Spatial Topological Relations Research Articles

Formal topological description of three-dimensional topological entities based on k-dimensional pseudo-manifold

This paper clarifies the necessity of studying three-dimensional spatial data models, analyzes the research progress and existing problems of topological spatial relationship description methods, and proposes a complete and formal description framework of three-dimensional topological spatial relations based on point set topological theory and dimension expansion method. On this basis, the topological spatial relations existing in three-dimensional spatial objects are classified, and five fundamental topological spatial relations are defined. The mutual exclusivity and completeness of the minimal set of 3D topological space relations are proved. Based on point set topology and k-dimensional pseudo-manifold, this paper proposes the formal description of three-dimensional topological properties and spatial relations between spatial entities. The simplicial homology is applied to manifolds, the topological properties of three-dimensional space entities are revealed, and the formal description method of three-dimensional space entities is given through the geometric structural relationship between simplex and simplicial k-complex.

Formal Verification of a Topological Spatial Relations Model for Geographic Information Systems in Coq

Geographic information systems have undergone rapid growth for decades. Topology has provided valuable modeling tools in the development of this field. Formal verification ofthe model of topological spatial relations can provide a reliable guarantee for the correctness of geographic information systems. We present a proof of the topological spatial relations model that has been formally verified in the Coq proof assistant. After an introduction to the formalization of the axiomatic set theory of Morse–Kelley, the formal description of the elementary concepts and properties of general topology is developed. The topological spatial relations between two sets are described by using the concept of the intersection value. Finally, we formally proved the topological spatial relations between two sets which are restricted to the regularly closed and the planar spatial regions. All the proof details are strictly completed in Coq, which shows that the correctness of the theoretical model for geographic information systems can be checked by a computer. This paper provides a novel method to verify the correctness of the topological spatial relations model. This work can also contribute to the creation and validation of various geological models and software.

Soil Erosion Type and Risk Identification from the Perspective of Directed Weighted Complex Network

Identifying the geographic distribution and erosion risks of various soil erosion regions are critical inputs to the implementation of extensive and effective land protection planning. To obtain more accurate and sufficient erosion information on a large scope, this paper introduced the complex network theory to quantitatively simulate the topographic spatial structure and topological relationship of the erosion area. The watershed was selected as the basic study unit and the directed weighted complex network (DWCN) of each watershed was constructed from DEM data. The directed weighted complex network factor (DWCNF) of each watershed was calculated by the DWCN. After combining DWCNFs with existing SEEF, the soil erosion types and risks of sample areas in the Chinese Loess Plateau were identified by the random forest model. The results show that in both typical and atypical sample areas, the identification performance of soil erosion by combining DWCNFs with existing SEEFs was performed better than that by employing only the DWCNFs or SEEFs dataset. It is suggested that the quantitative description of the spatial structure and topological relationship of the watershed from the perspective of a complex network contributes to obtaining more accurate soil erosion information. The DWCNF of structural entropy, betweenness centrality, and degree centrality were of high importance, which can reliably and effectively identify the types and risks of soil erosion, thus providing a broader factor reference for relevant research. The method proposed in this paper of vectoring terrain into complex network structures is also a novel sight for geological research under complex terrain conditions.

Feature Line Extraction from Building Façade Point Clouds by Exploring Spatial Topological Relationship

After using a terrestrial laser scanner to acquire building facade point clouds, the extraction of feature lines can simplify the expression of building objects, thereby contributing to the accurate construction of building facade geometric models. To address the problems of missing extraction and low accuracy in existing methods, this study proposes a feature line extraction method for building facade point clouds by exploring the different spatial topological relationship between feature and non‐feature points. The method comprises three steps: feature point extraction, feature line generation, and feature line merging and optimization. First, feature points are extracted using the convex hull distance value and relative angle, as defined in this study. Thereafter, feature points are clustered by combining the random sample consensus and region growing algorithms, and the feature lines are obtained by utilizing the iterative weighted least squares method based on the IGGIII weight function. Finally, the feature lines are merged and optimized using an endpoint search method to improve the discontinuity and missing common endpoints of the original feature lines. The experimental results obtained using simulated and measured point cloud data show that this method can accurately extract feature points, and the extracted feature lines obtained from building facade point clouds have better accuracy and completeness, which is more practical than the existing methods and can be used in many applications such as building facade measurement and urban three‐dimensional modeling.

