Abrupt Depth Change Research Articles

Learning deformable hypothesis sampling for patchmatch multi-view stereo in the wild

The learnable PatchMatch formulations have recently made progress in Multi-View Stereo (MVS). However, their performance often degrades under complex wild scenes. In this study, we observe that the degradation is mainly caused by the noisy depth hypothesis sampling during iterations of PatchMatch MVS: (i) Within a single iteration, the method mixes all information of a fixed-shape region in the spatial dimension, which introduces sampling noise, especially in regions with abrupt depth changes; (ii) Between iterations, the depth candidate hypotheses are sampled indiscriminately in the depth dimension, which fails to filter out noise in the sampling range and propagates errors to the next iteration. Accordingly, we propose a deformable sampling learning strategy (DefLearn) guided by matching uncertainty to determine the hypothesis set from two perspectives: (i) Encoding the matching uncertainty within the image allows the search region of sampling to fit the depth distribution in the spatial dimension; (i) Modeling the cross-image matching uncertainty more accurately based on the obtained valid hypotheses to capture scene structure information for fine-grained hypothesis searching in the depth dimension. With DefLearn, we develop a deep probabilistic PatchMatch MVS network (PPMNet) for accurate depth estimation with a high awareness of diverse scene structures. Extensive experiments conducted on three challenging datasets demonstrate that our PPMNet significantly outperforms state-of-the-art methods in terms of accuracy and generalization ability, even in particularly challenging wild scenes. Code is available at https://github.com/Geo-Tell/PPMNet.

Flexural Behavior of RC Beams with an Abrupt Change in Depth: Experimental Work

The most crucial components in the case of roofs with two levels or a variable floor height are variable depth beams. In order to investigate the flexural behavior of reinforced concrete (RC) beams with varying depths under static loads, experimental research was conducted. Under the four-point bending flexural test, two reference beams with constant depth, six dapped beams at the soffit, and four dapped beams at the top were tested. For all beams with a 150 mm depth, a 100 mm increase in depth occurred at the middle span of the beams. The primary characteristics included the impact of increasing depth, the impact of stirrups’ absence and their various ratios, and the characteristics of the longitudinal bars at the locations of sudden depth changes in either the top or bottom bars. Both the cracks’ progression and the load-deflection relationship along the beam’s length were observed. The ultimate carrying load (Pu) was reduced by 23.56% and 27.35% as a result of the 100 mm increase in the half-span of the beam over the constant depth in case of changes at the top and soffit, respectively. The Pu was increased by a ratio ranging from 20.9% to 31.35% for the bottom dapped beams and by a ratio of 29.79% for the top dapped beams due to the various stirrup ratios in the dapped area. The ductility was significantly impacted by the elevated stirrup ratios in the dapped area. The predicted results and the experimental results matched when the Pu of the tested beams was evaluated using the strut and tie model.

Image stitching by disparity-guided multi-plane alignment

Image stitching aims to warp and align two or more images with overlapping areas to generate a panorama with a larger field of view. Due to the wide baseline or the abrupt depth changes caused by the foreground objects, the phenomenon that adjacent pixels or regions in one image are not adjacent in another image happens. It is difficult to avoid severe parallax artifacts and get good alignment results when stitching such images. In this paper, focusing on the images with large parallax, we design a multi-plane alignment algorithm guided by the disparity map. The concept of average tolerable parallax is proposed to help distinguish one background plane and multiple foreground objects from the image, which are robust to small parallax. In order to obtain the reliable disparity map of the image pairs got from any camera with unknown camera parameters, we propose an optimal homography estimation method based on the relative projection biases. This helps to satisfy the common epipolar line constraint when applying stereo matching modules. Experimental results demonstrate that our algorithm provides accurate stitching results on images with large parallax, and outperforms other existing state-of-the-art methods both qualitatively and quantitatively.

