2D Kernel Research Articles

Estrategias computacionales para la implementación de modelado elástico 2D sobre GPU

El modelado de onda elástico presenta un reto de implementación debido a que es un procedimiento computacionalmente costoso. En la actualidad, debido al incremento en la potencia en GPU junto con el desarrollo de la computación HPC, es posible ejecutar modelado elástico con mejores tiempos de ejecución y uso de memoria. Este estudio evalúa el desempeño de 2 estrategias para implementar modelado elástico usando diferentes diseños para ejecución de kernel, estrategias de asignación de memoria para el cálculo de CPML y administración del almacenamiento del campo de onda. Las mediciones de desempeño muestran que el algoritmo que incluye diseño de ejecución de kernel 2D, la estrategia de memoria reducida CPML y el almacenamiento en memoria global de GPU del campo de onda alcanza un máximo de 88.4% mejor tiempo de ejecución y utiliza un 13.3 veces menos memoria para obtener los mismos resultados de modelado elástico. Existe también una creciente tendencia de mejora de tiempo de ejecución y ahorro de memoria cuando se trabaja con modelos de tamaños más grandes con esta estrategia.

Kernel two-dimensional ridge regression for subspace clustering

Subspace clustering methods have been extensively studied in recent years. For 2-dimensional (2D) data, existing subspace clustering methods usually convert 2D examples to vectors, which severely damages inherent structural information and relationships of the original data. In this paper, we propose a novel subspace clustering method, named KTRR, for 2D data. The KTRR provides us with a way to learn the most representative 2D features from 2D data in learning data representation. In particular, the KTRR performs 2D feature learning and low-dimensional representation construction simultaneously, which renders the two tasks to mutually enhance each other. 2D kernel is introduced to the KTRR, which renders the KTRR to have enhanced capability of capturing nonlinear relationships from data. An efficient algorithm is developed for its optimization with provable decreasing and convergent property in objective value. Extensive experimental results confirm the effectiveness and efficiency of our method.

An implicit 3D corotational formulation for frictional contact dynamics of beams against rigid surfaces using discrete signed distance fields

The interaction of beam-like structures against surfaces is a challenging problem with applications in engineering (wheel–rail contact, pipeline–soil interaction, ropes sliding on the seabed) and in medical applications such as surgical planning and training (catheter navigation, aneurysm coiling, stent deployment). This contact problem is traditionally solved using Total Lagrangian beam formulations, which interact against Lagrangian triangulated surfaces. Overall, the computational speed is affected, due to the nonlinearities of the beam formulation and, as well as due to the expensive search algorithms, required to find the close point projection. In the search towards an efficient beam to surface contact algorithm, this paper explores the combined use of (1) a corotational beam formulation, where the motion of the beam element is decomposed in rigid body and pure deformational parts and (2) an implicit description of the surface by means of discrete signed distance fields (SDF), which can be seen as a Lagrangian beam immersed within an Eulerian (rigid) solid. To do so, a previously reported implicit corotational formulation for beam dynamics is modified to account for frictional contact, by means of a penalty term. The new contributions are fully linearized to update the tangent operator and the system is integrated in time by means of the HHT-α method. Overall, a consistent implicit contact dynamics formulation is provided. A SDF, defined in a voxel-type grid, is used to represent implicitly the surface geometry. The SDF values and derivatives are computed at the Lagrangian point of integration of the beam by means of an efficient tensor product of compact, high order, 1D Kernels, as widely used in immersed Fluid–Structure Interaction techniques. A wide variety of validation tests are presented which prove the accuracy and robustness of the proposed algorithm.

Standardizing Single-Frame Phase Singularity Identification Algorithms and Parameters in Phase Mapping During Human Atrial Fibrillation.

