Shape from periodic texture using the eigenvectors of local affine distortion

This paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization, We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery

Signal Processing in Large Systems: a New Paradigm

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to \infty$. Modern technological and societal advances now demand the study of sometimes extremely large populations and simultaneously require fast signal processing due to accelerated system dynamics. This results in not-so-large practical ratios $n/N$, sometimes even smaller than one. A disruptive change in classical signal processing methods has therefore been initiated in the past ten years, mostly spurred by the field of large dimensional random matrix theory. The early works in random matrix theory for signal processing applications are however scarce and highly technical. This tutorial provides an accessible methodological introduction to the modern tools of random matrix theory and to the signal processing methods derived from them, with an emphasis on simple illustrative examples

Robust statistical approaches for local planar surface fitting in 3D laser scanning data

This paper proposes robust methods for local planar surface fitting in 3D laser scanning data. Searching through the literature revealed that many authors frequently used Least Squares (LS) and Principal Component Analysis (PCA) for point cloud processing without any treatment of outliers. It is known that LS and PCA are sensitive to outliers and can give inconsistent and misleading estimates. RANdom SAmple Consensus (RANSAC) is one of the most well-known robust methods used for model fitting when noise and/or outliers are present. We concentrate on the recently introduced Deterministic Minimum Covariance Determinant estimator and robust PCA, and propose two variants of statistically robust algorithms for fitting planar surfaces to 3D laser scanning point cloud data. The performance of the proposed robust methods is demonstrated by qualitative and quantitative analysis through several synthetic and mobile laser scanning 3D data sets for different applications. Using simulated data, and comparisons with LS, PCA, RANSAC, variants of RANSAC and other robust statistical methods, we demonstrate that the new algorithms are significantly more efficient, faster, and produce more accurate fits and robust local statistics (e.g. surface normals), necessary for many point cloud processing tasks.Consider one example data set used consisting of 100 points with 20% outliers representing a plane. The proposed methods called DetRD-PCA and DetRPCA, produce bias angles (angle between the fitted planes with and without outliers) of 0.20° and 0.24° respectively, whereas LS, PCA and RANSAC produce worse bias angles of 52.49°, 39.55° and 0.79° respectively. In terms of speed, DetRD-PCA takes 0.033 s on average for fitting a plane, which is approximately 6.5, 25.4 and 25.8 times faster than RANSAC, and two other robust statistical methods, respectively. The estimated robust surface normals and curvatures from the new methods have been used for plane fitting, sharp feature preservation and segmentation in 3D point clouds obtained from laser scanners. The results are significantly better and more efficiently computed than those obtained by existing methods

A Robust Localization System for Inspection Robots in Sewer Networks †

Sewers represent a very important infrastructure of cities whose state should be monitored periodically. However, the length of such infrastructure prevents sensor networks from being applicable. In this paper, we present a mobile platform (SIAR) designed to inspect the sewer network. It is capable of sensing gas concentrations and detecting failures in the network such as cracks and holes in the floor and walls or zones were the water is not flowing. These alarms should be precisely geo-localized to allow the operators performing the required correcting measures. To this end, this paper presents a robust localization system for global pose estimation on sewers. It makes use of prior information of the sewer network, including its topology, the different cross sections traversed and the position of some elements such as manholes. The system is based on a Monte Carlo Localization system that fuses wheel and RGB-D odometry for the prediction stage. The update step takes into account the sewer network topology for discarding wrong hypotheses. Additionally, the localization is further refined with novel updating steps proposed in this paper which are activated whenever a discrete element in the sewer network is detected or the relative orientation of the robot over the sewer gallery could be estimated. Each part of the system has been validated with real data obtained from the sewers of Barcelona. The whole system is able to obtain median localization errors in the order of one meter in all cases. Finally, the paper also includes comparisons with state-of-the-art Simultaneous Localization and Mapping (SLAM) systems that demonstrate the convenience of the approach.Unión Europea ECHORD ++ 601116Ministerio de Ciencia, Innovación y Universidades de España RTI2018-100847-B-C2

Contributions to Robust Methods: Modified Rank Covariance Matrix and Spatial-EM Algorithm

