Pyramid Graph Research Articles

FP-GCN: Frequency Pyramid Graph Convolutional Network for Enhancing Pathological Gait Classification.

Gait, a manifestation of one's walking pattern, intricately reflects the harmonious interplay of various bodily systems, offering valuable insights into an individual's health status. However, the current study has shortcomings in the extraction of temporal and spatial dependencies in joint motion, resulting in inefficiencies in pathological gait classification. In this paper, we propose a Frequency Pyramid Graph Convolutional Network (FP-GCN), advocating to complement temporal analysis and further enhance spatial feature extraction. specifically, a spectral decomposition component is adopted to extract gait data with different time frames, which can enhance the detection of rhythmic patterns and velocity variations in human gait and allow a detailed analysis of the temporal features. Furthermore, a novel pyramidal feature extraction approach is developed to analyze the inter-sensor dependencies, which can integrate features from different pathways, enhancing both temporal and spatial feature extraction. Our experimentation on diverse datasets demonstrates the effectiveness of our approach. Notably, FP-GCN achieves an impressive accuracy of 98.78% on public datasets and 96.54% on proprietary data, surpassing existing methodologies and underscoring its potential for advancing pathological gait classification. In summary, our innovative FP-GCN contributes to advancing feature extraction and pathological gait recognition, which may offer potential advancements in healthcare provisions, especially in regions with limited access to medical resources and in home-care environments. This work lays the foundation for further exploration and underscores the importance of remote health monitoring, diagnosis, and personalized interventions.

Multi-task Contexture Learning Network for automated vertebrae segmentation and tumor diagnosis from MRI

Automated vertebrae segmentation and tumor diagnosis from magnetic resonance imaging (MRI) scans play a crucial role in early detection of spinal tumors. However, the task is challenging due to the variability in fields of view across MRI images and the diverse appearances of tumors. To address these challenges, we propose a novel approach, the Multi-task Contexture Learning Network (MCLN), which concurrently performs accurate vertebrae segmentation and precise identification of tumors. Specifically, MCLN first constructs a spatial pyramid graph convolutional network and a label attention network to effectively capture long-range contextual information and generate a precise segmentation mask. Then, MCLN incorporates the input MRI image and the segmentation mask to recognize vertebral tumors utilizing a mixed kernel multi-loss network. We evaluate our proposed MCLN on a challenging dataset consisting of 600 MRI images, achieving impressive results with a mean Dice coefficient of 90.03% for vertebrae segmentation and a mean accuracy of 95.11% for tumor diagnosis. These results demonstrate the remarkable performance of MCLN in addressing automated vertebrae segmentation and tumor diagnosis from MRI.

Optimal transport based pyramid graph kernel for autism spectrum disorder diagnosis

Brain network, which characterizes the functional and structural interactions of brain regions with graph theory, has been widely utilized to diagnose brain diseases, such as autism spectrum disorder (ASD). It is a challenge to measure the network (or graph) similarity in brain network analysis. Graph kernel (i.e., kernel defined on graphs) offers an efficient tool for measuring the similarity of paired brain networks and yields the excellent classification performance in brain disease diagnosis. However, most of the existing graph kernels neglected the hierarchical architecture information of brain networks. To address this problem, in this paper, we propose an optimal transport based pyramid graph kernel for measuring brain network similarity and then apply it to brain disease classification. The main idea is to transform brain networks into pyramid structures, which reflect the hierarchical architecture information of the brain network with multi-resolution histograms. The optimal transport distance in pyramid structures is calculated for measuring transport costs between paired brain networks. Finally, the optimal transport based pyramid graph kernel is computed based on this optimal transport distance. To evaluate the effectiveness of the proposed optimal transport based pyramid graph kernel, the extensive experiments are performed in functional magnetic resonance imaging data of brain disease from the Autism Brain Imaging Data Exchange database. The experimental results show that our proposed optimal transport based pyramid graph kernel outperforms the state-of-the-art methods in ASD classification tasks.

