Unveiling the Urban Morphology of Small Towns in the Eastern Qinba Mountains: Integrating Earth Observation and Morphometric Analysis

Abstract

In the context of the current information age, leveraging Earth observation (EO) technology and spatial analysis methods enables a more accurate understanding of the characteristics of small towns. This study conducted an in-depth analysis of the urban morphology of small towns in the Qinba Mountain Area of Southern Shaanxi by employing large-scale data analysis and innovative urban form measurement methods. The U-Net3+ model, based on deep learning technology, combined with the concave hull algorithm, was used to extract and precisely define the boundaries of 31,799 buildings and small towns. The morphological characteristics of the town core were measured, and the core areas of the small towns were defined using calculated tessellation cells. Hierarchical clustering methods were applied to analyze 12 characteristic indicators of 89 towns, and various metrics were calculated to determine the optimal number of clusters. The analysis identified eight distinct clusters based on the towns’ morphological differences. Significant morphological differences between the small towns in the Qinba Mountain Area were observed. The clustering results revealed that the towns exhibited diverse shapes and distributions, ranging from irregular and sparse to compact and dense forms, reflecting distinct layout patterns influenced by the unique context of each town. The use of the morphometric method, based on cellular and biological morphometry, provided a new perspective on the urban form and deepened the understanding of the spatial structure of the small towns from a micro perspective. These findings not only contribute to the development of quantitative morphological indicators for town development and planning but also demonstrate a novel, data-driven approach to conventional urban morphology studies.

1. Introduction

Small towns throughout the world exhibit vastly diverse characteristics, and in contrast to large cities, their scope has not been the subject of extensive research. Small towns serve as a transition between urban and rural areas, representing the lowest tier of the urban system [1]. Nevertheless, they cannot be classified as “micro-cities” [2] but are closer to a hybrid form with both urban and rural characteristics [3]. Defining small towns is by no means an easy task. Internationally, the definition and perception of small towns vary due to differences in population size, economic activities, and geographical location. The criteria for the definition of small towns differ widely between countries. For instance, Germany considers towns with a population between 5000 and 20,000 as small towns [4], whereas the definition adopted in the United States also refers to “urban clusters”, with a total range of 25,000 to 50,000 [5]. Chinese small towns are significantly different from those in other countries. In China, small towns are typically considered administrative regions, encompassing both the town center and the surrounding rural areas [6,7]. These small towns represent the lowest level in China’s urban system, situated between cities and villages, and exhibit the characteristics of both urban and rural areas. The towns extracted and studied in this work are administrative units known as “established towns”. For a long time, small towns have been neglected, whether as research subjects or in public policy [8]. Research measuring the spatial characteristics of small towns is even scarcer.

In A Theory of Good City Form, Lynch argues that the quality of a place results from the interaction between the urban form and the society that inhabits the city [9]. Urban morphology refers to the physical characteristics of the urban form, such as the spatial arrangement of buildings, urban landscapes, and their transformations [10]. Scholars have found that planning strategies designed to optimize the physical forms of cities play a crucial role in promoting sustainable urban development [11]. It is thus essential to investigate the traits of urban morphology and uncover the underlying drivers of these transformative strategies. From a comparative perspective, Oliveira et al. [12] detail different approaches to urban morphology, emphasizing the importance of combining methods to enhance our understanding of the urban form and its evolution. In morphological studies, one of the most important methods is morphometrics—measuring the geometric shapes or relations of urban elements [13,14]. The measurement and classification of urban forms have been some of the most important themes in the field of urban geography and urban planning in recent years. For example, Fleischmann et al. [15] categorized 450 research articles identifying urban morphology indicators into six types: dimensions, shapes, spatial distribution, intensity, connectivity, and diversity. The identified indicators can be measured at diverse scales and scopes. Statistical clustering techniques were utilized by Berghauser Pont et al. [16] to describe contemporary urban forms in five European cities and allowed them to perform a quantitative city comparison.

By numerically describing urban elements such as buildings, streets, and enclosed spaces, it is possible to reveal the patterns of urban organization and the potential relationships among different forms. The measurement of the urban form is linked with the measurement of the cellular and organismal morphology. From this point of view, cities can be considered analogously to organisms: streets and buildings play the roles of cells and tissue, and the city itself is a “tissue structure”. In this case, most of the concepts used in urban morphology, such as the “urban fabric” and “urban cells”, are essentially morphological concepts in biology [17]. Fleischmann et al. [18] drew an analogy between this approach and the methods of early biologists, who sought to classify biological species based on their morphological similarities. This analogy is not limited to the morphological structure but also includes a response to environmental factors, such as the cities’ ability to adapt to climate change and the mechanisms’ evolution [19]. As emphasized by Lobo and others in their research [20], progress in cell morphology analysis highlights the need for standardized morphological indicators, including the cell area, aspect ratio, convex hull perimeter, convex hull area, roundness, and ellipticity, to assess the significance of the cell morphology in the context of regenerative medicine. Cell shapes can be seen as the result of the interaction between internal and external constraints, a “structural” outcome [21]. The concept of fractal dimensions applied to the demarcation of small-town boundaries is inspired by insights from the measurement of organisms and cell morphometry. The central regions of small towns can be seen as analogous to the “nuclei” of biological cells.

