The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Martin Vetterli - One of the best experts on this subject based on the ideXlab platform.
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SHAPE: Linear-Time Camera Pose Estimation With Quadratic Error-Decay
arXiv: Computer Vision and Pattern Recognition, 2016Co-Authors: Alireza Ghasemi, Adam Scholefield, Martin VetterliAbstract:We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction Error that decreases at least Quadratically, as the number of feature point correspondences increase. Inspired by ideas from triangulation and frame quantisation theory, we define consistent reconstruction and then present SHAPE, our proposed consistent pose estimation algorithm. We compare this algorithm with state-of-the-art pose estimation techniques in terms of accuracy and Error decay rate. The experimental results verify our hypothesis on the optimal worst-case Quadratic decay and demonstrate its promising performance compared to other approaches.
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ICASSP - Shape: Linear-time camera pose estimation with Quadratic Error-decay
2016 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2016Co-Authors: Alireza Ghasemi, Adam Scholefield, Martin VetterliAbstract:We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction Error that decreases at least Quadratically, as the number of feature point correspondences increase., Inspired by ideas from triangulation and frame quantisation theory, we define consistent reconstruction and then present SHAPE, our proposed consistent pose estimation algorithm. We compare this algorithm with state-of-the-art pose estimation techniques in terms of accuracy and Error decay rate. The experimental results verify our hypothesis on the optimal worst-case Quadratic decay and demonstrate its promising performance compared to other approaches.
Alireza Ghasemi - One of the best experts on this subject based on the ideXlab platform.
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SHAPE: Linear-Time Camera Pose Estimation With Quadratic Error-Decay
arXiv: Computer Vision and Pattern Recognition, 2016Co-Authors: Alireza Ghasemi, Adam Scholefield, Martin VetterliAbstract:We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction Error that decreases at least Quadratically, as the number of feature point correspondences increase. Inspired by ideas from triangulation and frame quantisation theory, we define consistent reconstruction and then present SHAPE, our proposed consistent pose estimation algorithm. We compare this algorithm with state-of-the-art pose estimation techniques in terms of accuracy and Error decay rate. The experimental results verify our hypothesis on the optimal worst-case Quadratic decay and demonstrate its promising performance compared to other approaches.
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ICASSP - Shape: Linear-time camera pose estimation with Quadratic Error-decay
2016 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2016Co-Authors: Alireza Ghasemi, Adam Scholefield, Martin VetterliAbstract:We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction Error that decreases at least Quadratically, as the number of feature point correspondences increase., Inspired by ideas from triangulation and frame quantisation theory, we define consistent reconstruction and then present SHAPE, our proposed consistent pose estimation algorithm. We compare this algorithm with state-of-the-art pose estimation techniques in terms of accuracy and Error decay rate. The experimental results verify our hypothesis on the optimal worst-case Quadratic decay and demonstrate its promising performance compared to other approaches.
Andrei Zinovyev - One of the best experts on this subject based on the ideXlab platform.
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data analysis with arbitrary Error measures approximated by piece wise Quadratic pqsq functions
International Joint Conference on Neural Network, 2018Co-Authors: Alexander N. Gorban, Evgeny M Mirkes, Andrei ZinovyevAbstract:Defining an Error function (a measure of deviation of a model prediction from the data) is a critical step in any optimization-based data analysis method, including regression, clustering and dimension reduction. Usual Quadratic Error function in case of real-life high-dimensional and noisy data suffers from non-robustness to presence of outliers. Therefore, using non-Quadratic Error functions in data analysis and machine learning (such as L1 norm-based) is an active field of modern research but the majority of methods suggested are either slow or imprecise (use arbitrary heuristics). We suggest a flexible and highly performant approach to generalize most of existing data analysis methods to an arbitrary Error function of subQuadratic growth. For this purpose, we exploit PQSQ functions (piece-wise Quadratic of subQuadratic growth), which can be minimized by a simple and fast splitting-based iterative algorithm. The theoretical basis of the PQSQ approach is an application of min-plus (idempotent) algebra to data approximation. We introduce the general idea of the approach and illustrate it on four standard tools of machine learning: simple regression, regularized regression, k-mean clustering and principal component analysis. In all cases, PQSQ-based methods achieve better robustness with respect to the presence of strong noise in the data compared to the standard methods.