Characters as graphs: Interpretable handwritten Chinese character recognition via Pyramid Graph Transformer

It is meaningful but challenging to teach machines to recognize handwritten Chinese characters. However, conventional approaches typically view handwritten Chinese characters as either static images or temporal trajectories, which may ignore the inherent geometric semantics of characters. Instead, here we first propose to represent handwritten characters as skeleton graphs, explicitly considering the natural characteristics of characters (i.e., characters as graphs). Furthermore, we propose a novel Pyramid Graph Transformer (PyGT) to specifically process the graph-structured characters, which fully integrates the advantages of Transformers and graph convolutional networks. Specifically, our PyGT can learn better graph features through (i) capturing the global information from all nodes with graph attention mechanism and (ii) modelling the explicit local adjacency structures of nodes with graph convolutions. Furthermore, the PyGT learns the multi-resolution features by constructing a progressive shrinking pyramid. Compared with existing approaches, it is more interpretable to recognize characters as geometric graphs. Moreover, the proposed method is generic for both online and offline handwritten Chinese character recognition (HCCR), and it also can be feasibly extended to handwritten text recognition. Extensive experiments empirically demonstrate the superiority of PyGT over the prevalent approaches including 2D-CNN, RNN/1D-CNN, and Vision Transformer (ViT) for HCCR. The code is available at https://github.com/ganji15/PyGT-HCCR.

Spatial-Temporal Graph Network for Video Crowd Counting

In recent years, researchers have developed many deep-learning-based methods to count crowd numbers in static images. However, much fewer works focus on video-based crowd counting, in which the critical challenge of temporal correlation has not been well explored. This paper proposes a Spatial-Temporal Graph Network (STGN) to achieve efficient and accurate crowd counting in videos via learning pixel-wise and patch-wise relations in local spatial-temporal domains. Specifically, we design a pyramid graph module to leverage multi-scale features. In each scale, we sequentially construct three graphs: spatial-temporal pixel graph, temporal patch graph, and spatial pixel graph, in which we apply the self-attention mechanism to capture pixel-wise relation, learn structure-aware relation, and aggregate local features, respectively. Furthermore, we propose spatial-aware channel-wise attention to effectively fuse multi-scale features. To demonstrate the effectiveness of the proposed method, we conduct experiments on five crowd counting datasets, including a large-scale video crowd dataset (FDST). Moreover, the proposed model is also applied in the vehicle counting dataset (TRANCOS). The results show that the proposed model outperforms existing spatial-temporal crowd counting models and achieves state-of-the-art. The code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/wuzhe71/STGN</uri>

Exploring Spatial Significance via Hybrid Pyramidal Graph Network for Vehicle Re-Identification

Existing vehicle re-identification methods commonly use spatial pooling operations to aggregate feature maps extracted via off-the-shelf backbone networks, such as visual geometry group network (VGGNet), Google network (GoogLeNet) and residual network (ResNet). They ignore exploring the spatial significance of feature maps, eventually degrading the vehicle re-identification performance. In this paper, firstly, an innovative spatial graph network (SGN) is proposed to elaborately explore the spatial significance of feature maps. The SGN stacks multiple spatial graphs (SGs). Each SG assigns feature map’s elements as nodes and utilizes spatial neighborhood relationships to determine edges among nodes. During the SGN’s propagation, each node and its spatial neighbors on an SG are aggregated to the next SG. On the next SG, each aggregated node is re-weighted with a learnable parameter to find the significance at the corresponding location. Secondly, a novel pyramidal graph network (PGN) is designed to comprehensively explore the spatial significance of feature maps at multiple scales. The PGN organizes multiple SGNs in a pyramidal manner and makes each SGN handles feature maps of a specific scale. Finally, a hybrid pyramidal graph network (HPGN) is developed by embedding the PGN behind a ResNet-50 based backbone network. Extensive experiments on three large scale vehicle databases (i.e., VeRi776, VehicleID, and VeRi-Wild) demonstrate that the proposed HPGN is superior to state-of-the-art vehicle re-identification approaches in terms of accuracy, parameter cost, and computation cost. In addition, experiments show that the proposed PGN is universal to various backbone networks.

Spatial-Temporal Pyramid Graph Reasoning for Action Recognition.

