74,502 research outputs found
Review of the mathematical foundations of data fusion techniques in surface metrology
The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed
Learning to Select Pre-Trained Deep Representations with Bayesian Evidence Framework
We propose a Bayesian evidence framework to facilitate transfer learning from
pre-trained deep convolutional neural networks (CNNs). Our framework is
formulated on top of a least squares SVM (LS-SVM) classifier, which is simple
and fast in both training and testing, and achieves competitive performance in
practice. The regularization parameters in LS-SVM is estimated automatically
without grid search and cross-validation by maximizing evidence, which is a
useful measure to select the best performing CNN out of multiple candidates for
transfer learning; the evidence is optimized efficiently by employing Aitken's
delta-squared process, which accelerates convergence of fixed point update. The
proposed Bayesian evidence framework also provides a good solution to identify
the best ensemble of heterogeneous CNNs through a greedy algorithm. Our
Bayesian evidence framework for transfer learning is tested on 12 visual
recognition datasets and illustrates the state-of-the-art performance
consistently in terms of prediction accuracy and modeling efficiency.Comment: Appearing in CVPR-2016 (oral presentation
2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images
In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective
Regularized adaptive long autoregressive spectral analysis
This paper is devoted to adaptive long autoregressive spectral analysis when
(i) very few data are available, (ii) information does exist beforehand
concerning the spectral smoothness and time continuity of the analyzed signals.
The contribution is founded on two papers by Kitagawa and Gersch. The first one
deals with spectral smoothness, in the regularization framework, while the
second one is devoted to time continuity, in the Kalman formalism. The present
paper proposes an original synthesis of the two contributions: a new
regularized criterion is introduced that takes both information into account.
The criterion is efficiently optimized by a Kalman smoother. One of the major
features of the method is that it is entirely unsupervised: the problem of
automatically adjusting the hyperparameters that balance data-based versus
prior-based information is solved by maximum likelihood. The improvement is
quantified in the field of meteorological radar
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
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