Anomalous statistics and large deviations of turbulent water waves past a step

A computational strategy based on large deviation theory (LDT) is used to study the anomalous statistical features of turbulent surface waves propagating past an abrupt depth change created via a step in the bottom topography. The dynamics of the outgoing waves past the step are modeled using the truncated Korteweg–de Vries equation with random initial conditions at the step drawn from the system’s Gibbs invariant measure of the incoming waves. Within the LDT framework, the probability distributions of the wave height can be obtained via the solution of a deterministic optimization problem. Detailed numerical tests show that this approach accurately captures the non-Gaussian features of the wave height distributions, in particular their asymmetric tails leading to high skewness. These calculations also give the spatiotemporal pattern of the anomalous waves most responsible for these non-Gaussian features. The strategy shows potential for a general class of nonlinear Hamiltonian systems with highly non-Gaussian statistics.

Moho Depth of Northern Baja California, Mexico, From Teleseismic Receiver Functions

AbstractWe estimated Moho depths from data recorded by permanent and temporary broadband seismic stations deployed in northern Baja California, Mexico, using the receiver function technique. This region is composed of two subregions of contrasting geological and topographical characteristics: the Peninsular Ranges of Baja California (PRBC), a batholith with high elevations (up to 2,600 m); and the Mexicali Valley (MV) region, a sedimentary environment close to sea level. Crustal thickness derived from the P‐to‐S converted phases at 29 seismic stations were analyzed in three profiles: Two that cross the two subregions, in ∼W‐E direction, and the third one that runs over the PRBC in a N‐S direction. For the PRBC, Moho depths vary from 35 to 45 km, from 33°N to 32°N; and from 30 to 46 km depth from 32°N to 30.5°N. From a profile that crosses the subregions in the W‐E direction; Moho depths vary from 45 to ∼34 km under western and eastern PRBC, respectively; with an abrupt change of depth under the Main Gulf Escarpment (30°), from ∼32 to 30 km; and depths of 17–20 km under the MV. Moho depths of the profile in an ∼ W‐E direction at ∼31.5°N are from ∼30 to 40 km, under topography that increases from 0 to 2,600 m; and became shallower (16 km depth) as the profile reaches the Gulf of California. These results show that deeper Moho is related to higher elevations with an abrupt change under the Main Gulf Escarpment, except for western PRBC where the Moho depth is not simply reflecting isostatic compensation.

Fast computational depth segmentation using orthogonal fringe patterns without pattern sequence changing.

The recently proposed omnidirectional depth segmentation method (ODSM) has advantages over traditional depth segmentation in terms of robustness and computational costs. However, this method uses at least six fringe patterns and changes their sequences multiple times to perform depth segmentation, which limits its segmentation speed and increases computational complexity. This paper proposes a fast computational depth segmentation (FCDS) method in which only five patterns are used for object segmentation at different depths into isolated regions without the requirement of pattern sequence changing. Phase singularity points are fully utilized due to their significance as depth segmentation markers to extract segmenting lines used for depth determination. Meanwhile, a modified Fourier transform algorithm (MFTA) is introduced to calculate the wrapped phase sequences, which uses two groups of orthogonal phase-shifting fringe patterns and a DC component pattern (five in total). The segmenting lines along orthogonal directions can be extracted with the FCDS method without changing the fringe sequences, which not only solves the problem of phase insensitivity but reduces the calculation costs. Besides, the problem of mis-segmentation is solved with an optimization algorithm for depth segmenting lines and successfully segments objects with abrupt depth changes. The simulation results demonstrate the effectiveness and precision of the proposed method. The experimental results prove the success of the proposed method for segmenting objects of similar color with a segmentation speed that is up to a 120% increase relative to previous methods.

Bayesian network based general correspondence retrieval method for depth sensing with single-shot structured light

This study reinvestigated one of the most fundamental problems in structure light depth sensing field: correspondence retrieval of features between patterns and images. We formulate the global optimum correspondence retrieval by maximizing a conditional probability of correspondence given observed features, which is depicted by a Bayesian network. Different from traditional “code-only” based correspondence retrieval methods, the proposed Bayesian network based method exploits the positional correlations of correspondences of neighboring features, namely, the correspondences of poorly detected features are estimated with the aid of the correspondences of well detected features. The method performs especially well on challenging scenes with rich depth variations, abrupt depth changes, edges, etc. Experiments show that the proposed method increase the correspondence accuracy by about 40% on challenging scenes, compared with traditional “code-only” based correspondence retrieval methods.