Incorporating circuit theory, complex networks, and carbon offsets into the multi-objective optimization of ecological networks: A case study on karst regions in China

Ecological networks (ENs) are important for maintaining regional ecological security and improving ecosystem service capacity. Therefore, it is important to consider spatial topological relationships and the need for carbon neutrality in the optimization of ENs. The optimization of EN structures and functions should be a systematic multi-objective process. This study combined landscape ecology, the complex network model, and spatial analysis technology, proposing an ecological barrier–topological feature–carbon offset-based (BTC-based) model research framework to deeply analyze and optimize ENs. First, the EN was preliminarily identified using the circuit theory model and the ecological barrier areas were simulated. Then, based on the complex network model, an undirected and unweighted complex network was established and its topological structural characteristics were analyzed. By constructing the estimation model for the carbon offset rate, its spatial distribution characteristics were calculated and interpreted. Finally, the BTC-based model was used to optimize the EN. Based on this model, Guizhou Province (a typical karst region in China) was taken as the research area for this study. The results showed that ecological improvement and degradation coexisted, and measures must be taken to optimize the EN. Based on the 2018 EN, the areas that required optimization were identified. Additionally, a restoration strategy was proposed for edge addition optimization for ecological corridors to promote the ecological protection and quality improvement of ecological sources and corridors. This approach would ensure the accurate implementation of ecological restoration projects and the effective management of ecosystems. The model proposed in this study also provides methodological support for EN optimization in other types of ecological regions.

A Method for the Automatic Extraction of Support Devices in an Overhead Catenary System Based on MLS Point Clouds

A mobile laser scanning (MLS) system can acquire railway scene information quickly and provide a data foundation for regular railway inspections. The location of the catenary support device in an electrified railway system has a direct impact on the regular operation of the power supply system. However, multi-type support device data accounts for a tiny proportion of the whole railway scene, resulting in its poor characteristic expression in the scene. Therefore, using traditional point cloud filtering or point cloud segmentation methods alone makes it difficult to achieve an effective segmentation and extraction of the support device. As a result, this paper proposes an automatic extraction algorithm for complex railway support devices based on MLS point clouds. First, the algorithm obtains hierarchies of the pillar point clouds and the support device point clouds in the railway scene through high stratification and then realizes the noise that was point-cloud-filtered in the scene. Then, the center point of the pillar device is retrieved from the pillar corridor by a neighborhood search, and then the locating and initial extracting of the support device are realized based on the relatively stable spatial topological relationship between the pillar and the support device. Finally, a post-processing optimization method integrating the pillar filter and the voxelized projection filter is designed to achieve the accurate and efficient extraction of the support device based on the feature differences between the support device and other devices in the initial extraction results. Furthermore, in the experimental part, we evaluate the treatment effect of the algorithm in six types of support devices, three types of support device distribution scenes, and two types of railway units. The experimental results show that the average extraction IoU of the multi-type support device, support device distribution scenes, and railway unit were 97.20%, 94.29%, and 96.11%, respectively. In general, the proposed algorithm can achieve the accurate and efficient extraction of various support devices in different scenes, and the influence of the algorithm parameters on the extraction accuracy and efficiency is elaborated in the discussion section.

Enhanced Multiview Fuzzy Clustering Using Double Visible-Hidden View Cooperation and Network LASSO Constraint

Multiview clustering is an important topic in multiview learning, where the cooperation of different views is used to improve clustering performance. Although multiview clustering has made considerable progress, most existing methods only utilize the information of the original visible views, or only consider some hidden space information shared by different views. Two of the challenges are: 1) insufficient exploitation of cooperative learning between visible and hidden information despite some preliminary attempts, and 2) inadequate consideration of topological information for improving multiview clustering. To meet the challenges, we propose the cooperation enhanced multiview fuzzy clustering method (CE-MVFC) in this article. First, we characterize multiview data with two hidden views, which are obtained by adaptive multiview non-negative matrix factorization (NMF) and fuzzy partition information of each sample in different clusters. Then, we integrated the hidden views and the original visible views to realize visible-hidden cooperation learning. Furthermore, we establish a similarity matrix for each visible view and the hidden view obtained through NMF to describe the data topology in these views. Based on the spatial topological relationship of the samples and the representation of hidden view obtained by fuzzy partition, the network least absolute shrinkage and selection operator is constructed to constrain multiview learning. Finally, we develop the multiview clustering method by exploiting the visible-hidden information cooperation and the spatial topological information constraints. Experiments on benchmark multiview datasets are conducted to demonstrate the highly competitive performance of the proposed CE-MVFC against the state-of-the-art methods.

