Boundary Graph Research Articles

Distributed Shortest Distance Labeling on Large-Scale Graphs

Distance labeling approaches are widely adopted to speed up the shortest-distance query performance. Due to the explosive growth of data graphs, a single machine can hardly satisfy the requirements of both computational power and memory capacity, which causes an urgent need for efficient distributed methods. As the graph is distributed across different machines, it is inevitable to frequently exchange messages among different machines when deploying the existing centralized distance labeling methods on the distributed environment, thereby producing serious communication costs and weakening the scalability. To alleviate this problem, we design a distributed hop-based index DH-Index , which is designed based on a newly proposed boundary graph structure and restricts the index-based hop number of each connected vertex pair within 4 hops. In addition, we propose a hierarchical algorithm to accelerate the index construction and reduce the communication cost. Furthermore, a bidirectional searching strategy is proposed to efficiently resolve the query tasks based on DH-Index. The comprehensive experimental results on eight real-world graphs demonstrate that DH-Index achieves up to 65.5× and 3 orders of magnitude speedup than the existing methods in indexing time and query performance respectively, and exhibits superior capabilities on memory space, communication cost, and scalability.

Boundary Graph Neural Networks for 3D Simulations

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

MFBGR: Multi-scale feature boundary graph reasoning network for polyp segmentation

At present, adding Transformer to CNN has promoted the rapid development of colorectal polyp image processing. However, from the perspective of multi-scale feature interaction and boundary coherence, there are mainly some limitations: (1) ignore the local and global correlation within the scale feature, which may cause the missed detection of tiny polyps, (2) lack of multi-scale features to explore the target region, which hinders the learning of multi-variant polyps, and (3) the semantic connection between the target area and the boundary is ignored, cause incoherent segmentation boundaries. In this regard, we design a multi-scale feature boundary graph inference network for polyp segmentation, namely MFBGR. First, the Transformer block captures local–global cues inside the multi-scale information learned by the CNN branches. Second, for the multi-scale global information generated by the Transformer block, we design a cross-scale feature fusion module (CSFM). CSFM performs scale-variation interaction and cascaded fusion to capture the correlation between features across scales and solve the scale-variation problem of segmented objects. Finally, the traditional boundary refinement or enhancement idea is generalized to the graph convolutional reasoning layer (BGRM). BGRM receives CNN’s low-level feature information and CSFM’s fusion features, or intermediate prediction results, and propagates cross-domain feature information between graph vertices, explores information between target regions and boundary regions, and achieves more accurate boundary segmentation. On the CVC-300, CVC-ClinicDB, CVC-ColonDB, Kvasir-SEG, ETIS datasets, MFBGR and mainstream polyp segmentation networks were compared and tested. MFBGR achieved good results, and Dice, IOU, BAcc, and Haudo were the best. The values reached 94.16%, 89.35% and 97.42%, 3.7442, and the segmentation accuracy of colorectal polyp images has been improved to a certain extent.

On a Countable Family of Boundary Graph Classes for the Dominating Set Problem

On a Countable Family of Boundary Graph Classes for the Dominating Set Problem

The Cahn--Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward dynamic boundary condition at the limit. This is done in a very general setting, with nonlinear terms admitting maximal monotone graphs both in the bulk and on the boundary. The two graphs are related by a growth condition, with the boundary graph that dominates the other one. It turns out that in the limiting procedure the solution of the problem looses some regularity and the limit equation has to be properly interpreted in the sense of a subdifferential inclusion. However, the limit problem is still well-posed since a continuous dependence estimate can be proved. Moreover, in the case when the two graphs exhibit the same growth, it is shown that the solution enjoys more regularity and the boundary condition holds almost everywhere. An error estimate can also be shown, for a suitable order of the diffusion parameter.

Relations between Spectrum Curves of Discrete Sturm-Liouville Problem with Nonlocal Boundary Conditions and Graph Theory. II

In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary conditions.