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piece wise Quadratic approximations of arbitrary Error functions for fast and robust machine learning
Neural Networks, 2016Co-Authors: Alexander N. Gorban, Eugenij Moiseevich Mirkes, Andrei ZinovyevAbstract:Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient Quadratic optimization methods. However, when faced with high-dimensional and noisy data, the Quadratic Error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-Quadratic Error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0
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Piece-wise Quadratic approximations of arbitrary Error functions for fast and robust machine learning
Neural networks : the official journal of the International Neural Network Society, 2016Co-Authors: Alexander N. Gorban, Eugenij Moiseevich Mirkes, Andrei ZinovyevAbstract:Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient Quadratic optimization methods. However, when faced with high-dimensional and noisy data, the Quadratic Error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-Quadratic Error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0
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Piece-wise Quadratic lego set for constructing arbitrary Error potentials and their fast optimization.
arXiv: Learning, 2016Co-Authors: Alexander N. Gorban, Eugenij Moiseevich Mirkes, Andrei ZinovyevAbstract:Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient Quadratic optimization methods. However, when faced with high-dimensional and noisy data, the Quadratic Error functionals demonstrate many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited the properties of non-Quadratic Error functionals based on L1 norm or even sub-linear potentials corresponding to fractional norms. The back side of these approaches is tremendous increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with {\it arbitrary} Error functionals, in a flexible and computationally efficient framework. In this paper, we develop the theory and basic universal data approximation algorithms ($k$-means, principal components, principal manifolds and graphs), based on piece-wise Quadratic Error potentials of subQuadratic growth (PQSQ potentials). We develop a new and universal framework to minimize {\it arbitrary sub-Quadratic Error potentials} using an algorithm with guaranteed fast convergence to the local or global Error minimum. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized regression, leading to the improvement in the computational cost/accuracy trade-off.
Chia-hsing Yang - One of the best experts on this subject based on the ideXlab platform.
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second order extended h_ infty filter for nonlinear discrete time systems using Quadratic Error matrix approximation
IEEE Transactions on Signal Processing, 2011Co-Authors: Chia-hsing YangAbstract:In this paper, the second-order extended (SOE) H∞ filter for nonlinear discrete-time systems is derived based on an approximation to the Quadratic Error matrix. The solution is obtained by the game theory approach. It is shown that the result bears a strong resemblance to the SOE Kalman filter when the performance bound goes to infinity. An example of vehicle state tracking is simulated to compare the performances of the SOE Kalman filter, the first order extended and the SOE H∞ filter. Noises with unknown bias are injected into both process dynamics and measurements. The results show that the SOE H∞ filter has the smallest state tracking Error.
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Second-Order Extended $H_{\infty}$ Filter for Nonlinear Discrete-Time Systems Using Quadratic Error Matrix Approximation
IEEE Transactions on Signal Processing, 2011Co-Authors: Chia-hsing YangAbstract:In this paper, the second-order extended (SOE) H∞ filter for nonlinear discrete-time systems is derived based on an approximation to the Quadratic Error matrix. The solution is obtained by the game theory approach. It is shown that the result bears a strong resemblance to the SOE Kalman filter when the performance bound goes to infinity. An example of vehicle state tracking is simulated to compare the performances of the SOE Kalman filter, the first order extended and the SOE H∞ filter. Noises with unknown bias are injected into both process dynamics and measurements. The results show that the SOE H∞ filter has the smallest state tracking Error.
Denis Bosq - One of the best experts on this subject based on the ideXlab platform.
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Optimal asymptotic Quadratic Error of nonparametric regression function estimates for a continuous-time process from sampled-data
Statistics, 1999Co-Authors: Denis Bosq, Nathalie Cheze-payaudAbstract:For different classes of deterministic and random sampling (t k ), we establish the asymptotic expressions for the bias and the variance of the estimate r n(x) based on sampled data for the regression function r(x) = E(Y t X t = x) of unbounded continuous-time processes (not necessarily stationary). Under mild mixing conditions, we show that r n (x) has exactly the same asymptotic Quadratic Error as in the i.i.d. case. In order to prove this result, we use some large deviations inequalities for mixing processes.
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Optimal asymptotic Quadratic Error of density estimators for strong mixing or chaotic data
Statistics & Probability Letters, 1995Co-Authors: Denis BosqAbstract:Abstract Under mild mixing conditions, we show that the kernel density estimator has exactly the same asymptotic Quadratic Error as in the i.i.d. case. Curiously, that result remains almost valid if the data are chaotic.