Multistage Adaptive Point-Growth Network for Dense Point Cloud Completion

The point cloud data from actual measurements are often sparse and incomplete, making it difficult to apply them directly to visual processing and 3D reconstruction. The point cloud completion task can predict missing parts based on a sparse and incomplete point cloud model. However, the disordered and unstructured characteristics of point clouds make it difficult for neural networks to obtain detailed spatial structures and topological relationships, resulting in a challenging point cloud completion task. Existing point cloud completion methods can only predict the rough geometry of the point cloud, but cannot accurately predict the local details. To address the shortcomings of existing point cloud complementation methods, this paper describes a novel network for adaptive point cloud growth, MAPGNet, which generates a sparse skeletal point cloud using the skeletal features in the composite encoder, and then adaptively grows the local point cloud in the spherical neighborhood of each point using the growth features to complement the details of the point cloud in two steps. In this paper, the Offset Transformer module is added in the process of complementation to enhance the contextual connection between point clouds. As a result, MAPGNet improves the quality of the generated point clouds and recovers more local detail information. Comparing our algorithm with other state-of-the-art algorithms in different datasets, experimental results show that our algorithm has advantages in dense point cloud completion.

Refined Allocation of Water Resources in Pishihang Irrigation Area by Joint Utilization of Multiple Water Sources

Refined allocation of water resources is an important means of sustainable water resources utilization. Based on General Water Allocation and Simulation (GWAS), this study uses a Geographic Information System (GIS) to construct spatial topological relationships. A fairness optimal minimum was set as the objective function. Total quantity control, water supply potential, and quality-divided water supply were set as constraint conditions. Considering the dynamic mutual-feedback relationship between the middle-lower-reaches reservoir and the upstream reservoir, this study refines the allocation of water resources combined with the characteristics of “long cane knots melons” in the Pishihang irrigation area. Results showed that at 50%, 80%, and 90% frequencies in the base year, 2025, and 2035, respectively, the water deficient ratio is 0. For continuous drought years at 90% frequency, all water users are faced with different degrees of water shortage. In water source structures, water diversion in the irrigated area is the largest, followed by local surface water; reclaimed water and shallow groundwater are used as supplements. In the case of consecutive drought years, the water shortage degree can be reduced through rational development of local water and additional external water transfer. The model has thus been well applied. This study provides a more accurate method for optimizing water resources allocation.

Propagation path tracing of hydraulically created fractures based on microseismic monitoring

To evaluate the effect of hydraulic fracturing in a low-permeability reservoir, a propagation path tracing method for hydraulically created fractures was established based on microseismic monitoring data. First, the numerical simulation of the wave propagation process, grid search, and error-weight coefficient method was combined to locate the microseismic source. Then, the moment tensor inversion method was used to determine the tensile angle and source mechanism of hydraulically created fractures. Next, the tensile angle was used as the weight-index to determine the size of the mixed-source mechanism fracture combined with the shear and tensile source size quantization model. Finally, the spatial topological relationship between fractures was determined by comprehensively considering the spatial location and radius of the fractures, to realize the propagation path tracing of hydraulically created fractures. These tracking results can be used as one of the bases for the evaluation of the hydraulic fracturing effect.

Accessing interactively the spatio-temporal data-model of an archaeological site through its 3D virtual reconstruction

Information and communication technologies are increasingly used in all archaeological processes. However, archaeologists sometimes consider them as intrusive, too far from the traditional work methodology and even a hindrance. In this article we propose a framework to allow natural and therefore intuitive access to the archaeological record. The information retrieval process is carried out through a three-dimensional virtual reconstruction of the archaeological site. In this system, navigation and interaction with the three-dimensional elements of the environment triggers database queries. To achieve such functionality, a client-server architecture is designed in which the server maintains a spatio-temporal database with heterogeneous information, including the 3D models of the finds. To do this, a virtual replica of the site is created considering spatial restrictions and topological relationships among the finds.