Analisis Kekuatan Kolom Beton Bertulang Berdasarkan Diagram Interaksi Kolom

The column interaction diagram is a boundary area graph showing the various combinations of axial loads and moments that the column can safely hold. The benefit of a column interaction diagram provides an overview of the strength of the column in question. This study aims to analyze rectangular and circular columns using column interaction diagrams and then compare the strength of the columns in withstanding a combination of axial loads and bending moments with the same area. In this study, square and circular columns have the same number of reinforcement, diameter of reinforcement, steel strength, concrete quality, and cross-sectional area. The column is reviewed based on five conditions, namely pure axial load conditions, pure bending moment, and three failure conditions. Based on the five conditions that occurred, a column interaction diagram was created by using Microsoft Excel. Results of the analysis show that in the same area, the square column is stronger in withstanding the bending moment (Mu) of the circular column by 0.015 - 0.61%, while the circular column is stronger in resisting the axial force (Pu) of the square column by 1,9 - 4.4%.

Boundary graph convolutional network for temporal action detection

Temporal action proposal generation is a fundamental yet challenging to locate the temporal action in untrimmed videos. Although current proposal generation methods can generate the precise boundary of actions, few focus on considering the relation of proposals. In this paper, we propose a unified framework to generate the temporal boundary proposals with a graph convolution network based on the boundary proposals' feature named Boundary Graph Convolutional Network (BGCN). BGCN draws inspiration from boundary methods and uses edge graph convolution relay on the boundary proposals' feature. First, we use a base layer to fusion the two-stream video features to get two-branches of base features. Then the two-branches of base features enter into the same structure of Proposal Features Graph Convolutional Network (PFGCN): Action PFGCN to extract the action classification score and Boundary PFGCN to extract the ending score and staring score. In proposal features graph convolutional network, we first densely sampled the proposals' feature from the video features. We construct a proposal feature graph, where each proposal feature as a node and their relations between proposals' features as an edge with edge convolution for graph convolution. After that, map the relations into a 2D map score. Experiments on popular benchmarks THUMOS14 demonstrate the superiority of BGCN over (44.8% versus 42.8% at tIoU 0.5) the state-of-the-art proposal generator (e.g., G-TAD, TAL-Net, and BMN) at any of tIoU thresholds from 0.3 to 0.7. On ActivityNet1.3, BGCN also got better results. Moreover, BGCN has high efficiency for action detection with less than 2 MB model size and fast inference time.GCN based on boundary generation for densely produce the action proposals Efficient and novel BGCN model has a great capability to learn the proposal features Has a lower model size for temporal action proposals generation Has fast inference time for temporal action proposals generation.

Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theory

Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of spectrum curves. In this paper, relations between discrete Sturm-Liouville problem with nonlocal boundary conditions characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found.

A Model-based dehazing scheme for unmanned aerial vehicle system using radiance boundary constraint and graph model

Unmanned aerial vehicle system (UAVs) imaging has become a challenging area of research due to the dynamic atmospheric environment. The images captured by UAVs are often deteriorated by factors such as clouds occlusion, poor atmospheric illumination, and limited capability of the imaging system. To tackle problems, this paper presents a novel visibility restoration scheme for UAVs images by considering the following two assumptions: (1) The actual scene radiance of a UAVs image is bounded. (2) Pixels sharing the same appearance must have the same transmission value in a local neighborhood. Inspired by above assumptions, an image boundary constraint utilizing the median filter has been imposed on the RGB channel for the rough estimation of transmission-map in aerial images. Furthermore, a graph-model based optimization technique has been used for the transmission-map refinement. The experimental results demonstrate the efficiency of the proposed method in terms of metrics correspond to the human-visual-system (HVS).

Vanishing diffusion in a dynamic boundary condition for the Cahn–Hilliard equation

The initial boundary value problem for a Cahn–Hilliard system subject to a dynamic boundary condition of Allen–Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary condition is the point of emphasis. By the asymptotic analysis as the diffusion coefficient tends to 0, one can expect that the solutions of the surface diffusion problem converge to the solution of the problem without the surface diffusion. This is actually the case, but the solution of the limiting problem naturally looses some regularity. Indeed, the system we investigate is rather complicate due to the presence of nonlinear terms including general maximal monotone graphs both in the bulk and on the boundary. The two graphs are related each to the other by a growth condition, with the boundary graph that dominates the other one. In general, at the asymptotic limit a weaker form of the boundary condition is obtained, but in the case when the two graphs exhibit the same growth the boundary condition still holds almost everywhere.