PurposeRecent investigations failed to reproduce the positive rotor-guided ablation outcomes shown by initial studies for treating persistent atrial fibrillation (persAF). Phase singularity (PS) is an important feature for AF driver detection, but algorithms for automated PS identification differ. We aim to investigate the performance of four different techniques for automated PS detection.Methods2048-channel virtual electrogram (VEGM) and electrocardiogram signals were collected for 30 s from 10 patients undergoing persAF ablation. QRST-subtraction was performed and VEGMs were processed using sinusoidal wavelet reconstruction. The phase was obtained using Hilbert transform. PSs were detected using four algorithms: (1) 2D image processing based and neighbor-indexing algorithm; (2) 3D neighbor-indexing algorithm; (3) 2D kernel convolutional algorithm estimating topological charge; (4) topological charge estimation on 3D mesh. PS annotations were compared using the structural similarity index (SSIM) and Pearson’s correlation coefficient (CORR). Optimized parameters to improve detection accuracy were found for all four algorithms using Fβ score and 10-fold cross-validation compared with manual annotation. Local clustering with density-based spatial clustering of applications with noise (DBSCAN) was proposed to improve algorithms 3 and 4.ResultsThe PS density maps created by each algorithm with default parameters were poorly correlated. Phase gradient threshold and search radius (or kernels) were shown to affect PS detections. The processing times for the algorithms were significantly different (p < 0.0001). The Fβ scores for algorithms 1, 2, 3, 3 + DBSCAN, 4 and 4 + DBSCAN were 0.547, 0.645, 0.742, 0.828, 0.656, and 0.831. Algorithm 4 + DBSCAN achieved the best classification performance with acceptable processing time (2.0 ± 0.3 s).ConclusionAF driver identification is dependent on the PS detection algorithms and their parameters, which could explain some of the inconsistencies in rotor-guided ablation outcomes in different studies. For 3D triangulated meshes, algorithm 4 + DBSCAN with optimal parameters was the best solution for real-time, automated PS detection due to accuracy and speed. Similarly, algorithm 3 + DBSCAN with optimal parameters is preferred for uniform 2D meshes. Such algorithms – and parameters – should be preferred in future clinical studies for identifying AF drivers and minimizing methodological heterogeneities. This would facilitate comparisons in rotor-guided ablation outcomes in future works.

A 2D kernel determination problem in a visco‐elastic porous medium with a weakly horizontally inhomogeneity

We consider a system of hyperbolic integro‐differential equations of SH waves in a visco‐elastic porous medium. In this work, it is assumed that the visco‐elastic porous medium has weakly horizontally inhomogeneity. The direct problem is the initial‐boundary problem: the initial data is equal to zero, and the Neumann‐type boundary condition is specified at the half‐plane boundary and is an impulse function. As additional information, the oscillation mode of the half‐plane line is given. It is assumed that the unknown kernel has the form K(x,t)=K0(t)+ϵxK1(t)+…, where ϵ is a small parameter. In this work, we construct a method for finding K0,K1 up to a correction of the order of O(ϵ2).

The Problem of Determining the 2D Kernel in a System of Integro-Differential Equations of a Viscoelastic Porous Medium

The Problem of Determining the 2D Kernel in a System of Integro-Differential Equations of a Viscoelastic Porous Medium

2D or not 2D? Three-dimensional home range analysis better represents space use by an arboreal mammal

For animals which utilise vertically distributed habitat resources, home ranges quantified in two-dimensions (2D) likely misrepresent space use and constrain interpretations of species' ecology and behaviour. Three-dimensional (3D) home range estimation has proved useful for understanding space use over relatively large vertical ranges (e.g. 100's of meters), yet none have applied a 3D approach to describe space use over narrower vertical ranges (e.g. meters or 10's of metres) typical for many arboreal animals. This study demonstrates 3D home range estimation for the arboreal western ringtail possum (Pseudocheirus occidentalis) using temporally resolute locations (15 min intervals) of five radio collared animals. We hypothesised that, due to the use of vertically distributed habitat resources, 3D home ranges would be more complex, spanning a range of heights, and would subsequently be larger in size compared to those estimates derived from typical 2D analysis. A comparison of 50% (core) and 95% (total) 2D kernel density and 3D kernel density utilisation distributions reveal structurally complex home ranges that span the entire vertical range of vegetated habitat. Estimates of the total 3D home range size were significantly greater than those derived from 2D analysis, and the difference in size was positively related to the vertical range of available habitat. This study establishes that 3D home range analysis can reveal information on vertical space use of arboreal species over relatively small vertical ranges, and is likely to be valuable in understanding the use and identification of key habitats and resources, as well as interactions among sympatric species.

