sensitivity to perturbations in the maps that define the zipper are examined. In the second part of this note, the countable zipper fractal interpolation is used to obtain a parameterized family of zipper fractal Functions corresponding to a prescribed real-valued Lipschitz Continuous Function on a closed bounded interval in $$\mathbb {R}$$ R . An operator obtained by associating each Lipschitz Continuous Function to its fractal counterpart is approached from the standpoint of nonlinear Functional analysis and perturbation theory of operators.
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fractal approximation of a Function from a countable sample set and associated fractal operator
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2020Co-Authors: P ViswanathanAbstract:In the literature of fractal approximation theory, the notion of fractal interpolation Function is used to construct a family of fractal Functions, called the $$\alpha $$-fractal Functions, corresponding to a fixed real-valued Continuous Function on a compact interval. The said $$\alpha $$-fractal Function that simultaneously interpolates and approximates a prescribed Continuous Function is established using a finite set of sampled values of the original Function. Closer in this spirit, this note aims to enunciate the fractal approximate reconstruction of a Continuous Function from a countably infinite sample set. Some elementary properties of the fractal operator that maps the given Lipschitz Continuous Function to the reconstructed fractal counterpart is expounded from the view point of perturbation theory of operators. This may act as a first step to perceive the notion of fractal operator beyond the familiar terrain of bounded linear operators. Some sidelights are also presented.