Spatial-temporal relation reasoning is a significant yet challenging problem for video action recognition. Previous works typically apply local operations like 2D or 3D CNNs to conduct space-time interactions in video sequences, or simply capture space-time long-range relations of a single fixed scale. However, this is inadequate for obtaining a comprehensive action representation. Besides, most models treat all input frames equally for the final classification, without selecting key frames and motion-sensitive regions. This introduces irrelevant video content and hurts the performance of models. In this paper, we propose a generic Spatial-Temporal Pyramid Graph Network (STPG-Net) to adaptively capture long-range spatial-temporal relations in video sequences at multiple scales. Specifically, we design a temporal attention (TA) module and a spatial-temporal attention (STA) module to learn the contribution of each frame and each space-time region to an action at a feature level, respectively. We then apply the selected key information to build spatial-temporal pyramid graphs for long-range relation reasoning and more comprehensive action representation learning. STPG-Net can be flexibly integrated into 2D and 3D backbone networks in a plug-and-play manner. Extensive experiments show that it brings consistent improvements over many challenging baselines on several standard action recognition benchmarks (i.e., Something-Something V1 & V2, and FineGym), demonstrating the effectiveness of our approach.

Metric Dimension on Path-Related Graphs

Graph theory has a large number of applications in the fields of computer networking, robotics, Loran or sonar models, medical networks, electrical networking, facility location problems, navigation problems etc. It also plays an important role in studying the properties of chemical structures. In the field of telecommunication networks such as CCTV cameras, fiber optics, and cable networking, the metric dimension has a vital role. Metric dimension can help us in minimizing cost, labour, and time in the above discussed networks and in making them more efficient. Resolvability also has applications in tricky games, processing of maps or images, pattern recognitions, and robot navigation. We defined some new graphs and named them s − middle graphs, s -total graphs, symmetrical planar pyramid graph, reflection symmetrical planar pyramid graph, middle tower path graph, and reflection middle tower path graph. In the recent study, metric dimension of these path-related graphs is computed.

On the $e$-Positivity of $(claw, 2K_2)$-Free Graphs

Motivated by Stanley and Stembridge's conjecture about the $e$-positivity of claw-free incomparability graphs, Hamel and her collaborators studied the $e$-positivity of $(claw, H)$-free graphs, where $H$ is a four-vertex graph. In this paper we establish the $e$-positivity of generalized pyramid graphs and $2K_2$-free unit interval graphs, which are two important families of $(claw, 2K_2)$-free graphs. Hence we affirmatively solve one problem proposed by Hamel, Hoáng and Tuero, and another problem considered by Foley, Hoáng and Merkel.

Pyramidal Graph Convolutional Network for Skeleton-Based Human Action Recognition

The emergence of low-cost depth sensors opens up new potentials for skeleton-based human action recognition. The recent methods for this task have made significant progress by incorporating graph convolution. However, they (1) have limitations in modeling the complex and variable temporal dynamics, and (2) cannot maximize the complementarity of the spatial and temporal features. Besides, (3) the loss function of these methods has an inherent weakness in optimizing the intraclass compactness. To this end, we propose a pyramidal graph convolutional network (PY-GCN) in this paper. Specifically, (1) an effective yet efficient single-oriented pyramidal convolution is proposed. It involves multiple kernels with varying sizes and depths that are capable of capturing different levels of the temporal dynamics at multiple scales. (2) A pseudo-two-stream structure for the basic block of the network is proposed to comprehensively aggregate discriminative cross-spatiotemporal features. Moreover, (3) a pairwise Gaussian loss together with the cross-entropy loss is introduced to the model, which can focus on both intraclass compactness and interclass separability. Our PY-GCN achieves state-of-the-art performance on three challenging large-scale datasets.

An Adaptive Pyramid Graph and Variation Residual-Based Anomaly Detection Network for Rail Surface Defects

Anomaly detection is a crucial means to detect unbalanced and multi-class abnormal data in industrial products. The existing anomaly detection model is usually suitable for products with a simple or regular background texture. However, there is a lack of a universal surface defect anomaly detection framework for railway products when facing the challenges: the complex background texture, huge intra-class variation, uneven distribution of inter-class, and weak texture-featured defects. To fill this gap, an innovative generative adversarial network based on adaptive pyramid graph and variation residuals (APGVR-GAN) is proposed, aiming to improve the robustness of anomaly detection in railway products and other complex industrial supplies. First, the adaptive pyramid graph module is embedded in the encoder-decoder-encoder pattern, capturing the correlation description between neighbor regions, which is utilized to enhance the detection of abnormal defects with weak texture. Next, the variation residual module is employed to enhance the expression of various normal samples in the latent space, and improve the identification ability for abnormal samples. Then, the dual-probability prototype loss is proposed to make different normal samples have more concentrated expression and more similar probability distribution centers in latent space. Finally, an adaptive focal-gate loss and a regularized log-likelihood loss are designed to overcome the imbalance problem in training samples with different background information. The effectiveness of the model is verified on three new railway datasets and three other industrial public datasets. The results show that in anomaly detection, APGVR-GAN on the three railway data sets NEU-RSDD-1 dataset, NEU-RSDD-1 dataset and RSDD AUC results can reach 0.89, 0.81, and 0.87, and its detection accuracy reached 0.97, 0.96 and 0.92, which is much higher than other comparative anomaly detection algorithms. In the segmentation experiments on the RSDD dataset, compared with other known rail defect detection methods, the overall evaluation metric F-Score is 83.70 which also better than other methods.