HYPERSPECTRAL IMAGE CLASSIFICATION WITH LOCALIZED SPECTRAL FILTERING-BASED GRAPH ATTENTION NETWORK

Abstract. Graph-based deep learning has been proved a promising approach that has an apparent superiority for learning graph data and modeling spatial topological relations between features. In particular, graph attention networks (GATs) are good at efficiently processing the graph-structured hyperspectral data by leveraging masked self-attention layers to address the known shortcomings of previous frameworks based on graph convolutions or their approximations. In this study, we proposed a novel approach that combines localized spectral filtering and GAT for the hyperspectral image classification task. First, we conducted unsupervised t-SNE (t-distributed stochastic neighbor embedding) manifold learning-based feature dimensionality reduction to create localized hyperspectral data cubes. Then, these feature cubes combined with localized adjacent matrices were fed into a shallow graph attention network in a supervised learning manner. Finally, we obtained credible classification results and promising classification performance in distinguishing diversified land covers through reducing the possible redundancy of spectral information and enhancing the expression of local spatial-spectral information. Experiments on two real hyperspectral data sets (that is, Indian Pines-A (IA) and Huanghekou (HH) data sets) demonstrated that the presented approach offers promising classification performance, that is, the GAT using t-SNE acquires superior performance than that of using PCA (principal component analysis), and also proves the great importance of combining spatial- and spectral information for hyperspectral image classification.

IAGC: Interactive Attention Graph Convolution Network for Semantic Segmentation of Point Clouds in Building Indoor Environment

Point-based networks have been widely used in the semantic segmentation of point clouds owing to the powerful 3D convolution neural network (CNN) baseline. Most of the current methods resort to intermediate regular representations for reorganizing the structure of point clouds for 3D CNN networks, but they may neglect the inherent contextual information. In our work, we focus on capturing discriminative features with the interactive attention mechanism and propose a novel method consisting of the regional simplified dual attention network and global graph convolution network. Firstly, we cluster homogeneous points into superpoints and construct a superpoint graph to effectively reduce the computation complexity and greatly maintain spatial topological relations among superpoints. Secondly, we integrate cross-position attention and cross-channel attention into a single head attention module and design a novel interactive attention gating (IAG)-based multilayer perceptron (MLP) network (IAG–MLP), which is utilized for the expansion of the receptive field and augmentation of discriminative features in local embeddings. Afterwards, the combination of stacked IAG–MLP blocks and the global graph convolution network, called IAGC, is proposed to learn high-dimensional local features in superpoints and progressively update these local embeddings with the recurrent neural network (RNN) network. Our proposed framework is evaluated on three indoor open benchmarks, and the 6-fold cross-validation results of the S3DIS dataset show that the local IAG–MLP network brings about 1% and 6.1% improvement in overall accuracy (OA) and mean class intersection-over-union (mIoU), respectively, compared with the PointNet local network. Furthermore, our IAGC network outperforms other CNN-based approaches in the ScanNet V2 dataset by at least 7.9% in mIoU. The experimental results indicate that the proposed method can better capture contextual information and achieve competitive overall performance in the semantic segmentation task.

A Formal Representation of the Semantics of Structural Geological Models

A structural geological model describes the structure of subsurface and plays an important role in the exploration of mineral and petroleum resources. Despite the widespread use of three-dimensional geological models, the theoretical research of informatics in the field of structural geology is still very limited. We have noticed a lack of methods for integrating explicit semantics of field observation data and geophysical data into geological models. The existing model representation methods focus on accurately representing the geometric morphological information of underground structures, ignoring the high-level semantics implied in the model. The formal representation of the semantic information is necessary to promote the development of intelligent methods in geomodeling and geophysical inversion. In this paper, we propose a new framework to formally represent the semantics of structural geological models with a clear distinction of geometric and geological semantics. For the geometric semantics, based on the extension of the 9-intersection model, we mathematically define the spatial topological relations between geometric objects that make up the geological model. For the geological semantics, we define the geological contact and compositional relations between geological bodies and geological surfaces and reveal the temporal implications of these geological relationships. We design a multilayer heterogeneous network as a computer characterization of the semantics of the geological model. A better representation of semantic information aids in the creation and validation of geological models, as well as management, queries, and analyses of geological knowledge.

