As a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30$^{\rm th}$ of October 2020 taking place in the Icarian Sea (Greece) and the Tahtali dam around 30 km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtali dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed.
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Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the estimation of $f(\btheta)$ for a given functional $f:\scrH\rightarrow \RR$ based on $\bx_j$'s. The key element of our approach is a new method which we call High-Order Degenerate Statistical Expansion. It leverages the use of classical multivariate Taylor expansion and degenerate $U$-statistic and yields an elegant explicit formula. In the univariate case of $\scrH=\R$, the formula expresses the error of the proposed estimator as a sum of order $k$ degenerate $U$-products of the noises with coefficient $f^{(k)}(\btheta)/k!$ and an explicit remainder term in the form of the Riemann-Liouville integral as in the Taylor expansion around the true $\btheta$. For general $\scrH$, the formula expresses the estimation error in terms of the inner product of $f^{(k)}(\btheta)/k!$ and the average of the tensor products of $k$ noises with distinct indices and a parallel extension of the remainder term from the univariate case. This makes the proposed method a natural statistical version of the classical Taylor expansion. The proposed estimator can be viewed as a jackknife estimator of an ideal degenerate expansion of $f(\cdot)$ around the true $\btheta$ with the degenerate $U$-product of the noises, and can be approximated by bootstrap. Thus, the jackknife, bootstrap and Taylor expansion approaches all converge to the proposed estimator. We develop risk bounds for the proposed estimator and a central limit theorem under a second moment condition (even in expansions of higher than the second order). We apply this new method to generalize several existing results with smooth and nonsmooth $f$ to universal $\bep_j$'s with only minimum moment constraints.
Image registration is a fundamental task for medical imaging. Resampling of the intensity values is required during registration and better spatial resolution with finer and sharper structures can improve the resampling performance and hence the registration accuracy. Super-resolution (SR) is an algorithmic technique targeting at spatial resolution enhancement which can achieve an image resolution beyond the hardware limitation. In this work, we consider SR as a preprocessing technique and present a CNN-based resolution enhancement module (REM) which can be easily plugged into the registration network in a cascaded manner. Different residual schemes and network configurations of REM are investigated to obtain an effective architecture design of REM. In fact, REM is not confined to image registration, it can also be straightforwardly integrated into other vision tasks for enhanced resolution. The proposed REM is thoroughly evaluated for deformable registration on medical images quantitatively and qualitatively at different upscaling factors. Experiments on LPBA40 brain MRI dataset demonstrate that REM not only improves the registration accuracy, especially when the input images suffer from degraded spatial resolution, but also generates resolution enhanced images which can be exploited for successive diagnosis.
Kidney DCE-MRI aims at both qualitative assessment of kidney anatomy and quantitative assessment of kidney function by estimating the tracer kinetic (TK) model parameters. Accurate estimation of TK model parameters requires an accurate measurement of the arterial input function (AIF) with high temporal resolution. Accelerated imaging is used to achieve high temporal resolution, which yields under-sampling artifacts in the reconstructed images. Compressed sensing (CS) methods offer a variety of reconstruction options. Most commonly, sparsity of temporal differences is encouraged for regularization to reduce artifacts. Increasing regularization in CS methods removes the ambient artifacts but also over-smooths the signal temporally which reduces the parameter estimation accuracy. In this work, we propose a single image trained deep neural network to reduce MRI under-sampling artifacts without reducing the accuracy of functional imaging markers. Instead of regularizing with a penalty term in optimization, we promote regularization by generating images from a lower dimensional representation. In this manuscript we motivate and explain the lower dimensional input design. We compare our approach to CS reconstructions with multiple regularization weights. Proposed approach results in kidney biomarkers that are highly correlated with the ground truth markers estimated using the CS reconstruction which was optimized for functional analysis. At the same time, the proposed approach reduces the artifacts in the reconstructed images.
String vibration represents an active field of research in acoustics. Small-amplitude vibration is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion of nonlinear phenomena due to larger string stretchings is necessary to capture important features, and efficient numerical algorithms are currently lacking in this context. Of the available techniques, many lead to schemes which may only be solved iteratively, resulting in high computational cost, and the additional concerns of existence and uniqueness of solutions. Slow and fast waves are present concurrently in the transverse and longitudinal directions of motion, adding further complications concerning numerical dispersion. This work presents a linearly-implicit scheme for the simulation of the geometrically exact nonlinear string model. The scheme conserves a numerical energy, expressed as the sum of quadratic terms only, and including an auxiliary state variable yielding the nonlinear effects. This scheme allows to treat the transverse and longitudinal waves separately, using a mixed finite difference/modal scheme for the two directions of motion, thus allowing to accurately resolve the wave speeds at reference sample rates. Numerical experiments are presented throughout.
Illegal vehicle parking is a common urban problem faced by major cities in the world, as it incurs traffic jams, which lead to air pollution and traffic accidents. The government highly relies on active human efforts to detect illegal parking events. However, such an approach is extremely ineffective to cover a large city since the police have to patrol over the entire city roads. The massive and high-quality sharing bike trajectories from Mobike offer us a unique opportunity to design a ubiquitous illegal parking detection approach, as most of the illegal parking events happen at curbsides and have significant impact on the bike users. The detection result can guide the patrol schedule, i.e. send the patrol policemen to the region with higher illegal parking risks, and further improve the patrol efficiency. Inspired by this idea, three main components are employed in the proposed framework: 1)~{\em trajectory pre-processing}, which filters outlier GPS points, performs map-matching, and builds trajectory indexes; 2)~{\em illegal parking detection}, which models the normal trajectories, extracts features from the evaluation trajectories, and utilizes a distribution test-based method to discover the illegal parking events; and 3)~{\em patrol scheduling}, which leverages the detection result as reference context, and models the scheduling task as a multi-agent reinforcement learning problem to guide the patrol police. Finally, extensive experiments are presented to validate the effectiveness of illegal parking detection, as well as the improvement of patrol efficiency.