Classical multivariate statistical inference methods including multivariate analysis of variance, principal component analysis, factor analysis, canonical correlation analysis are based on sample covariance matrix. Those moment-based techniques are optimal (most efficient) under the normality distributional assumption. They are, however, extremely sensitive to outlying observations, susceptible to small perturbation in data and poor in the efficiency for heavy-tailed distributions. A straightforward treatment is to replace the sample covariance matrix with a robust one. Visuri et al. (2000) proposed a technique for robust covariance matrix estimation based on different notions of multivariate sign and rank. Among them, the spatial rank based covariance matrix estimator that utilizes a robust scale estimator (MRCM) is especially appealing due to its high robustness, computational ease and good efficiency. In this dissertation, properties of the estimator on orthogonal equivariance under any distribution and affine equivariance under elliptically symmetric distributions have been established. The major robustness properties of the estimator are studied by the breakdown point and influence function analysis. More specifically, the finite sample breakdown point is obtained and the upper bound of the finite sample breakdown point can be achieved by a proper choice of univariate robust scale estimator. The influence functions for eigenvalues and eigenvectors of the estimator are derived. They are found to be bounded under some mild assumptions. Moreover, empirical comparisons to popular robust MCD, M and S estimators show that MRCM has a competitive performance on efficiency as well as robustness. With rapid advances in information technology, data have been becoming huge in size and complex in structure. A single elliptical distribution is no longer sufficient to model such data. This motivates a generalization of our notion of MRCM to mixture models. In this dissertation, we propose a robust Spatial-EM algorithm for estimating parameters in the mixture model. Rather than using sample covariance matrix in each M-step, Spatial-EM ingeniously implements MRCM to enhance stability and robustness of the estimation procedure. Analyzing the log-likelihood function, the proposed one is found to be closely related to the maximum likelihood estimator (MLE) of Kotz type mixture model. Comparing with the direct MLE, Spatial-EM has advantages in computation ease as well as stability. Applications of Spatial-EM to data mining become natural. We illustrate procedures how to use Spatial-EM for supervised and unsupervised learning problems. More specifically, robust clustering and outlier detection methods based on Spatial-EM have been proposed. We adopt the outlier detection to taxonomic research on fish species novelty discovery. UCI Wisconsin diagnostic breast cancer data and Yeast cell cycle data are used for clustering analysis. Comparing with the regular EM and many other existing methods such as X-EM and SVM, Spatial-EM demonstrates its competitive classification power and high robustness. Classical multivariate statistical inference methods including multivariate analysis of variance, principal component analysis, factor analysis, canonical correlation analysis are based on sample covariance matrix. Those moment-based techniques are optimal (most efficient) under the normality distributional assumption. They are, however, extremely sensitive to outlying observations, susceptible to small perturbation in data and poor in the efficiency for heavy-tailed distributions. A straightforward treatment is to replace the sample covariance matrix with a robust one. Visuri et al. (2000) proposed a technique for robust covariance matrix estimation based on different notions of multivariate sign and rank. Among them, the spatial rank based covariance matrix estimator that utilizes a robust scale estimator (MRCM) is especially appealing due to its high robustness, computational ease and good efficiency. In this dissertation, properties of the estimator on orthogonal equivariance under any distribution and affine equivariance under elliptically symmetric distributions have been established. The major robustness properties of the estimator are studied by the breakdown point and influence function analysis. More specifically, the finite sample breakdown point is obtained and the upper bound of the finite sample breakdown point can be achieved by a proper choice of univariate robust scale estimator. The influence functions for eigenvalues and eigenvectors of the estimator are derived. They are found to be bounded under some mild assumptions. Moreover, empirical comparisons to popular robust MCD, M and S estimators show that MRCM has a competitive performance on efficiency as well as robustness. With rapid advances in information technology, data have been becoming huge in size and complex in structure. A single elliptical distribution is no longer sufficient to model such data. This motivates a generalization of our notion of MRCM to mixture models. In this dissertation, we propose a robust Spatial-EM algorithm for estimating parameters in the mixture model. Rather than using sample covariance matrix in each M-step, Spatial-EM ingeniously implements MRCM to enhance stability and robustness of the estimation procedure. Analyzing the log-likelihood function, the proposed one is found to be closely related to the maximum likelihood estimator (MLE) of Kotz type mixture model. Comparing with the direct MLE, Spatial-EM has advantages in computation ease as well as stability. Applications of Spatial-EM to data mining become natural. We illustrate procedures how to use Spatial-EM for supervised and unsupervised learning problems. More specifically, robust clustering and outlier detection methods based on Spatial-EM have been proposed. We adopt the outlier detection to taxonomic research on fish species novelty discovery. UCI Wisconsin diagnostic breast cancer data and Yeast cell cycle data are used for clustering analysis. Comparing with the regular EM and many other existing methods such as X-EM and SVM, Spatial-EM demonstrates its competitive classification power and high robustness