Multiscale superpixel method for segmentation of breast ultrasound

BackgroundIn medical diagnostics, breast ultrasound is an inexpensive and flexible imaging modality. The segmentation of breast ultrasounds to identify tumour regions is a challenging and complex task. The major problems of effective tumour identification are speckle noise, artefacts and low contrast. The gold standard for segmentation is manual processing; however, manual segmentation is a cumbersome task. To address this problem, the automatic multiscale superpixel method for the segmentation of breast ultrasounds is proposed. MethodsThe original breast ultrasound image was transformed into multiscaled images, and then, the multiscaled images were preprocessed. Next, a boundary efficient superpixel decomposition of the multiscaled images was created. Finally, the tumour region was generated by the boundary graph cut segmentation method. The proposed method was evaluated with 120 images from the Thammassat University Hospital database. The dataset consists of 30 malignant, 30 benign tumors, 60 fibroadenoma, and 60 cyst images. Popular metrics, such as the accuracy, sensitivity, specificity, Dice index, Jaccard index and Hausdorff distance, were used for the evaluation. ResultsThe results indicate that the proposed method achieves segmentation accuracy of 97.3% for benign tumors, 94.2% for malignant, 96.4% for cysts and 96.7% for fibroadenomas. The results validate that the proposed model outperforms selected state-of-the-art segmentation methods. ConclusionsThe proposed method outperforms selected state-of-the-art segmentation methods with an average segmentation accuracy of 94%.

SMINT

Sharing a pre-trained machine learning model, particularly a deep neural network via prediction APIs, is becoming a common practice on machine learning as a service (MLaaS) platforms nowadays. Although deep neural networks (DNN) have shown remarkable successes in many tasks, they are also criticized for the lack of interpretability and transparency. Interpreting a shared DNN model faces two additional challenges compared with interpreting a general model. (1) Limited training data can be disclosed to users. (2) The internal structure of the models may not be available. These two challenges impede the application of most existing interpretability approaches, such as saliency maps or influence functions, for DNN models. Case-based reasoning methods have been used for interpreting decisions; however, how to select and organize the data points under the constraints of shared DNN models is not discussed. Moreover, simply providing cases as explanations may not be sufficient for supporting instance level interpretability. Meanwhile, existing interpretation methods for DNN models generally lack the means to evaluate the reliability of the interpretation. In this article, we propose a framework named Shared Model INTerpreter (SMINT) to address the above limitations. We propose a new data structure called a boundary graph to organize training points to mimic the predictions of DNN models. We integrate local features, such as saliency maps and interpretable input masks, into the data structure to help users to infer the model decision boundaries. We show that the boundary graph is able to address the reliability issues in many local interpretation methods. We further design an algorithm named hidden-layer aware p-test to measure the reliability of the interpretations. Our experiments show that SMINT is able to achieve above 99% fidelity to corresponding DNN models on both MNIST and ImageNet by sharing only a tiny fraction of training data to make these models interpretable. The human pilot study demonstrates that SMINT provides better interpretability compared with existing methods. Moreover, we demonstrate that SMINT is able to assist model tuning for better performance on different user data.

Volume simplicity constraint in the Engle-Livine-Pereira-Rovelli spin foam model

We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending on its bivectors and the knotting class of its boundary graph. While this leads to no further condition for the 4-simplex, the constraint becomes non-trivial for more complicated boundary graphs. We show that, in the semi-classical limit of the hypercuboidal graph, the constraint turns into the geometricity condition observed recently by several authors.

Spin foams without spins

We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex. In doing so the sums over spins have been carried out. The boundary data of each n-valent node is explicitly reduced with respect to the local gauge invariance and has a manifest geometrical interpretation as a framed polyhedron of fixed total area. Ultimately, sums over spins are traded for contour integrals over simple poles and recoupling theory is avoided using generating functions.