Estimation of reservoir porosity based on seismic inversion results using deep learning methods

Location limitation of logged wells restricts the porosity estimation across the whole reservoir target, whereas seismic data are always collected to cover larger areas. In this paper, inversion results of seismic data are proposed as inputs for the prediction of reservoir porosity, even though the resolution is decreased, compared with well-log readings. The non-linear inversion scheme used is able to explore the complex relationship between rock properties and seismic data, which could potentially provide a higher quality of inversion results. As a regression process, Convolutional Neural Networks is then applied to estimate the reservoir porosity, based on the outputs of seismic inversion scheme. Incorporating 2D kernel filters which are convolved with input rock properties, the local information inside filters window is considered, and a better prediction performance is to be guaranteed. This is due to the fact that reservoir porosity is formed under depositional and digenetic rules, and it is intrinsically correlated with rock properties along the vertical direction in a short range. The designed workflow is applied to a real dataset from the Vienna Basin where compressibility and shear compliance are inverted and then used as inputs for the porosity estimation by Convolutional Neural Networks. For a comparison, the traditional Artificial Neural Networks is also trained and applied to the same dataset. It is concluded that the Convolutional Neural Networks can achieve a higher accuracy, and a 3D cube of reservoir porosity is obtained without location restriction of well logs.

High-Density Surface EMG-Based Gesture Recognition Using a 3D Convolutional Neural Network.

High-density surface electromyography (HD-sEMG) and deep learning technology are becoming increasingly used in gesture recognition. Based on electrode grid data, information can be extracted in the form of images that are generated with instant values of multi-channel sEMG signals. In previous studies, image-based, two-dimensional convolutional neural networks (2D CNNs) have been applied in order to recognize patterns in the electrical activity of muscles from an instantaneous image. However, 2D CNNs with 2D kernels are unable to handle a sequence of images that carry information concerning how the instantaneous image evolves with time. This paper presents a 3D CNN with 3D kernels to capture both spatial and temporal structures from sequential sEMG images and investigates its performance on HD-sEMG-based gesture recognition in comparison to the 2D CNN. Extensive experiments were carried out on two benchmark datasets (i.e., CapgMyo DB-a and CSL-HDEMG). The results show that, where the same network architecture is used, 3D CNN can achieve a better performance than 2D CNN, especially for CSL-HDEMG, which contains the dynamic part of finger movement. For CapgMyo DB-a, the accuracy of 3D CNN was 1% higher than 2D CNN when the recognition window length was equal to 40 ms, and was 1.5% higher when equal to 150 ms. For CSL-HDEMG, the accuracies of 3D CNN were 15.3% and 18.6% higher than 2D CNN when the window length was equal to 40 ms and 150 ms, respectively. Furthermore, 3D CNN achieves a competitive performance in comparison to the baseline methods.

An optimized deep convolutional neural network for dendrobium classification based on electronic nose

This paper introduces an optimized deep convolutional neural network (DCNN) using special banded 1D kernels at the convolutional and the pooling layers adapted for electronic nose (E-nose) data. It is used to classify multiple types of Chinese herbal medicine. The optimized DCNN network is composed of 5 special convolutional layers with 1D convolutional kernels, 2 special pooling layers with 1D size, 1 fully connected layer and 1 Softmax layer. Results show that the optimized DCNN achieves the best accuracy of 87.56%, outperforming the 81.67% from the second-best classifier DCNN. The optimized DCNN extracts features from E-nose data faster and better than common DCNN. This paper also proposes an insight of applying DCNN to small-scale and E-nose data.

