Adjacency Relations Research Articles

Subdivision of Maps of Digital Images

A digital image is a finite set of integer lattice points in an ambient Euclidean space together with a suitable adjacency relation between points. Subdivision, which is a process of enlarging a digital image in the photographic sense, provides a basic tool for operating with digital images. But given a map of digital images, there is as yet no general way to define a map of their subdivisions that might reasonably be called a subdivision of the map. In this paper, we construct such maps of subdivisions when the map of digital images has a 1- or 2-dimensional domain. From our constructions we deduce path covering and homotopy covering results that play a role in our development of the digital fundamental group.

Orebody Modeling Method Based on the Normal Estimation of Cross-Contour Polylines

The normal estimation of cross-contour polylines largely determines the implicit orebody modeling result. However, traditional methods cannot estimate normals effectively due to the complex topological adjacency relationship of the cross-contour polylines manually interpreted in the process of exploration and production. In this work, we present an orebody implicit modeling method based on the normal estimation of cross-contour polylines. The improved method consists of three stages: (1) estimating the normals of cross-contour polylines by using the least square plane fitting method based on principal component analysis; (2) reorienting the normal directions by using the method based on the normal propagation; (3) using an implicit function to construct an orebody model. The innovation of this method is that it can automatically estimate the normals of the cross-contour polylines and reorient normal directions without manual intervention. Experimental results show that the proposed method has the advantages of a small amount of calculation, high efficiency and strong reliability. Moreover, this normal estimation method is useful to improve the automation of implicit orebody modeling.

Digitally topological groups

<abstract><p>The purpose of the paper is to study digital topological versions of typical topological groups. In relation to this work, given a digital image $ (X, k), X \subset {\mathbb Z}^n $, we are strongly required to establish the most suitable adjacency relation in a digital product $ X \times X $, say $ G_{k^\ast} $, that supports both $ G_{k^\ast} $-connectedness of $ X \times X $ and $ (G_{k^\ast}, k) $-continuity of the multiplication $ \alpha: (X \times X, G_{k^\ast}) \to (X, k) $ for formulating a digitally topological $ k $-group (or $ DT $-$ k $-group for brevity). Thus the present paper studies two kinds of adjacency relations in a digital product such as a $ C_{k^\ast} $- and $ G_{k^\ast} $-adjacency. In particular, the $ G_{k^\ast} $-adjacency relation is a new adjacency relation in $ X \times X\subset {\mathbb Z}^{2n} $ derived from $ (X, k) $. Next, the paper initially develops two types of continuities related to the above multiplication $ \alpha $, e.g., the $ (C_{k^\ast}, k) $- and $ (G_{k^\ast}, k) $-continuity. Besides, we prove that while the $ (C_{k^\ast}, k) $-continuity implies the $ (G_{k^\ast}, k) $-continuity, the converse does not hold. Taking this approach, we define a $ DT $-$ k $-group and prove that the pair $ (SC_k^{n, l}, \ast) $ is a $ DT $-$ k $-group with a certain group operation $ \ast $, where $ SC_k^{n, l} $ is a simple closed $ k $-curve with $ l $ elements in $ {\mathbb Z}^{n} $. Also, the $ n $-dimensional digital space $ ({\mathbb Z}^n, 2n, +) $ with the usual group operation "$ + $" on $ {\mathbb Z}^n $ is a $ DT $-$ 2n $-group. Finally, the paper corrects some errors related to the earlier works in the literature.</p></abstract>

TOPOLOGICAL SPACES GENERATED BY GRAPH

n this paper we discuss topological spaces generated by simple graphs using adjacency relation and non adjacency relation on vertices. We establish important results showing relations between complete graph and discrete topological space. We also discuss the topological spaces related to complete graphs, isomorphic graphs and study their properties. Further we discuss the interior and closure operators and their properties. Our motivation is to give an fundamental step toward linkage between topology and graph so as to study different aspects of graphs in terms of topological properties

Morse functions to graphs and topological complexity for hyperbolic $3$-manifolds

Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in which the adjacency relation on handles may give an arbitrary graph. We show that for compact hyperbolic 3-manifolds, this is linearly related to a notion of metric complexity, based on the areas of level sets of Morse functions to graphs, which we call Gromov area.

