Sparse Boundary Research Articles

IMESH: A DSL for Mesh Processing

Mesh processing algorithms are often communicated via concise mathematical notation (e.g., summation over mesh neighborhoods). However, conversion of notation into working code remains a time-consuming and error-prone process, which requires arcane knowledge of low-level data structures and libraries—impeding rapid exploration of high-level algorithms. We address this problem by introducing a domain-specific language (DSL) for mesh processing called I MESH, which resembles notation commonly used in visual and geometric computing and automates the process of converting notation into code. The centerpiece of our language is a flexible notation for specifying and manipulating neighborhoods of a cell complex, internally represented via standard operations on sparse boundary matrices. This layered design enables natural expression of algorithms while minimizing demands on a code generation backend. In particular, by integrating I MESH with the linear algebra features of the I LA DSL and adding support for automatic differentiation, we can rapidly implement a rich variety of algorithms on point clouds, surface meshes, and volume meshes.

Global probability distribution structure-sparsity filter pruning for edge fault diagnosis in resource constrained wireless sensor networks

In this paper, a global probability distribution structure-sparsity filter pruning is proposed to address the problem of difficult deployment of diagnostic models in resource constrained wireless sensor networks (WSNs) for edge fault diagnosis. Firstly, local and global weight distributions are analyzed. A global probability distribution weight sparsity method is proposed to obtain the global sparse boundary and the important features of the model. Secondly, according to the distribution of weight amplitude, the problem of uneven weight distribution is disclosed. A computational acceleration sensing method is proposed to reduce the high computational cost caused by small weight amplitude with low importance estimation. Moreover, a novel layer filter clustering pruning scheme is proposed. The intra-layer filters are classified and redundant filters are removed by using the clustering idea according to the predetermined pruning rate. Thus, the structure-sparsity filter pruning is realized. Compared with other advanced filter pruning methods, the proposed method analyzes the global and local model weight distribution and the influence of weight importance on the computational complexity of the model. The proposed method then performs filter pruning on the importance of overall filters for each network layer rather than individual filters. The accuracy of the proposed method on experimental dataset for pruned ResNet8 model under pruning rate at 0.95 is 99.12% with 3.668K parameters and 3.636MFLOPs. The experimental results elucidate that the proposed method is more suitable for deployment in resource-constrained WSNs for fault diagnosis of rotating machinery. This provides a potential solution for practical engineering applications.

Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct dynamic sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

New type of the unique continuation property for a fractional diffusion equation and an inverse source problem

In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established.

CLASH: Complementary Learning with Neural Architecture Search for Gait Recognition.

Gait recognition, which aims at identifying individuals by their walking patterns, has achieved great success based on silhouette. The binary silhouette sequence encodes the walking pattern within the sparse boundary representation. Therefore, most pixels in the silhouette are under-sensitive to the walking pattern since the sparse boundary lacks dense spatial-temporal information, which is suitable to be represented with dense texture. To enhance the sensitivity to the walking pattern while maintaining the robustness of recognition, we present a Complementary Learning with neural Architecture SearcH (CLASH) framework, consisting of walking pattern sensitive gait descriptor named dense spatial-temporal field (DSTF) and neural architecture search based complementary learning (NCL). Specifically, DSTF transforms the representation from the sparse binary boundary into the dense distance-based texture, which is sensitive to the walking pattern at the pixel level. Further, NCL presents a task-specific search space for complementary learning, which mutually complements the sensitivity of DSTF and the robustness of the silhouette to represent the walking pattern effectively. Extensive experiments demonstrate the effectiveness of the proposed methods under both in-the-lab and in-the-wild scenarios. On CASIA-B, we achieve rank-1 accuracy of 98.8%, 96.5%, and 89.3% under three conditions. On OU-MVLP, we achieve rank-1 accuracy of 91.9%. Under the latest in-the-wild datasets, we outperform the latest silhouette-based methods by 16.3% and 19.7% on Gait3D and GREW, respectively.

Optimal sparse boundary control of cardiac defibrillation

This paper studies the feasibility of optimal sparse boundary control of the bidomain-bath model in cardiac electrophysiology. We incorporated the Luo–Rudy phase I (LR-I) ventricular action potential model, which accounts for more biophysical details of cellular dynamics. The boundary optimal control framework involves a standard quadratic objective functional that is to be minimized and the L1-norm of the control accounting for the sparsity. The existence of the bidomain-bath model using the LR-I is demonstrated, and the derivation of the first-order optimality system is shown. Then we provide the well-posedness and the sparsity of the optimal control problem. The numerical realization of such a boundary control framework for a successful defibrillation study is demonstrated.