Triplanar convolution with shared 2D kernels for 3D classification and shape retrieval

Increasing the depth of Convolutional Neural Networks (CNNs) has been recognized to provide better generalization performance. However, in the case of 3D CNNs, stacking layers increases the number of learnable parameters linearly, making it more prone to learn redundant features. In this paper, we propose a novel 3D CNN structure that learns shared 2D triplanar features viewed from the three orthogonal planes, which we term S3PNet. Due to the reduced dimension of the convolutions, the proposed S3PNet is able to learn 3D representations with substantially fewer learnable parameters. Experimental evaluations show that the combination of 2D representations on the different orthogonal views learned through the S3PNet is sufficient and effective for 3D representation, with the results outperforming current methods based on fully 3D CNNs. We support this with extensive evaluations on widely used 3D data sources in computer vision: CAD models, LiDAR point clouds, RGB-D images, and 3D Computed Tomography scans. Experiments further demonstrate that S3PNet has better generalization capability for smaller training sets, and learns more of kernels with less redundancy compared to kernels learned from 3D CNNs.

Noise-Resilient Training Method for Face Landmark Generation From Speech

Visual cues such as lip movements, when available, play an important role in speech communication. They are especially helpful for the hearing impaired population or in noisy environments. When not available, having a system to automatically generate talking faces in sync with input speech would enhance speech communication and enable many novel applications. In this article, we present a new system that can generate 3D talking face landmarks from speech in an online fashion. We employ a neural network that accepts the raw waveform as an input. The network contains convolutional layers with 1D kernels and outputs the active shape model (ASM) coefficients of face landmarks. To promote smoother transitions between video frames, we present a variant of the model that has the same architecture but also accepts the previous frame's ASM coefficients as an additional input. To cope with background noise, we propose a new training method to incorporate speech enhancement ideas at the feature level. Objective evaluations on landmark prediction show that the proposed system yields statistically significantly smaller errors than two state-of-the-art baseline methods on both a single-speaker dataset and a multi-speaker dataset. Experiments on noisy speech input with five types of non-stationary unseen noise show statistically significant improvements of the system performance thanks to the noise-resilient training method. Finally, subjective evaluations show that the generated talking faces have a significantly more convincing match with the input audio, achieving a similarly convincing level of realism as the ground-truth landmarks.

CNN-Based Learnable Gammatone Filterbank and Equal-Loudness Normalization for Environmental Sound Classification

For environmental sound classification (ESC), this letter presents a learnable auditory filterbank based on a one-dimensional (1D) convolutional neural network with strong psychophysiological inductive bias in the form of a gammatone filterbank and an equal-loudness prompting normalization. In the past, a number of ESC methods based on learnable auditory features obtained by performing plain 1D convolutions on raw input waveforms for outperforming traditional handcrafted features such as a mel-frequency filterbank have been proposed. However, the large number of parameters involved in the convolutions suggests that these methods will not generalize better than a model defined by a smaller number of parameters, which is considered in this letter. Here, a learnable gammatone filterbank layer consisting of 1D kernels represented by a parametric form of the bandpass gammatone filters is proposed for acquiring a time-frequency representation of the raw waveform. A normalization with learnable parameters that control the trade-off between energy equalization and structure preservation in the spectro-temporal domain is proposed. To verify the effectiveness of the considered network and the normalization, ESC experiments on the ESC-50 and UrbanSound8K datasets were conducted. Compared to other state-of-the-art networks, the considered network performed better on the two datasets. In addition, an ensemble architecture achieved further performance improvement.