Heterogeneous Images Change Detection Based on Iterative Joint Global–Local Translation

Most heterogeneous change detection methods based on transfer learning may not yield satisfactory results due to the lack of comprehensive utilization of the global and local characteristics of the image. In this paper, we propose an unsupervised heterogeneous change detection method based on iterative joint global-local translation (IJGLT). The two heterogeneous images are firstly segmented into superpixels with the same boundary. Unlike the transfer learning methods for classification tasks that directly reduce the distance of the distribution of all data, we construct a translation function to decrease the difference between unchanged superpixels while increasing the difference of changed superpixels. During the translation process, the overall distribution is constrained using pseudo change labels, and the local manifold preserving is utilized to maintain the spatial structure and local adjacency relationship of superpixels. By comparing the translated superpixels of the heterogeneous images, the change map is obtained and then refined with pseudo change labels taking an iterative approach until convergence. Using the public and self-made optical-SAR heterogeneous datasets with different resolutions, the experimental results demonstrate that IJGLT is superior to several typical comparison methods with a maximum overall accuracy of 0.98 and a kappa coefficient of 0.9.

RAGCN: Region Aggregation Graph Convolutional Network for Bone Age Assessment From X-Ray Images

Rapid and accurate measurement of bone age from hand X-ray images is a significant task for children’s maturity assessment and metabolic disorders diagnosis. With the development of deep learning technology, assessment methods based on Convolutional Neural Network (CNN) have become the mainstream. However, the existing CNN method generates the assessment results solely based on images, which ignores the clinical practice and thus weakens the evaluation performance. In this paper, an automatic bone age assessment method based on CNN and Graph Convolutional Network (GCN) is proposed. The overall method uses CNN for feature extraction and GCN for bone key regions inference, which mimics the physician’s clinical process. Specifically, the key regions of the hand bone are firstly defined according to the clinical standard. Then, independent CNN pathways are established to extract the features of different key regions. Finally, a novel Region Aggregation Graph Convolutional Network (RAGCN) is designed, which can aggregate the region features into the overall bone age representation according to the adjacency relation of the regions. In addition, RAGCN can also infer the importance of different regions in the feature aggregation process. The proposed method is validated on the RSNA dataset and the RHPE dataset. The MAE is 4.09 months on the RSNA dataset and 6.78 months on the RHPE dataset, it is competitive and superior over other state-of-the-art methods.

On the graph of partial orders

Any binary relation (where is an arbitrary set) generates a charac-teristic function on the set : If , then , otherwise . In terms of characteristic functions on the set of all binary rela-tions of the set we introduced the concept of a binary of reflexive relation of adjacency and determined the algebraic system consisting of all binary re-lations of a set and all unordered pairs of various adjacent binary rela-tions. If is finite set then this algebraic system is a graph “ a graph of graphs” in this work we investigated some features of the structures of the graph of partial orders.

Anatomically constrained squeeze-and-excitation graph attention network for cortical surface parcellation

In order to understand the organizational structures of healthy cerebral cortex and the abnormalities in neurological and psychiatric diseases, it is significant to parcellate the cortical surface. The cortical surface, however, is a highly folded complex geometric structure which challenges automatic cortical surface parcellation. Nowadays, the parcellation methods of cerebral cortex are mostly based on geometric simplification, i.e., iteratively inflating and mapping the cortical surface to a spherical surface for processing, which is time-consuming and cannot make full use of the intrinsic structural information of the original cortical surface. In this study, we proposed an anatomically constrained squeeze-and-excitation graph attention network (ASEGAT) for an end-to-end brain cortical surface parcellation on the original cortical surface manifold. The ASEGAT is formed by two graph attention modules and a squeeze-and-excitation module that incorporate self-attention and head attention for rendering features of each node. Furthermore, we designed an anatomic constraint loss to introduce the anatomical priori of regional adjacency relationships, which could improve the consistency of region labeling. We evaluated our model on a public dataset of 100 manually labeled brain surfaces. Compared with several advanced methods, the results showed that our proposed approach achieved state-of-the-art performance, obtaining an accuracy of 90.65% and a dice score of 89.00%.