Pyramid graph cut: Integrating intensity and gradient information for grayscale medical image segmentation

Segmentation of grayscale medical images is challenging because of the similarity of pixel intensities and poor gradient strength between adjacent regions. The existing image segmentation approaches based on either intensity or gradient information alone often fail to produce accurate segmentation results. Previous approaches in the literature have approached the problem by embedded or sequential integration of different information types to improve the performance of the image segmentation on specific tasks. However, an effective combination or integration of such information is difficult to implement and not sufficiently generic for closely related tasks. Integration of the two information sources in a single graph structure is a potentially more effective way to solve the problem. In this paper we introduce a novel technique for grayscale medical image segmentation called pyramid graph cut, which combines intensity and gradient sources of information in a pyramid-shaped graph structure using a single source node and multiple sink nodes. The source node, which is the top of the pyramid graph, embeds intensity information into its linked edges. The sink nodes, which are the base of the pyramid graph, embed gradient information into their linked edges. The min-cut uses intensity information and gradient information, depending on which one is more useful or has a higher influence in each cutting location of each iteration. The experimental results demonstrate the effectiveness of the proposed method over intensity-based segmentation alone (i.e. Gaussian mixture model) and gradient-based segmentation alone (i.e. distance regularized level set evolution) on grayscale medical image datasets, including the public 3DIRCADb-01 dataset. The proposed method archives excellent segmentation results on the sample CT of abdominal aortic aneurysm, MRI of liver tumor and US of liver tumor, with dice scores of 90.49±5.23%, 88.86±11.77%, 90.68±2.45%, respectively.

A study on the Development of a Korean Metabolic Syndrome Questionnaire

Segmentation of grayscale medical images is challenging because of the similarity of pixel intensities and poor gradient strength between adjacent regions. The existing image segmentation approaches based on either intensity or gradient information alone often fail to produce accurate segmentation results. Previous approaches in the literature have approached the problem by embedded or sequential integration of different information types to improve the performance of the image segmentation on specific tasks. However, an effective combination or integration of such information is difficult to implement and not sufficiently generic for closely related tasks. Integration of the two information sources in a single graph structure is a potentially more effective way to solve the problem. In this paper we introduce a novel technique for grayscale medical image segmentation called pyramid graph cut, which combines intensity and gradient sources of information in a pyramid-shaped graph structure using a single source node and multiple sink nodes. The source node, which is the top of the pyramid graph, embeds intensity information into its linked edges. The sink nodes, which are the base of the pyramid graph, embed gradient information into their linked edges. The min-cut uses intensity information and gradient information, depending on which one is more useful or has a higher influence in each cutting location of each iteration. The experimental results demonstrate the effectiveness of the proposed method over intensity-based segmentation alone (i.e. Gaussian mixture model) and gradient-based segmentation alone (i.e. distance regularized level set evolution) on grayscale medical image datasets, including the public 3DIRCADb-01 dataset. The proposed method archives excellent segmentation results on the sample CT of abdominal aortic aneurysm, MRI of liver tumor and US of liver tumor, with dice scores of 90.49±5.23%, 88.86±11.77%, 90.68±2.45%, respectively.

The Complexity of Some Classes of Pyramid Graphs Created from a Gear Graph

The methods of measuring the complexity (spanning trees) in a finite graph, a problem related to various areas of mathematics and physics, have been inspected by many mathematicians and physicists. In this work, we defined some classes of pyramid graphs created by a gear graph then we developed the Kirchhoff's matrix tree theorem method to produce explicit formulas for the complexity of these graphs, using linear algebra, matrix analysis techniques, and employing knowledge of Chebyshev polynomials. Finally, we gave some numerical results for the number of spanning trees of the studied graphs.