Scale–Relation Joint Decoupling Network for Remote Sensing Image Semantic Segmentation

As we all know, remote sensing (RS) images contain multi-scale and numerous RS objects, along with massive and complex spatial topological relationships, such as the adjacency, proximity relations of same-scale objects, and inclusion relations of cross-scale objects. However, the existing semantic segmentation methods have never explored the cross-scale relations, which are especially important when comes to the situation that the RS objects cannot be accurately identified, they could be supplemented by the surrounding contents. To address the above concern, we propose a scale-relation joint decoupling network (SRJDN) for the semantic segmentation of RS images by simultaneously considering decoupling scales and decoupling relations to excavate more complete relationships of multi-scale RS objects. The SRJDN is performed by following three steps, namely scale decoupling (SD), relation decoupling (RD), and fine-granularity guided fusion (FGF). The SD module uses dilated convolution with different rates to decouple RS objects into different scale feature groups, from small to large scales. Afterward, the RD considers all the spatial topological relationships and decouples these relationships according to the scale, which is divided into two parts, including same-scale relation extraction (SSRE) and cross-scale relation extraction (CSRE). The SSRE establishes the graph structures at each scale independently to mine the relationships of same-scale RS objects and the CSRE constructs the graph in a unified pattern between cross-scales to explore cross-scale target relationships. Third, the FGF module regards small-scale features as fine-granularity representation and applies its attention map to guide the learning of other scale features, which could mine more reliable and comprehensive saliency information and improve the feature consistency. Numerical experiments conducted on two large-scale fine-resolution RS image datasets empirically demonstrate the robustness of the proposed joint decoupling strategy and the effectiveness of the fine-granularity guided fusion in RS image semantic segmentation tasks.

BIM-based graph data model for automatic generative design of modular buildings

As volumetric modular construction is gaining attention worldwide, there is a growing interest in the representation and model-based data exchange for modular buildings to optimise and communicate the design generation to prefabrication. This paper presents a Building Information Modelling (BIM)-based graph data model for the theoretic representation of essential characteristics in modular buildings, intending to automate and optimise the generative design for modular construction. The proposed new method involves the establishment of Industry Foundation Classes (IFC) model view definition (MVD) to comprehensively describe the required information for designing modular buildings. Following this, the IFC MVD is mapped to a graph data model, which includes the explicit formulation of absent spatial attributes, topological relationships, geometries, and semantics for volumetric modules. In compliance with the graph-theoretic representation, data transformation algorithms are developed to convert the required information in BIM to the graph model for assorted information query. Provided the extracted information, a prototype system is developed and examined via an illustrative example focusing on the automatic generative design of modular buildings.

Multiple Instance Classification for Gastric Cancer Pathological Images Based on Implicit Spatial Topological Structure Representation

Gastric cancer is a malignant tumor with high incidence. Computer-aided screening systems for gastric cancer pathological images can contribute to reducing the workload of specialists and improve the efficiency of disease diagnosis. Due to the high resolution of images, it is common to divide the whole slide image (WSI) into a set of image patches with overlap before utilizing deep neural networks for further analysis. However, not all patches split from the same cancerous WSI contain information of cancerous issues. This restriction naturally satisfies the assumptions of multiple instance learning (MIL). Moreover, the spatial topological structure relationships between local areas in a WSI are destroyed in the process of patch partitioning. Most existing multiple instance classification (MIC) methods fail to take into account the topological relationships between instances. In this paper, we propose a novel multiple instance classification framework based on graph convolutional networks (GCNs) for gastric microscope image classification. Firstly, patch embeddings were generated by feature extraction. Then, a graph structure was introduced to model the spatial topological structure relationships between instances. Additionally, a graph classification model with hierarchical pooling was constructed to achieve this multiple instance classification task. To certify the effectiveness and generalization of our method, we conducted comparative experiments on two different modes of gastric cancer pathological image datasets. The proposed method achieved average fivefold cross-validation precisions of 91.16% and 98.26% for gastric cancer classification on the two datasets, respectively.