ROOF RECONSTRUCTION FROM AIRBORNE LASER SCANNING DATA BASED ON IMAGE PROCESSING METHODS

The paper presents a new data-driven approach to generate CityGML building models from airborne laser scanning data. The approach is based on image processing methods applied to an interpolated height map and avoids shortcomings of established methods for plane detection like Hough transform or RANSAC algorithms on point clouds. The improvement originates in an interpolation algorithm that generates a height map from sparse point cloud data by preserving ridge lines and step edges of roofs. Roof planes then are detected by clustering the height map’s gradient angles, parameterizations of planes are estimated and used to filter out noise around ridge lines. On that basis, a raster representation of roof facets is generated. Then roof polygons are determined from region outlines, connected to a roof boundary graph, and simplified. Whereas the method is not limited to churches, the method’s performance is primarily tested for church roofs of the German city of Krefeld because of their complexity. To eliminate inaccuracies of spires, contours of towers are detected additionally, and spires are rendered as solids of revolution. In our experiments, the new data-driven method lead to significantly better building models than the previously applied model-driven approach.

ROOF RECONSTRUCTION FROM AIRBORNE LASER SCANNING DATA BASED ON IMAGE PROCESSING METHODS

Abstract. The paper presents a new data-driven approach to generate CityGML building models from airborne laser scanning data. The approach is based on image processing methods applied to an interpolated height map and avoids shortcomings of established methods for plane detection like Hough transform or RANSAC algorithms on point clouds. The improvement originates in an interpolation algorithm that generates a height map from sparse point cloud data by preserving ridge lines and step edges of roofs. Roof planes then are detected by clustering the height map’s gradient angles, parameterizations of planes are estimated and used to filter out noise around ridge lines. On that basis, a raster representation of roof facets is generated. Then roof polygons are determined from region outlines, connected to a roof boundary graph, and simplified. Whereas the method is not limited to churches, the method’s performance is primarily tested for church roofs of the German city of Krefeld because of their complexity. To eliminate inaccuracies of spires, contours of towers are detected additionally, and spires are rendered as solids of revolution. In our experiments, the new data-driven method lead to significantly better building models than the previously applied model-driven approach.

Oriented boundary graph: An efficient structuring model for segmentation of 3D images

From a theoretical point of view, most of image segmentation methods that have been developed for 2D images can be generalized to higher dimensions. In actual practice, the cost in space to encode 3D data structure and the cost in time to run 3D algorithms does not allow to conveniently implement those classical segmentation algorithms in the 3D case. In this article, we describe a new model to efficiently represent and update both the topological and the geometrical structure of the regions of a 3D segmented image. This model has been defined from a pragmatical approach that consists in specifying a basic region-based segmentation framework, and then in building a minimal model that encodes all the relationships needed for an efficient implementation of this framework. This approach leads to a model suitable for a wide range of segmentation methods and allowing an efficient computation of most of the segmentation criteria involved in image segmentation.

A Bijective Proof of Loehr-Warrington's Formulas for the Statistics $${\rm{ctot}_\frac{q}{p}}$$ ctot q p and $${\rm{mid}_\frac{q}{p}}$$ mid q p

Loehr and Warrington introduced partitional statistics \({\rm{ctot}_\frac{q}{p}}\) (D) and \({\rm{mid}_\frac{q}{p}}\) (D) and provided formulas for these statistics in terms of the boundary graph of the Young diagram D. In this paper we give a bijective proof of Loehr-Warrington's formulas by using the following simple combinatorial observation: given a Young diagram D and two numbers a and l, the number of boxes in D with the arm length a and the leg length l is one less than the number of boxes with the same properties in the complement to D. Here the complement is taken inside the positive quadrant or, equivalently, a very large rectangle.

Dynamics of Boundary Graphs

In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. A vertex v is a boundary vertex of a vertex u if for all The boundary graph B(G) based on a connected graph G is a simple graph which has the vertex set as in G. Two vertices u and v are adjacent in B(G) if either u is a boundary of v or v is a boundary of u. If G is disconnected, then each vertex in a component is adjacent to all other vertices in the other components and is adjacent to all of its boundary vertices within the component. Given a positive integer m, the mth iterated boundary graph of G is defined as A graph G is periodic if for some m. A graph G is said to be an eventually periodic graph if there exist positive integers m and k >0 such that We give the necessary and sufficient condition for a graph to be eventually periodic. Keywords: Boundary graph; Periodic graph. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v5i3.14866 J. Sci. Res. 5 (3), xxx-xxx (2013)