Face recognition via fast dense correspondence

Face recognition plays a significant role in computer vision. It is well know that facial images are complex stimuli signals that suffer from non-rigid deformations, including misalignment, orientation, pose changes, and variations of facial expression, etc. In order to address these variations, this paper introduces an improved sparse-representation based face recognition method, which constructs dense pixel correspondences between training and testing facial samples. Specifically, we first construct a deformable spatial pyramid graph model that simultaneously regularizes matching consistency at multiple spatial extents - ranging from an entire image, though coarse grid cells, to every single pixel. Secondly, a matching energy function is designed to perform face alignment based on dense pixel correspondence, which is very effective to address the issue of non-rigid deformations. Finally, a novel coarse-to-fine matching scheme is designed so that we are able to speed up the optimization of the matching energy function. After the training samples are aligned with respect to testing samples, an improved sparse representation model is employed to perform face recognition. The experimental results demonstrate the superiority of the proposed method over other methods on ORL, AR, and LFWCrop datasets. Especially, the proposed approach improves nearly 4.4 % in terms of recognition accuracy and runs nearly 10 times faster than previous sparse approximation methods.

Research on Infrared and Visible Images Registration Algorithm Based on Graph

In this paper, we proposed a registration algorithm based on the combination of pyramid hierarchical idea and graph theory. It can solve the challenging problem of extracting consistent characteristics and matching the infrared and visible images. First, extracting the maximally stable extremal regions (MSERs) in the determining maximum down-sampling images and each MSER is represented by a polygon. Then constructing the gragh features and the mapping relationship of MSERs between the infrared and visible images are determined by the graph matching method. Next we can construct the initial point set for matching according to the mapping relationship. Finally, using the random sample consensus (RANSAC) algorithm to obtain the optimal parameters and determine the error evaluation parameters. According to the idea of pyramid stratification, the above process is repeated in the high resolution images under the constraint condition of current matching error. The experiment results show that the algorithm can make full use of the visual similarity structures between images, and can achieve a smaller matching error under the premise of ensuring the robustness of the matching.

Antimagic labeling of generalized pyramid graphs

An antimagic labeling of a graph with q edges is a bijection from the set of edges to the set of positive integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex. A graph is antimagic if it has an antimagic labeling.

Towards an Optimal Separation of Space and Length in Resolution

Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field of proof complexity, the resources of time and memory correspond to the length and space of resolution proofs. There has been a long line of research trying to understand these proof complexity measures, as well as relating them to the width of proofs, i.e., the size of a largest clause in the proof, which has been shown to be intimately connected with both length and space. While strong results have been proven for length and width, our understanding of space has been quite poor. For instance, it has remained open whether the fact that a formula is provable in short length implies that it is also provable in small space (which is the case for length versus width), or whether these measures are unrelated in the sense that short proofs can be arbitrarily complex with respect to space.In this paper, we present some evidence indicating that the latter case should hold and provide a roadmap for how such an optimal separation result could be obtained. We do so by proving a tight bound of Θ(n√) on the space needed for so-called pebbling contradictions over pyramid graphs of size n. This yields the first polynomial lower bound on space that is not a consequence of a corresponding lower bound on width, as well as an improvement of the weak separation of space and width of Nordstrom (STOC 2006) from logarithmic to polynomial.

On the Complexity of a Class of Pyramid Graphs and Chebyshev Polynomials

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this paper we define a class of pyramid graphs and derive simple formulas of the complexity, number of spanning trees, of these graphs, using linear algebra, Chebyshev polynomials, and matrix analysis techniques.

Path Search in the Pyramid and in Other Graphs

We are given an acyclic directed graph with one source, and a subset of its edges that contains exactly one outgoing edge for every nonsink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every vertex, which determines which way the water arriving to that vertex flows further. We are interested in determining either the sink as the flow arrives, or the whole path, with as few questions as possible. The questions we can ask correspond to the vertices of the graph, and the answer describes the switch, that is, tells which outgoing edge is in our given subset. Originally the problem was proposed by Soren Riis (who posed the question for pyramid graphs) in the following more general form: We are given a natural number k, and k questions can be asked in a round. The goal is to minimize the number of rounds. We completely solve this problem for complete t-ary trees. Also, for pyramid graphs we present some nontrivial partial results.