Pre-defined Sparsity for Low-Complexity Convolutional Neural Networks

The high energy cost of processing deep convolutional neural networks impedes their ubiquitous deployment in energy-constrained platforms such as embedded systems and IoT devices. This article introduces convolutional layers with pre-defined sparse 2D kernels that have support sets that repeat periodically within and across filters. Due to the efficient storage of our periodic sparse kernels, the parameter savings can translate into considerable improvements in energy efficiency due to reduced DRAM accesses, thus promising significant improvements in the trade-off between energy consumption and accuracy for both training and inference. To evaluate this approach, we performed experiments with two widely accepted datasets, CIFAR-10 and Tiny ImageNet in sparse variants of the ResNet18 and VGG16 architectures. Compared to baseline models, our proposed sparse variants require up to ~82% fewer model parameters with 5.6× fewer FLOPs with negligible loss in accuracy for ResNet18 on CIFAR-10. For VGG16 trained on Tiny ImageNet, our approach requires 5.8× fewer FLOPs and up to ~83.3% fewer model parameters with a drop in top-5 (top-1) accuracy of only 1.2% (~2.1%). We also compared the performance of our proposed architectures with that of ShuffleNet and MobileNetV2. Using similar hyperparameters and FLOPs, our ResNet18 variants yield an average accuracy improvement of ~2.8%.

Convolutional neural networks for classification of music-listening EEG: comparing 1D convolutional kernels with 2D kernels and cerebral laterality of musical influence

This paper highlights the ability of convolutional neural networks (CNNs) at classifying EEG data listening to different kinds of music without the requirement for handcrafted features. Deep learning architectures presented in this paper include CNN of different depths and different convolutional kernels. Support vector machine (SVM) taking in EEG features describing the frequency spectrum, signal regularity, and cross-channel correlation has been applied for performance comparison with CNN. The best performing CNN model presented in this paper achieves the tenfold cross-validation (CV) binary classification average accuracy of 98.94% (validation) and 97.46% (test), and the tenfold CV three-class classification accuracy of 97.68% (validation) and 95.71% (test). In comparison, the SVM classifier achieves tenfold CV binary classification accuracy of 80.23% (validation). The CNN model presented is able to not only differentiate EEG of subjects listening to music from that of subjects without auditory input, but it is also capable of accurately differentiating the EEG of subjects listening to different music. In the context of designing neural computing models for EEG analysis, this paper shows that decomposing two-dimensional spatiotemporal convolutional kernels into separate one-dimensional spatial and one-dimensional temporal kernels significantly reduces the number of trainable parameters (size) of the model while retaining the classification performance. This finding is useful, especially in designing CNN for memory-critical embedded systems for EEG processing. In neurological aspect, auditory stimulus is found to have altered the EEG pattern of the frontal lobe and the left cerebral hemisphere more than the other brain regions.

Multi-projection deep learning network for segmentation of 3D medical images

Segmentation of three-dimensional (3D) medical images using deep learning is a challenging task due to the lack of a 3D medical image dataset and their ground truth, resource memory limitations, and imbalanced dataset problem. In this paper, we propose advanced deep learning network for segmentation of 3D medical images. The proposed Multi-projection Network can preserve resource memory by applying two-dimensional (2D) kernels while still obtaining the 3D information from the image by incorporating slices from different planar projections of the 3D image to achieve good segmentation results. The proposed network uses a weighted cost function to address the imbalanced dataset problem and introduces an adaptive weight that considers the probability of each class in the image. The experimental results showed that the proposed Multi-projection Network can produce the highest sensitivity (true positive rate) compared to other architectures despite the high class imbalance in the dataset and small amount of training data.