Cross-scale Graph Interaction Network for Semantic Segmentation of Remote Sensing Images

Semantic segmentation of remote sensing (RS) images plays a vital role in a variety of fields, including urban planning, natural disaster monitoring, and land resource management. Due to the complexity and low resolution of RS images, many approaches have been proposed to handle the related task. However, these previously developed approaches dedicate to contextual interaction but ignore the cross-scale semantic correlation and multi-scale boundary information. Therefore, we propose a Cross-scale Graph Interaction Network (CGIN) to address semantic segmentation problems of RS images, which consists of a semantic branch and a boundary branch. In the semantic branch, we first apply atrous convolution to extract multi-scale semantic features of RS images. Particularly, based on the multi-scale semantic features, a Cross-scale Graph Interaction (CGI) module is introduced, which establishes cross-scale graph structures and performs adaptive graph reasoning to capture the cross-scale semantic correlation of RS objects. In the boundary branch, we propose a Multi-scale Boundary Feature Extraction (MBFE) module that utilizes atrous convolutions with different dilation rates to extract multi-scale boundary features. Finally, to address the problem of sparse boundary pixels in the fusion process of the two branches, we propose a Multi-scale Similarity-guided Aggregation (MSA) module by calculating the similarity of semantic features and boundary features at the corresponding scale, which can emphasize the boundary information in semantic features. Our proposed CGIN outperforms state-of-the-art approaches in numerical experiments conducted on two benchmark remote sensing datasets.

Crack identification using smart paint and machine learning

Information on the presence and location of cracks in civil structures can be precious to support operators in making decisions related to structural management and scheduling informed maintenance. This paper investigates the efficacy of supervised machine learning to solve the inverse electrical impedance tomography problem and to reconstruct the conductivity distribution of a piezoresistive sensing film. This film consists of a conductive paint applied onto structural components, and operators can use its conductivity distribution to identify crack sizes and locations in the underlying structure. A deep neural network is employed to reconstruct a dense conductivity distribution within the painted area by using only voltage measurements collected at sparse boundary locations. Since one of the most challenging aspects of using supervised learning tools for real-world applications is generating a representative training dataset, this paper presents a new approach to test the suitability of synthetic datasets built using a finite element model of the sensing film. Results are reported for four sensing specimens fabricated with two different techniques (i.e., using carbon nanotubes and graphene nanosheets, respectively). Crack-like damage is induced to the substrate of the sensing film and identified using the proposed machine learning technique. Promising results are obtained as compared to conventional methods.

A Semantics-Geometry Framework for Road Extraction From Remote Sensing Images

Road extraction from remote sensing images in very high resolution is important for autonomous driving and road planning. Compared with large-scale objects, roads are smaller, winding, and likely to be covered by buildings’ shadows, causing deep convolutional neural networks (DCNNs) to be difficult to identify roads. The paper proposes a semantics-geometry framework (SGNet) with a two-branch backbone, i.e., semantics-dominant branch and geometry-dominant branch. The semantics-dominant branch inputs images to predict dense semantic features, and the geometry-dominant branch takes images to generate sparse boundary features. Then, dense semantic features and boundary details generated by two branches are adaptively fused. Further, by utilizing affinity between neighborhood pixels, a feature refinement module is proposed to refine textures and road details. We evaluate the SGNet on the Ottawa road dataset. Experiments show that the SGNet outperforms other competitors on the road extraction task. Codes is available at https://github.com/qiuluyi/SGNet.

Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely determine the semi-discrete source. This means the observed area can be extremely small, and that is the reason we call it sparse boundary data. For the numerical reconstruction, we formulate the problem from the Bayesian sequential prediction perspective and conduct the numerical examples which estimate the space-time-dependent source state by state. To better demonstrate the method’s performance, we solve two common multiscale problems from two models with a long source sequence. The numerical results illustrate that the inversion is accurate and efficient.

Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By using a sequence of harmonic functions, we construct useful quantitative relation between the unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.

Domain Generalization for Named Entity Boundary Detection via Metalearning.