Spectral Laplacian methods, widely used in computer graphics and manifold learning, have been recently proposed for the Statistical Process Control (SPC) of a sequence of manufactured parts, whose 3-dimensional metrology is acquired with non-contact sensors. These techniques provide an {\em intrinsic} solution to the SPC problem, that is, a solution exclusively based on measurements on the scanned surfaces or 2-manifolds without making reference to their ambient space. These methods, therefore, avoid the computationally expensive, non-convex registration step needed to align the parts, as required by previous methods for SPC based on 3-dimensional measurements. Once a SPC mechanism triggers and out-of-control alarm, however, an additional problem remains: that of locating where on the surface of the part that triggered the SPC alarm there is a significant shape difference with respect to either an in-control part or its nominal (CAD) design. In the past, only registration-based solutions existed for this problem. In this paper, we present a new registration-free solution to the part localization problem. Our approach uses a functional map between the manifolds to be compared, that is, a map between functions defined on each manifold based on intrinsic differential operators, in particular, the Laplace-Beltrami operator, in order to construct a point to point mapping between the two manifolds and be able to locate defects on the suspected part. A recursive partitioning algorithm is presented to define a region of interest on the surface of the part where defects are likely to occur, which results in considerable computational advantages. The functional map method involves a very large number of point-to-point comparisons based on noisy measurements, and a statistical thresholding method is presented to filter the false positives in the underlying massive multiple comparisons problem.
We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and the theory of single variable polynomials. Our approach gives both qualitative and quantitative results in the case that the degree of the unperturbed polynomial can change under a perturbation of its coefficients, a case that naturally occurs, for instance, in stability theory of polynomials, singular perturbation theory, or in the perturbation theory for generalized eigenvalue problems. An application of our results in multivariate stability theory is provided which is important in, for example, the study of hyperbolic polynomials or realizability and synthesis problems in passive electrical network theory, and will be of general interest to mathematicians as well as physicists and engineers.
We propose a learning-based method for light-path construction in path tracing algorithms, which iteratively optimizes and samples from what we refer to as spatio-directional Gaussian mixture models (SDMMs). In particular, we approximate incident radiance as an online-trained $5$D mixture that is accelerated by a $k$D-tree. Using the same framework, we approximate BSDFs as pre-trained $n$D mixtures, where $n$ is the number of BSDF parameters. Such an approach addresses two major challenges in path-guiding models. First, the $5$D radiance representation naturally captures correlation between the spatial and directional dimensions. Such correlations are present in e.g. parallax and caustics. Second, by using a tangent-space parameterization of Gaussians, our spatio-directional mixtures can perform approximate product sampling with arbitrarily oriented BSDFs. Existing models are only able to do this by either foregoing anisotropy of the mixture components or by representing the radiance field in local (normal aligned) coordinates, which both make the radiance field more difficult to learn. An additional benefit of the tangent-space parameterization is that each individual Gaussian is mapped to the solid sphere with low distortion near its center of mass. Our method performs especially well on scenes with small, localized luminaires that induce high spatio-directional correlation in the incident radiance.
The sense of touch plays a key role in enabling humans to understand and interact with surrounding environments. For robots, tactile sensing is also irreplaceable. While interacting with objects, tactile sensing provides useful information for the robot to understand the object, such as distributed pressure, temperature, vibrations and texture. During robot grasping, vision is often occluded by its end-effectors, whereas tactile sensing can measure areas that are not accessible by vision. In the past decades, a number of tactile sensors have been developed for robots and used for different robotic tasks. In this chapter, we focus on the use of tactile sensing for robotic grasping and investigate the recent trends in tactile perception of object properties. We first discuss works on tactile perception of three important object properties in grasping, i.e., shape, pose and material properties. We then review the recent development in grasping stability prediction with tactile sensing. Among these works, we identify the requirement for coordinating vision and tactile sensing in the robotic grasping. To demonstrate the use of tactile sensing to improve the visual perception, our recent development of vision-guided tactile perception for crack reconstruction is presented. In the proposed framework, the large receptive field of camera vision is first leveraged to achieve a quick search of candidate regions containing cracks, a high-resolution optical tactile sensor is then used to examine these candidate regions and reconstruct a refined crack shape. The experiments show that our proposed method can achieve a significant reduction of mean distance error from 0.82 mm to 0.24 mm for crack reconstruction. Finally, we conclude this chapter with a discussion of open issues and future directions for applying tactile sensing in robotic tasks.
We present R-LINS, a lightweight robocentric lidar-inertial state estimator, which estimates robot ego-motion using a 6-axis IMU and a 3D lidar in a tightly-coupled scheme. To achieve robustness and computational efficiency even in challenging environments, an iterated error-state Kalman filter (ESKF) is designed, which recursively corrects the state via repeatedly generating new corresponding feature pairs. Moreover, a novel robocentric formulation is adopted in which we reformulate the state estimator concerning a moving local frame, rather than a fixed global frame as in the standard world-centric lidar-inertial odometry(LIO), in order to prevent filter divergence and lower computational cost. To validate generalizability and long-time practicability, extensive experiments are performed in indoor and outdoor scenarios. The results indicate that R-LINS outperforms lidar-only and loosely-coupled algorithms, and achieve competitive performance as the state-of-the-art LIO with close to an order-of-magnitude improvement in terms of speed.
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