GeoBi-GNN: Geometry-aware Bi-domain Mesh Denoising via Graph Neural Networks

Mesh denoising is an essential geometric processing step for raw meshes generated by 3D scanners and depth cameras. It is intended to remove noise while preserving surface intrinsic features of the underlying model. Existing mesh denoising wisdoms of (1) updating mesh vertices directly (referred to as one-step mesh denoising in the spatial domain) or (2) normal filtering followed by vertex updating (referred to as two-step mesh denoising in the normal domain) seldom consider the correlation between vertex updating and normal filtering. This paper proposes a novel end-to-end geometry-aware dual-graph neural network, called GeoBi-GNN, to perform denoising in spatial and normal domains simultaneously. For the first time, we optimize both positions and normals (i.e., dual domains) in a unified framework of GNN, and show the powerful inter-coordination between the dual domains. GeoBi-GNN fully excavates the native dual-graph structure in the mesh, and creates two graph structures for the spatial noise and the normal noise respectively through the adjacency relationship between vertices and surfaces. We design each GNN as a three-layer U-Net architecture to gradually extract multi-scale features from the input graphs. In addition, a specific graph pooling layer with a cascaded weight estimation strategy is designed to improve the robustness and denoising effect. Due to the intuitive relation between the mesh connectivity and the dual graphs, the proposed method is simple to implement. Comprehensive experiments exhibit that the proposed method is significantly superior to the state-of-the-arts of mesh denoising, especially for the large-scale noise and the complex real scans. Our code is available at https://github.com/zhangyk18/GeoBi-GNN.

C-graphs - A Mixed Graphical Representation of Groups

Corresponding to each group Γ, a mixed graph G = (Γ,E,E′) called C-graph is assigned, such that the vertex set of G is the group itself. Two types of adjacency relations, that is, one way and two way communication is defined for vertices, to get a clear idea of the underlying group structure. An effort to answer the question, ‘Is there any relation between the order of an element in the group and degrees of the corresponding vertex in the C-graph’, by proposing a mathematical formula connecting them is made. Established an upper bound for the total number of edges in a C-graph G. For a vertex z in G, the concept Connector Edge CEz is defined, which convey some structural properties of the group Γ. The Connector Edge Set is defined for both a vertex z and the whole C-graph G, and is denoted as C E z and C E G respectively. Proposed the result, C E G = E if and only if |Γ| = 2n, n ∈ N. Finally, the properties of G, which the Connector Edge Set C E G carry out are discussed.

TriangleConv: A Deep Point Convolutional Network for Recognizing Building Shapes in Map Space

The classification and recognition of the shapes of buildings in map space play an important role in spatial cognition, cartographic generalization, and map updating. As buildings in map space are often represented as the vector data, research was conducted to learn the feature representations of the buildings and recognize their shapes based on graph neural networks. Due to the principles of graph neural networks, it is necessary to construct a graph to represent the adjacency relationships between the points (i.e., the vertices of the polygons shaping the buildings), and extract a list of geometric features for each point. This paper proposes a deep point convolutional network to recognize building shapes, which executes the convolution directly on the points of the buildings without constructing the graphs and extracting the geometric features of the points. A new convolution operator named TriangleConv was designed to learn the feature representations of each point by aggregating the features of the point and the local triangle constructed by the point and its two adjacency points. The proposed method was evaluated and compared with related methods based on a dataset consisting of 5010 vector buildings. In terms of accuracy, macro-precision, macro-recall, and macro-F1, the results show that the proposed method has comparable performance with typical graph neural networks of GCN, GAT, and GraphSAGE, and point cloud neural networks of PointNet, PointNet++, and DGCNN in the task of recognizing and classifying building shapes in map space.

Discourse Diversity in Language Use: A Pragmatic Inference of ‘I’m Coming’ in Ghanaian Interpersonal Communication

In the context of speech act, one may ordinarily want to communicate with the other in a natural and coherent manner in order to generate and to give information. Such information delivery in speech is obviously expected to have a desirable adjacency relation within the confines of the communication channel, so that the interlocutors could achieve a very effective discourse of giving and receiving a better response system. This act of turn-taking relation is held supreme in all linguistic situations, but does not so obtain in all communicative situations. Within Ghanaian context, this study seeks to look into various discoursal roles and diversities that the expression ‘I’m coming’ fulfils in different communicative situations to champion a reflective course of interlocutors. In doing this, the study adopts Wilson and Sperber’s (1995) Relevance Theory, which sees every speech event to be dictated by different communicative factors. It also attempts to examine how meaning is derived and interpreted to suit its rightful context of communication in human discourse. Data used for the study was derived from a primary source where the researchers observed the use of ‘I’m coming’ in different social contexts. The study observes that, in Ghanaian socio-pragmatic contexts, ‘I’m coming’ could express diverse definitive roles and that, even though, it has become a general expression, it is genuinely used to provide different meanings in different situations.