Named entity recognition (NER) aims to recognize mentions of rigid designators from text belonging to predefined semantic types, such as person, location, and organization. In this article, we focus on a fundamental subtask of NER, named entity boundary detection, which aims at detecting the start and end boundaries of an entity mention in the text, without predicting its semantic type. The entity boundary detection is essentially a sequence labeling problem. Existing sequence labeling methods either suffer from sparse boundary tags (i.e., entities are rare and nonentities are common) or they cannot well handle the issue of variable size output vocabulary (i.e., need to retrain models with respect to different vocabularies). To address these two issues, we propose a novel entity boundary labeling model that leverages pointer networks to effectively infer boundaries depending on the input sequence. On the other hand, training models on source domains that generalize to new target domains at the test time are a challenging problem because of the performance degradation. To alleviate this issue, we propose Metabdry, a novel domain generalization approach for entity boundary detection without requiring any access to target domain information. Especially, adversarial learning is adopted to encourage domain-invariant representations. Meanwhile, metalearning is used to explicitly simulate a domain shift during training so that metaknowledge from multiple resource domains can be effectively aggregated. As such, Metabdry explicitly optimizes the capability of "learning to generalize," resulting in a more general and robust model to reduce the domain discrepancy. We first conduct experiments to demonstrate the effectiveness of our novel boundary labeling model. We then extensively evaluate Metabdry on eight data sets under domain generalization settings. The experimental results show that Metabdry achieves state-of-the-art results against the recent seven baselines.

On the full-waveform inversion of seismic moment tensors

In this work, we propose a full-waveform technique for the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion. The approach is formulated in the frequency domain, and it allows for the simultaneous inversion of multiple point-like events. In the core of the proposed methodology is a grid search for the source locations that encapsulates the optimality condition on the respective moment tensors. The developments cater for compactly supported elastic bodies in R2; however our framework is directly extendable to inverse (seismic) source problems in R3 involving both bounded and unbounded elastic domains. A set of numerical results, targeting laboratory applications, is included to illustrate the performance of the inverse solution in situations involving: (i) reconstruction of multiple events, (ii) sparse (pointwise) boundary measurements, (iii) “off-grid” location of the micro-seismic events, and (iv) inexact knowledge of the medium’s elastic properties.

Contour evolution method for precise boundary delineation of medical images

Image segmentation is an important precursor to boundary delineation of medical images. One of the major challenges in applying automatic image segmentation in medical images is the imperfection in the imaging process which can result in inconsistent contrast and brightness levels, and low image sharpness and vanishing boundaries. Although recent advances in deep learning produce vast improvements in the quality of image segmentation, the accuracy of segmentation around object boundaries still requires improvement. We developed a new approach to contour evolution that is more intuitive but shares some common principles with the active contour model method. The method uses two concepts, namely the boundary grid and sparse boundary representation, as an implicit and explicit representation of the boundary points. We tested our method using lumbar spine MRI images of 515 patients. The experiment results show that our method performs up to 10.2 times faster and more flexible than the geodesic active contours method. Using BF-score contour-based metric, we show that our method improves the boundary accuracy from 74% to 84% as opposed to 63% by the latter method.

Neural Text Segmentation and its Application to Sentiment Analysis

Text segmentation is a fundamental task in natural language processing. Depending on the levels of granularity, the task can be defined as segmenting a document into topical segments, or segmenting a sentence into elementary discourse units (EDUs). Traditional solutions to the two tasks heavily rely on carefully designed features. The recently proposed neural models do not need manual feature engineering, but they either suffer from sparse boundary tags or cannot efficiently handle the issue of variable size output vocabulary. In light of such limitations, we propose a generic end-to-end segmentation model, namely <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> , which first uses a bidirectional recurrent neural network to encode an input text sequence. <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> then uses another recurrent neural networks, together with a pointer network, to select text boundaries in the input sequence. In this way, <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> does not require any hand-crafted features. More importantly, <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> inherently handles the issue of variable size output vocabulary and the issue of sparse boundary tags. In our experiments, <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> outperforms state-of-the-art models on two tasks: document-level topic segmentation and sentence-level EDU segmentation. As a downstream application, we further propose a hierarchical attention model for sentence-level sentiment analysis based on the outcomes of <inline-formula><tex-math notation="LaTeX">${\mathrm{S}\scriptstyle{\mathrm{EG}}}{\mathrm{B}\scriptstyle{\mathrm{OT}}}$</tex-math></inline-formula> . The hierarchical model can make full use of both word-level and EDU-level information simultaneously for sentence-level sentiment analysis. In particular, it can effectively exploit EDU-level information, such as the inner properties of EDUs, which cannot be fully encoded in word-level features. Experimental results show that our hierarchical model achieves new state-of-the-art results on the Movie Review and Stanford Sentiment Treebank benchmarks.