Reliable a-posteriori error estimators for hphp-adaptive finite element approximations of eigenvalue/eigenvector problems

We present reliable a-posteriori error estimates for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on $h$ adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the $hp$-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.Comment: submitte

Outlier detection and robust normal-curvature estimation in mobile laser scanning 3D point cloud data

This paper proposes two robust statistical techniques for outlier detection and robust saliency features, such as surface normal and curvature, estimation in laser scanning 3D point cloud data. One is based on a robust z-score and the other uses a Mahalanobis type robust distance. The methods couple the ideas of point to plane orthogonal distance and local surface point consistency to get Maximum Consistency with Minimum Distance (MCMD). The methods estimate the best-fit-plane based on most probable outlier free, and most consistent, points set in a local neighbourhood. Then the normal and curvature from the best-fit-plane will be highly robust to noise and outliers. Experiments are performed to show the performance of the algorithms compared to several existing well-known methods (from computer vision, data mining, machine learning and statistics) using synthetic and real laser scanning datasets of complex (planar and non-planar) objects. Results for plane fitting, denoising, sharp feature preserving and segmentation are significantly improved. The algorithms are demonstrated to be significantly faster, more accurate and robust. Quantitatively, for a sample size of 50 with 20% outliers the proposed MCMD_Z is approximately 5, 15 and 98 times faster than the existing methods: uLSIF, RANSAC and RPCA, respectively. The proposed MCMD_MD method can tolerate 75% clustered outliers, whereas, RPCA and RANSAC can only tolerate 47% and 64% outliers, respectively. In terms of outlier detection, for the same dataset, MCMD_Z has an accuracy of 99.72%, 0.4% false positive rate and 0% false negative rate; for RPCA, RANSAC and uLSIF, the accuracies are 97.05%, 47.06% and 94.54%, respectively, and they have misclassification rates higher than the proposed methods. The new methods have potential for local surface reconstruction, fitting, and other point cloud processing tasks

Doctor of Philosophy

dissertationLocation information of people is valuable for many applications including logistics, healthcare, security and smart facilities. This dissertation focuses on localization of people in wireless sensor networks using radio frequency (RF) signals, speci cally received signal strength (RSS) measurements. A static sensor network can make RSS measurements of the signal from a transmitting badge that a person wears in order to locate the badge. We call this kind of localization method radio device localization. Since the human body causes RSS changes between pairwise sensor nodes of a static network, we can also use RSS measurements from pairwise nodes of a network to locate people, even if they are not carrying any radio device. We call this device-free localization (DFL). The rst contribution of this dissertation is to radio device localization. The human body has a major e ect on the antenna gain pattern of the transmitting badge that the person is wearing, however, existing r

On Improved Accuracy Chirp Parameter Estimation using the DFRFT with Application to SAR-based Vibrometry

The Discrete Fractional Fourier Transform (DFRFT) has in recent years, become a useful tool for multicomponent chirp signal analysis. Chirp signals are transformed into spectral peaks in the chirp rate versus center frequency representation, whose coordinates are related to the underlying chirp parameters via a computed empirical peak to parameter mapping incorporated into the Santhanam-Peacock algorithm. In this thesis, we attempt to quantify the accuracy of the DFRFT approach by first studying the discretization error sources that arise from the transitioning of the continuous FRFT to DFRFT. Then, we refine prior work by Ishwor Bhatta to develop analytical expressions for the chirp rate and center frequency parameters instead of the empirical mapping approach. We further study the extensions of this refined DFRFT approach using zero padding, spectral peak interpolation, and chirp-z-transform based zooming. The performance of the refined estimators is compared versus the Cramer-Rao lower bound and shown to asymptotically approach the bound. This refined DFRFT approach is then applied to Synthetic Aperture Radar Vibrometry data from several vibrating targets and the estimated acceleration information and vibration frequencies are shown to be very close to the corresponding ground-truth accelerometer measurements