Enumeration of connected components of acyclic digraph

We established the concept of a binary reflexive relation of adjacency and determined the algebraic system consisting of all binary relations of set X and all unordered pairs of binary relations in terms of characteristic functions on the set of all binary relations of the set X. We investigated some properties of algebraic system of the structure of acyclic digraph. Also, we prove that if σ and τ are adjacent relations, then σ is acyclic relation (finite acyclic digraph) if and only if τ is an acyclic relation. Finally, the number of connected components of an acyclic relations graph is given an exact formula.

Repair of Geological Models Based on Multiple Material Marching Cubes

In this paper, we present a multi-domain implicit surface reconstruction algorithm for geological modeling based on the labeling of voxel points. The improved algorithm sets a label for each voxel point to represent the type of its geological domain and then obtains all the voxel points in the void areas. After that, the improved algorithm modifies the labels of the voxel points in the void areas and finally reconstructs the geological models through the Multiple Material Marching Cubes (M3C) algorithm. The improved algorithm solves the problems of some unexpected overlaps and voids in geological modeling by setting and modifying the labels of the voxel points. Our key contribution is proposing a labeling processing method to repair the overlap and void defects generated in the geological modeling and realizing the improved M3C algorithm. The experimental results of some geological models show the performance of the improved method. Compared with the original method, the improved method can repair the overlap and void defects in geological modeling to ensure the raw structural adjacency relationships of the geological bodies.

A Parallel Method for Open Hole Filling in Large-Scale 3D Automatic Modeling Based on Oblique Photography

Common methods of filling open holes first reaggregate them into closed holes and then use a closed hole filling method to repair them. These methods have problems such as long calculation times, high memory consumption, and difficulties in filling large-area open holes. Hence, this paper proposes a parallel method for open hole filling in large-scale 3D automatic modeling. First, open holes are automatically identified and divided into two categories (internal and external). Second, the hierarchical relationships between the open holes are calculated in accordance with the adjacency relationships between partitioning cells, and the open holes are filled through propagation from the outer level to the inner level with topological closure and height projection transformation. Finally, the common boundaries between adjacent open holes are smoothed based on the Laplacian algorithm to achieve natural transitions between partitioning cells. Oblique photography data from an area of 28 km2 in Dongying, Shandong, were used for validation. The experimental results reveal the following: (i) Compared to the Han method, the proposed approach has a 12.4% higher filling success rate for internal open holes and increases the filling success rate for external open holes from 0% to 100%. (ii) Concerning filling efficiency, the Han method can achieve hole filling only in a small area, whereas with the proposed method, the size of the reconstruction area is not restricted. The time and memory consumption are improved by factors of approximately 4–5 and 7–21, respectively. (iii) In terms of filling accuracy, the two methods are basically the same.

Second Zagreb and Sigma Indices of Semi and Total Transformations of Graphs

The study of structure-property relations including the transformations of molecules is of utmost importance in correlations with corresponding physicochemical properties. The graph topological indices have been used effectively for such study and, in particular, bond-based indices play a vital role. The bond-additive topological indices of a molecular graph are defined as a sum of edge measures over all edges in which edge measures can be computed based on degrees, closeness, peripherality, and irregularity. In this study, we provide the mathematical characterization of the transformation of a structure that can be accomplished by the novel edge adjacency and incidence relations. We derive the exact expressions of bond type indices such as second Zagreb, sigma indices, and their coindices of total transformation and two types of semitransformations of the molecules which in turn can be used to characterize the topochemical and topostructural properties.