Neural Named Entity Boundary Detection

In this paper, we focus on named entity boundary detection, which is to detect the start and end boundaries of an entity mention in text, without predicting its type. The detected entities are input to entity linking or fine-grained typing systems for semantic enrichment. We propose BdryBot, a recurrent neural network encoder-decoder framework with a pointer network to detect entity boundaries from a given sentence. The encoder considers both character-level representations and word-level embeddings to represent the input words. In this way, BdryBot does not require any hand-crafted features. Because of the pointer network, BdryBot overcomes the problem of variable size output vocabulary and the issue of sparse boundary tags. We conduct two sets of experiments, in-domain detection and cross-domain detection, on six datasets. Our results show that BdryBot achieves state-of-the-art performance against five baselines. In addition, our proposed approach can be further enhanced when incorporating contextualized language embeddings into token representations.

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance, and transmission boundary conditions. In particular, we aim to quantify diffracted fields originated by small stochastic perturbations of a given relatively smooth nominal shape. Using first-order shape Taylor expansions, we derive tensor deterministic first-kind boundary integral equations for the statistical moments of the scattering problems considered. These are then approximated by sparse tensor Galerkin discretizations via the combination technique [M. Griebel, M. Schneider, and C. Zenger, A combination technique for the solution of sparse grid problems, in Iterative Methods in Linear Algebra, P. de Groen and P. Beauwens, eds., Elsevier, Amsterdam, 1992, pp. 263--281; H. Harbrecht, M. Peters, and M. Siebenmorgen, J. Comput. Phys., 252 (2013), pp. 128--141]. We supply extensive numerical experiments confirming the predicted error convergence rates with polylogarithmic growth in the number of degrees of freedom and accuracy in approximation of the moments. Moreover, we discuss implementation details such as preconditioning to finally point out further research avenues.

Gravity modeling for crustal-scale models of rifted continental margins using a constrained 3D inversion method

We have developed a new constrained inversion method that is based on a probabilistic approach for resolving crustal structure from regional gravity data. The smoothness of estimated structures is included in the inversion by using a model covariance matrix, and the sparse boundary information obtained from seismic data is incorporated in the inversion by using linear equality constraints. Moreover, constraints on the average anomalous densities expected for different crustal layers are applied instead of using a depth-weighting function. Bathymetric data and sediment thicknesses are included in the inversion by using an a priori model. Using the proposed method, model structures with sharp boundaries can be obtained while the existing boundary information and sparse seismic constraints are honored. We determine through a synthetic example and a real-world example that the proposed constrained inversion method is a valid tool for studying crustal-scale structures.

Steel surface defects recognition based on multi-type statistical features and enhanced twin support vector machine

For steel surface defect recognition, feature extraction and classification are very important steps. In this paper, multi-type statistical features and enhanced twin support vector machine classifier are formulated and applied. Firstly, four types of statistical features for different attributes of defect region are proposed. They are insensitive to affine transformation in scale and rotation. And those attributes include shape distance and local binary pattern operators with sign and magnitude. Then, dummy boundary samples and representative samples are extracted from steel surface defect dataset. Dummy boundary samples include the sparse boundary information of dataset. They can reduce the adverse impact of noise samples. Representative samples with local and global properties are used to replace samples with quadratic loss. They can exclude noise samples. Based on dummy boundary samples and representative samples, enhanced twin support vector machine is formulated. On one hand, it can solve multi-class classification problem. On the other hand, it has anti-noise ability and high classification efficiency. At last, enhanced twin support vector machine classifier and multi-type statistical features are applied to recognize five types of steel surface defects. The experimental results show that our proposed multi-class classifier has perfect performance in efficiency and accuracy. And multi-type statistical features are in favor of improving classification performance.

Convolutional Oriented Boundaries: From Image Segmentation to High-Level Tasks.

We present Convolutional Oriented Boundaries (COB), which produces multiscale oriented contours and region hierarchies starting from generic image classification Convolutional Neural Networks (CNNs). COB is computationally efficient, because it requires a single CNN forward pass for multi-scale contour detection and it uses a novel sparse boundary representation for hierarchical segmentation; it gives a significant leap in performance over the state-of-the-art, and it generalizes very well to unseen categories and datasets. Particularly, we show that learning to estimate not only contour strength but also orientation provides more accurate results. We perform extensive experiments for low-level applications on BSDS, PASCAL Context, PASCAL Segmentation, and NYUD to evaluate boundary detection performance, showing that COB provides state-of-the-art contours and region hierarchies in all datasets. We also evaluate COB on high-level tasks when coupled with multiple pipelines for object proposals, semantic contours, semantic segmentation, and object detection on MS-COCO, SBD, and PASCAL; showing that COB also improves the results for all tasks.