On the Nonlinearity of Winter Northern Hemisphere Atmospheric Variability

Abstract Nonlinearity in the Northern Hemisphere’s wintertime atmospheric flow is investigated from both an intermediate-complexity model of the extratropics and reanalyses. A long simulation is obtained using a three-level quasigeostrophic model on the sphere. Kernel empirical orthogonal functions (EOFs), which help delineate complex structures, are used along with the local flow tendencies. Two fixed points are obtained, which are associated with strong bimodality in two-dimensional kernel principal component (PC) space, consistent with conceptual low-order dynamics. The regimes reflect zonal and blocked flows. The analysis is then extended to ERA-40 and JRA-55 using daily sea level pressure (SLP) and geopotential heights in the stratosphere (20 hPa) and troposphere (500 hPa). In the stratosphere, trimodality is obtained, representing disturbed, displaced, and undisturbed states of the winter polar vortex. In the troposphere, the probability density functions (PDFs), for both fields, within the two-dimensional (2D) kernel EOF space are strongly bimodal. The modes correspond broadly to opposite phases of the Arctic Oscillation with a signature of the negative North Atlantic Oscillation (NAO). Over the North Atlantic–European sector, a trimodal PDF is also obtained with two strong and one weak modes. The strong modes are associated, respectively, with the north (or +NAO) and south (or −NAO) positions of the eddy-driven jet stream. The third weak mode is interpreted as a transition path between the two positions. A climate change signal is also observed in the troposphere of the winter hemisphere, resulting in an increase (a decrease) in the frequency of the polar high (low), consistent with an increase of zonal flow frequency.

Bimodality of hemispheric winter atmospheric variability via average flow tendencies and kernel EOFs

The topic of the existence of planetary winter circulation regimes has gone through a long debate. This article contributes to this debate by investigating nonlinearity in a 3-level quasi-geostrophic model and the Japanese JRA-55 reanalysis. The method uses averaged flow tendencies and kernel principal component (PC) analysis. Within two-dimensional (2D) kernel PCs the model reveals two fixed (or stationary) points. The probability density function (PDF) within this space is strongly bimodal where the modes match the regions of low tendencies in consistency with low-order conceptual models. The circulation regimes represent respectively zonal and blocked flows. Application to daily winter northern hemisphere sea level pressure and 500-hPa geopotential height yields strong bimodal PDFs. The modes represent respectively polar highs and lows with signatures of North Atlantic Oscillation. A clear climate change signal is observed showing a clear reduction (increase) of occurrence probability of polar high (low), translating into an increase of probability of zonal flow. Relation of the climate change signal to the polar amplification hypothesis is discussed.

Deep Motion-Appearance Convolutions for Robust Visual Tracking

Visual tracking is a challenging task due to unconstrained appearance variations and dynamic surrounding backgrounds, which basically arise from the complex motion of the target object. Therefore, the information and the correlation between the target motion and its resulting appearance should be considered comprehensively to achieve robust tracking performance. In this paper, we propose a deep neural network for visual tracking, namely the Motion-Appearance Dual (MADual) network, which employs a dual-branch architecture, by using deep two-dimensional (2D) and deep three-dimensional (3D) convolutions to integrate the local and global information of the target object's motion and appearance synchronously. For each frame of a tracking video, 2D convolutional kernels of the deep 2D branch slide over the frame to extract its global spatial-appearance features. Meanwhile, 3D convolutional kernels of the deep 3D branch are used to collaboratively extract the appearance and the associated motion features of the visual target from successive frames. By sliding the 3D convolutional kernels along a video sequence, the model is able to learn the temporal features from previous frames, and therefore, generate the local patch-based motion patterns of the target. Sliding the 2D kernels on a frame and the 3D kernels on a frame cube synchronously enables a better hierarchical motion-appearance integration, and boosts the performance for the visual tracking task. To further improve the tracking precision, an extra ridge-regression model is trained for the tracking process, based not only on the bounding box given in the first frame, but also on its synchro-frame-cube using our proposed Inverse Temporal Training method (ITT). Extensive experiments on popular benchmark datasets, OTB2013, OTB50, OTB2015, UAV123, TC128, VOT2015 and VOT2016, demonstrate that the proposed MADual tracker performs favorably against many state-of-the-art methods.

Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis

We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and postmultiplication by plane waves. It is shown to converge exponentially in the polynomial degree and supports multilevel approximation techniques. Our convergence analysis may be employed to establish exponential convergence of certain classes of fast methods for discretizations of the Helmholtz integral operator that feature polylogarithmic-linear complexity.