Surface wavepackets subject to an abrupt depth change. Part 1. Second-order theory

Abstract

Surface wavepackets subject to an abrupt depth change. Part 2. Experimental analysis

Abstract

Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

Recent laboratory experiments of Bolles et al. (Phys Rev Fluids 4(1):011801, 2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (Proc Natl Acad Sci 116(10):3982–3987, 2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Korteweg-de Vries (TKdV) system that successfully captures key qualitative features of the experiments including the robust emergence of anomalous statistics and heightened skewness in the outgoing wavefield. Here, we extend these parallel experimental and modeling efforts with several new findings that have resulted from a synergetic interaction between the two. By precisely relating model parameters to physical ones, we calibrate the model inverse temperature to the specific conditions present in the experiments, thereby permitting a quantitative comparison. We find theoretically predicted distributions of surface displacement to match the experimental measurements with surprising detail. Prompted by the presence of surface slope in the TKdV Hamiltonian, we present new experimental measurements on surface slope statistics and compare them to model predictions. Analysis of some deterministic trajectories of TKdV elucidates the experimental length and time scales required for the statistical transition to a skewed state. Finally, the theory predicts a peculiar relationship between the outgoing displacement skewness and the change in slope variance, specifically how their ratio depends on the wave amplitude and depth ratio. New experimental measurements provide convincing evidence for this prediction.

Dynamic fracture of CrN coating by highly-resolved nano-impact

Nano-impact testing has provided localized high strain rate deformation information in either (i) repetitive impact for fatigue of brittle materials or (ii) high-resolution data acquisition of single impacts for energy dissipation and dynamic hardness in ductile materials. The current study focusses on whether high-resolution data acquisition can be used to determine fracture occurring during a single impact event. A PVD CrN coating on 42CrMo4 high speed steel (HSS) was impacted with a cube corner indenter over a range of different acceleration forces. By analyzing the high precision depth-time curves during the first contact phase of the impact, an abrupt depth change was observed at and above 30 mN acceleration force. Focused ion beam technology confirmed through-thickness coating fracture without delamination on tests where the step was observed. The step was absent at lower force or on the more ductile HSS throughout the load range. The fracture dissipated energy and fracture toughness of the coating was estimated under 50 mN acceleration force based on the analysis of impact energy. The calculated dynamic fracture toughness of CrN coating is in the range of 2.75–7.74 MPa·m1/2, depended on the indenter geometry constant, which is comparable with the reported value of about 3.13 MPa·m1/2.

Using machine learning to predict extreme events in complex systems

Extreme events and the related anomalous statistics are ubiquitously observed in many natural systems, and the development of efficient methods to understand and accurately predict such representative features remains a grand challenge. Here, we investigate the skill of deep learning strategies in the prediction of extreme events in complex turbulent dynamical systems. Deep neural networks have been successfully applied to many imaging processing problems involving big data, and have recently shown potential for the study of dynamical systems. We propose to use a densely connected mixed-scale network model to capture the extreme events appearing in a truncated Korteweg-de Vries (tKdV) statistical framework, which creates anomalous skewed distributions consistent with recent laboratory experiments for shallow water waves across an abrupt depth change, where a remarkable statistical phase transition is generated by varying the inverse temperature parameter in the corresponding Gibbs invariant measures. The neural network is trained using data without knowing the explicit model dynamics, and the training data are only drawn from the near-Gaussian regime of the tKdV model solutions without the occurrence of large extreme values. A relative entropy loss function, together with empirical partition functions, is proposed for measuring the accuracy of the network output where the dominant structures in the turbulent field are emphasized. The optimized network is shown to gain uniformly high skill in accurately predicting the solutions in a wide variety of statistical regimes, including highly skewed extreme events. The technique is promising to be further applied to other complicated high-dimensional systems.