Automatic Landform Recognition from the Perspective of Watershed Spatial Structure Based on Digital Elevation Models

Landform recognition is one of the most significant aspects of geomorphology research, which is the essential tool for landform classification and understanding geomorphological processes. Watershed object-based landform recognition is a new spot in the field of landform recognition. However, in the relevant studies, the quantitative description of the watershed generally focused on the overall terrain features of the watershed, which ignored the spatial structure and topological relationship, and internal mechanism of the watershed. For the first time, we proposed an effective landform recognition method from the perspective of the watershed spatial structure, which is separated from the previous studies that invariably used terrain indices or texture derivatives. The slope spectrum method was used herein to solve the uncertainty issue of the determination on the watershed area. Complex network and P–N terrain, which are two effective methodologies to describe the spatial structure and topological relationship of the watershed, were adopted to simulate the spatial structure of the watershed. Then, 13 quantitative indices were, respectively, derived from two kinds of watershed spatial structures. With an advanced machine learning algorithm (LightGBM), experiment results showed that the proposed method showed good comprehensive performances. The overall accuracy achieved 91.67% and the Kappa coefficient achieved 0.90. By comparing with the landform recognition using terrain indices or texture derivatives, it showed better performance and robustness. It was noted that, in terms of loess ridge and loess hill, the proposed method can achieve higher accuracy, which may indicate that the proposed method is more effective than the previous methods in alleviating the confusion of the landforms whose morphologies are complex and similar. In addition, the LightGBM is more suitable for the proposed method, since the comprehensive manifestation of their combination is better than other machine learning methods by contrast. Overall, the proposed method is out of the previous landform recognition method and provided new insights for the field of landform recognition; experiments show the new method is an effective and valuable landform recognition method with great potential as well as being more suitable for watershed object-based landform recognition.

EddyGraph: The Tracking of Mesoscale Eddy Splitting and Merging Events in the Northwest Pacific Ocean

This paper proposes an algorithm named EddyGraph for tracking mesoscale eddy splitting and merging events. Twenty-seven years (January 1993–December 2019) of sea level anomaly (SLA) data are analyzed in the Northwest Pacific Ocean (105°E–165°W, 0°N–60°N). First, we propose a multilevel eddy identification method based on SLA to obtain an eddytree data set, representing a spatial topological tree structure of closed SLA contours with mononuclear eddies, multicore eddies and eddy seeds as the leaf nodes and eddygroups (reflecting the spatial topological relationship among eddies) as the intermediate nodes. The EddyGraph tracking algorithm is applied to the eddytree data set, which results in eddy-directed acyclic graphs (Eddy-DAGs). Only eddies contained within a common eddygroup are tracked as sources in merging events or sinks in splitting events. Furthermore, we extract typical splitting and merging events and composite the sea surface temperature anomalies (SSTAs) inside the eddygroups and eddies during these events. The results confirm that merging eddies in the same eddygroup degenerate into a single eddy and that a splitting eddy evolves into eddies within the same parent eddygroup. Moreover, we match a merging event of cyclonic eddies with in situ data of both drifters and loopers in Lagrangian trajectories. Finally, we present EddyGraph, a data set of mesoscale eddy tracking in the Northwest Pacific Ocean (105°E–165°W, 0°N–60°N).

A topological-based approach for determining spatial relationships of complex volumetric parcels in land administration systems

Present changes in land property originate from sizable density growth of the urban environment, led by the high demand of land, especially in industrial and commercial centers. This urbanization development - above and below ground - causes an acute need for developing land administration systems to accommodate current and future demands in land management on the one hand, and urban planning perspectives on the other hand. One approach calls for the design of 3D cadastral registration and management systems, which are planned to replace the well-established 2D systems. One of the key processes that these systems should handle for various cadastral workflows, such as parcel insertion and partition, is accurately determining the spatial topological relationship that exist between 3D Volumetric Parcels. These processes are relatively simple to implement between non-complex 3D Volumetric Parcels, but the reality is that the 3D Volumetric Parcels are mostly geometrically complex. In this paper, we suggest methods and processes based on simplifying unbounded, hollowed, curved, and concaved 3D Volumetric Parcels to enable their robust and accurate spatial relationship determination. As part of the comprehensive solution, we propose a subdivision algorithm used for concaved 3D Volumetric Parcels. We have analyzed the various processes on a realistic simulation, proving that the proposed processes were accurate in handling complex 3D Volumetric Parcels by automatically validating their spatial relatioships. We believe that implementing and embedding the developed set of tools in 3D land administration systems is a step forward in the realization of comprehensive land processes that are essential for the automatic management of our complex and developing urbanization.