Automated geological map deconstruction for 3D model construction using <i>map2loop</i> 1.0 and <i>map2model</i> 1.0

Abstract. At a regional scale, the best predictor for the 3D geology of the near-subsurface is often the information contained in a geological map. One challenge we face is the difficulty in reproducibly preparing input data for 3D geological models. We present two libraries (map2loop and map2model) that automatically combine the information available in digital geological maps with conceptual information, including assumptions regarding the subsurface extent of faults and plutons to provide sufficient constraints to build a prototype 3D geological model. The information stored in a map falls into three categories of geometric data: positional data, such as the position of faults, intrusive, and stratigraphic contacts; gradient data, such as the dips of contacts or faults; and topological data, such as the age relationships of faults and stratigraphic units or their spatial adjacency relationships. This automation provides significant advantages: it reduces the time to first prototype models; it clearly separates the data, concepts, and interpretations; and provides a homogenous pathway to sensitivity analysis, uncertainty quantification, and value of information studies that require stochastic simulations, and thus the automation of the 3D modelling workflow from data extraction through to model construction. We use the example of the folded and faulted Hamersley Basin in Western Australia to demonstrate a complete workflow from data extraction to 3D modelling using two different open-source 3D modelling engines: GemPy and LoopStructural.

Geometric Feature Extraction of Point Cloud of Chemical Reactor Based on Dynamic Graph Convolution Neural Network.

Geometric features are an important factor for the classification of drugs and other transport objects in chemical reactors. The moving speed of drugs and other transport objects in chemical reactors is fast, and it is difficult to obtain their features by imaging and other methods. In order to avoid the mistaken and missed distribution of drugs and other objects, a method of extracting geometric features of the drug’s point cloud in a chemical reactor based on a dynamic graph convolution neural network (DGCNN) is proposed. In this study, we first use MATLAB R2019a to add a random number of noise points in each point cloud file and label the point cloud. Second, k-nearest neighbor (KNN) is used to construct the adjacency relationship of all nodes, and the effect of DGCNN under different k values and the confusion matrix under the optimal k value are analyzed. Finally, we compare the effect of DGCNN with PointNet and PointNet++. The experimental results show that when k is 20, the accuracy, precision, recall, and F1 score of DGCNN are higher than those of other k values, while the training time is much shorter than that of k = 25, 30, and 35; in addition, the effect of DGCNN in extracting geometric features of the point cloud is better than that of PointNet and PointNet++. The results show that it is feasible to use DGCNN to analyze the geometric characteristics of drug point clouds in a chemical reactor. This study fills the gap of the end-to-end extraction method for a point cloud’s corresponding geometric features without a data set. In addition, this study promotes the institutionalization, standardization, and intelligent design of safe production and management of drugs and other objects in the chemical reactor, and it has positive significance for the production cost and resource utilization of the whole pharmaceutical process. At the same time, it provides a new method for the intelligent processing of point cloud data.

AAGCN: Adjacency-aware Graph Convolutional Network for person re-identification

Person re-identification (ReID) is an important topic of computer vision. Existing works in this field focus primarily on learning a feature extractor that maps the pedestrian images into a feature space, in which feature vectors corresponding to the same identity are close to each other. In this paper, we propose the adjacency-aware Graph Convolutional Network (AAGCN) to smooth the intra-class features and thus reduce the intra-class variance. Specifically, our AAGCN takes the features learned by a backbone as the input nodes; it first establishes the connections or adjacency relations for the intra-class features, then the adjacent nodes (i.e., the intra-class features) would be smoothed thanks to the property of low-pass filtering of Graph Convolutional Network (GCN). In this paper, we propose two methods, i.e., the Mahalanobis Neighborhood Adjacency (MNA) and Non-Linear Mapping (NLM), to learn the adjacency relations for the intra-class features. The MNA defines the adjacency weight between two nodes as the negative exponent of the Mahalanobis distance between their corresponding features, therefore it aims to learn a small Mahalanobis distance between the intra-class features and a large Mahalanobis distance between the inter-class ones. The NLM enables the non-linear mapping from the features of the nodes to their corresponding adjacency weights. The experimental results on both visible ReID and visual–infrared ReID verify the effectiveness of our method, for instance, our model achieves 95.7% rank-1 and 93.1% mAP on Market1501, as well as 58.6% rank-1 and 60.0% mAP on SYSU.