Statistical Phase Transitions and Extreme Events in Shallow Water Waves with an Abrupt Depth Change

Predicting extreme events in complex nonlinear systems is an extremely challenging and important area in climate science. Important examples include extreme events near coastal continental shelves for shallow and deep water waves. Recent laboratory experiments reveal a remarkable transition from near Gaussian to highly skewed anomalous statistics with extreme events by measuring the surface water wave displacements in shallow water across an abrupt depth change (ADC). A statistical dynamical model has been proposed and used to accurately predict the representative statistical transition using Gibbs invariant measures for the truncated KdV equation at low and high inverse temperatures representing flows before and after the ADC. In this paper, we use much lower dimensional truncated paradigm models to understand the statistical phase transition and the creation of extreme events. Especially, a two-mode interacting model with exact integrable dynamics is adopted to characterize the core transition mechanism as the model parameter varies. The choice of the radically truncated two-mode model is motivated by the self-similar solution structures with reducing numbers of truncated modes. A clear separation of distinct dynamics in the phase space is discovered for the Gibbs ensembles sampled from different inverse temperatures. Direct numerical tests with various model truncation sizes are presented to illustrate the statistical transition in parameter regimes. The analysis here can also provide a theoretical guideline for a wider variety of models concerning the generation of extreme events and anomalous statistics.

Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change

Understanding and predicting extreme events and their anomalous statistics in complex nonlinear systems are a grand challenge in climate, material, and neuroscience as well as for engineering design. Recent laboratory experiments in weakly turbulent shallow water reveal a remarkable transition from Gaussian to anomalous behavior as surface waves cross an abrupt depth change (ADC). Downstream of the ADC, probability density functions of surface displacement exhibit strong positive skewness accompanied by an elevated level of extreme events. Here, we develop a statistical dynamical model to explain and quantitatively predict the above anomalous statistical behavior as experimental control parameters are varied. The first step is to use incoming and outgoing truncated Korteweg-de Vries (TKdV) equations matched in time at the ADC. The TKdV equation is a Hamiltonian system, which induces incoming and outgoing statistical Gibbs invariant measures. The statistical matching of the known nearly Gaussian incoming Gibbs state at the ADC completely determines the predicted anomalous outgoing Gibbs state, which can be calculated by a simple sampling algorithm verified by direct numerical simulations, and successfully captures key features of the experiment. There is even an analytic formula for the anomalous outgoing skewness. The strategy here should be useful for predicting extreme anomalous statistical behavior in other dispersive media.

Anomalous wave statistics induced by abrupt depth change

Laboratory experiments reveal that variations in bottom topography can qualitatively alter the distribution of randomized surface waves. A normally-distributed, unidirectional wave field becomes highly skewed and non-Gaussian upon encountering an abrupt depth transition. A short distance downstream of the transition, wave statistics conform closely to a gamma distribution, affording simple estimates for skewness, kurtosis, and other statistical properties. Importantly, the exponential decay of the gamma distribution is much slower than Gaussian, signifying that extreme events occur more frequently. Under the conditions considered here, the probability of a rogue wave can increase by a factor of 50 or more. We also report on the surface-slope statistics and the spectral content of the waves produced in the experiments.

HARMONIC WAVES ON AN ABRUPT TRANSITION

A simple long-wave reflection and transmission over an abrupt depth change with constant channel width are presented. Firstly, the wave propagation is modeled on a two-step abrupt transition, and the waves are reflected and transmitted only once. The model is extended to include more than one re-reflection and retransmission as well as depth-limited breaking-wave height criteria. The Dean beach profile is also modeled. The profile is a function of the median grain size of the beach material. It is found that the wave energy is conserved when the waves are re-reflected and retransmitted more than five times. The breaking waves reduce the reflection coefficient by 30%. The results are compared with other research on the reflection coefficient occurring in a smooth sloping beach model. On a small sloping beach, an abrupt depth change gives a significant difference in the value of the reflection coefficient. The reflection coefficient on the smooth small sloping beach is close to zero, while the abrupt depth change can increase the reflectioncoefficient to about 60% in this case.

Nonlinear wave dynamics in self-consistent water channels

We study long-wave dynamics in a self-consistent water channel of variable cross-section, taking into account the effects of weak nonlinearity and dispersion. The self-consistency of the water channel is considered within the linear shallow water theory, which implies that the channel depth and width are interrelated, so the wave propagates in such a channel without inner reflection from the bottom even if the water depth changes significantly. In the case of small-amplitude weakly dispersive waves, the reflection from the bottom is also small, which allows the use of a unidirectional approximation. A modified equation for Riemann waves is derived for the nondispersive case. The wave-breaking criterion (gradient catastrophe) for self-consistent channels is defined. If both weak nonlinearity and dispersion are accounted for, the variable-coefficient Korteweg–de Vries (KdV) equation for waves in self-consistent channels is derived. Note that this is the first time that a KdV equation has been derived for waves in strongly inhomogeneous media. Soliton transformation in a channel with an abrupt change in depth is also studied.

Graphene Oxide Demonstrates Experimental Confirmation of Abraham Pressure on Solid Surface

The century-old controversy over two contradicting theories on radiation pressure of light proposed by Abraham and Minkowski can come to an end if there is a direct method to measure the surface deformation of the target material due to momentum transfer of photons. Here we have investigated the effect of radiation pressure on the surface morphology of Graphene Oxide (GO) film, experienced due to low power focused laser irradiation. In-depth investigation has been carried out to probe the bending of the GO surface due to radiation pressure by Atomic Force Microscopy (AFM) and subsequently the uniaxial strain induced on the GO film has been probed by Raman Spectroscopy. Our results show GO film experience an inward pressure due to laser radiation resulting in inward bending of the surface, which is consistent with the Abraham theory. The bending diameter and depth of the irradiated spot show linear dependence with the laser power while an abrupt change in depth and diameter of the irradiated spot is observed at the breaking point. Such abrupt change in depth is attributed to the thinning of the GO film by laser irradiation.

EFFECT OF CHANGE OF COASTAL ZONE DEPTH ON SPECTRUM OF IRREGULAR WAVES

Transformation of the irregular wave spectrum on inhomogenety of bottom surface that is characterized by a sharp change of depth is studied. The normal incidence of waves is considered. The superposition of two TMA spectra, in which the finite depth of fluid is taken into account, with different frequencies of spectral maxima corresponding to surface waves and swell is used as the unidirectional spectrum model of waves. Following RDT (Rapid Distortion Theory) approach, the linear theory for investigating of the spectrum transformation under action of abrupt change of the depth is applied. It is assumed that the modification of spectral components is caused by abrupt change of depth, and nonlinear effects of their interaction are manifested at some distance from the considered region. The expansion of sotution into a series of eigenfunctions is used to solve the boundary-value problem of wave transformation. The dependence of coefficient of transmission of waves over abrupt change of depth on the wave number of incident wave is obtained on the base of the improve reduction method. The features of transformed spectrum for different parameters of the problem are analized. It is shown that spectral amplitudes grow after step and corresponding wave lengths decrease, that is, waves become more steep and can be broken down..

Estimation of Lateral Variations of the Mohorovičić Discontinuity Using 2D Modeling of Receiver Functions

We used 2D finite‐difference modeling and azimuthally binned receiver functions (RFs) to explore whether abrupt offsets in Moho depth can be detected by one or a few closely spaced P ‐wave RFs. Our results show that 2D synthetic RFs generated in the immediate vicinity above a Moho depth change can provide important clues to the abruptness of the offset. In particular, diffraction of the waves impinging onto the Moho offset may generate a split P S arrival, causing systematic variation of peak‐to‐peak P ‐ P S delay times with increasing ray parameter, depending on the location relative to the Moho offset and the incidence direction of the RFs. We outline an approach using a slant‐stack method to constrain the location of a relatively abrupt depth change of Moho (![Graphic][1] ) using separate RF stacks incident from opposite directions. For a station located on the western border of the Caspian Sea in Azerbaijan (LKR), our 2D models with an ∼8 km transition from a shallower Moho to the east and deeper Moho to the west generate synthetic RFs with features in general agreement with observations. These models, which include step‐ and ramp‐like offsets of Moho, are in general agreement with estimates of crustal thickness from seismic data. Thus, our results suggest that characteristics in one or a few azimuthally binned radial P ‐wave RFs can be used in concert with a slant‐stack analysis to pinpoint a relatively abrupt change in underlying Moho depth. Online Material: Discussion and figures of a verification study of receiver functions (RFs) computed by different methods, crustal phases generated in our 2D model using animations of the simulated wave propagations, as well as estimated crustal structures, and RFs for Moho offset models, including realistic levels of noise. [1]: /embed/inline-graphic-1.gif