Research on small towns is relatively limited, despite significant strides having been made through the quantitative study of the urban morphology. The reasons for this mainly lie in the fact that collecting relevant data pertinent to those small towns is very complicated, which constrains research both in scope and depth. In addition, the morphological characteristics and developmental tendencies are relatively high, which makes this area of study challenging. With the continuous enhancement of Earth observation technology and its data acquisition capabilities, these obstacles are expected to be overcome, leading to a better understanding and description of the urban morphology of small towns [22]. The increasing availability of spatial data and the emergence of new geospatial tools offer tremendous potential for the analysis of the urban form [23]. Earth observation (EO) has recently been proven to be an essential tool in capturing the urban morphology. Thus far, different methods including pixel-based or object-based analysis, machine learning, and visual image interpretation have been used, and the spatial-scale variations across urban areas, cities, settlements, or individual buildings have been applied in EO research [24]. EO offers a less expensive and rapid means of data acquisition that provides planners with records of the number, size, footprint, density, and layout of buildings [25]. This study focuses on building layers, as they are the primary human-made elements. Their quantitative morphological indicators, such as their density and shape, largely reflect their socioeconomic characteristics [26].

Considering these factors, studying the urban morphology of the small towns in the eastern part of the Qinba Mountain Area in Southern Shaanxi could be interesting from multiple perspectives. Currently, there is a notable lack of quantitative analyses of the spatial morphology of small towns, and data collection for small towns in mountainous areas with complicated terrain is challenging. Moreover, when urban theorists discuss the “urban form”, they predominantly refer to large cities, overlooking small towns and their unique characteristics. Specifically, at the small-townlevel, the methods of morphological analysis are distinct from those used for large cities and rural areas. With few studies available nowadays, particularly in the quantitative analysis of small towns’ spatial forms, discussions relating to the urban morphology in small towns may thus fill this gap and enrich the literature on urban morphology. Discussions of such topics would help to identify the characteristics and features of the urban morphology in small towns and formulate corresponding planning strategies to optimize the physical forms of small cities toward sustainable development. The study of the urban morphology at the small-townlevel has become possible through various improvements, including the current levels of technology in Earth observation and data acquisition. Spatial data based on geospatial tools provide a data-driven approach to decision support for planning and development activities in these small towns. The main objective of this study is to conduct an in-depth analysis of the urban morphology of the small towns in the Qinba Mountain Area of Southern Shaanxi using large-scale data analysis and innovative urban form measurement methods. This will provide a comprehensive understanding of the spatial structure and characteristics unique to this region, contributing valuable insights for town development and planning.

2. Materials and Methods

2.1. Study Area

The main study area covers the eastern region of the Qinba Mountains in Southern Shaanxi, Shangluo City (Figure 1). The Qinba Mountain Area boasts a diverse and rich array of natural vegetation types and biological resources, serving as a critical ecological security barrier in Central China. The Qinba Key Ecological Function Zone was among the first areas in China designated as a critical environmental function zone. However, the region’s ecological environment is fragile, with deficiencies in land resources as well as serious soil erosion and frequent natural disasters, which all restrict the sustainable development of the Qinba Mountain Area. Shangluo is one of several cities in the Qinba Mountain Area, characterized by abundant natural resources and a complex geography [27,28,29]. Shangluo City is located on the southern edge of the Qinling Mountains and is characterized by extremely high bio-geomorphic diversity and complexity, including mountains, hills, and plains that form an intricate net. Such a complicated natural background provides numerous examples and a varied town background that is well suited to the research of small towns in this region. Shangluo City includes towns and villages that have developed across different terrains from adjacent mountains to hills. Research has demonstrated that the spatial growth models of rural settlements in the Qinba Mountain Area remain distinct, exhibiting a variety of terrains and differences in economic development intensity, transportation accessibility, etc. [30]. The intertwined mountains and rivers in the Qinba Mountain Area have had a profound impact on the development of urban and rural spaces [31]. Due to their unique topographical conditions, mountain towns face specific restrictions and challenges in their development. For example, to some extent, the complexity of the terrain and the heterogeneity of the space limit the development of the transportation network and the effective use of land resources, affecting the spatial layout and economic development of these towns. At the same time, the natural resources and environmental conditions of mountainous areas have a profound impact on the lifestyles and economic activities of the local residents. These factors together influence the formation and evolution of the urban form [28].

2.2. Research Methodology

In this study, as illustrated in Figure 2, a novel research methodology was utilized for the large-scale measurement and classification of urban forms in small towns within the Qinba Mountain Area of Southern Shaanxi. This approach enabled a comprehensive analysis of the urban morphology, facilitating a deeper understanding of the spatial structures and characteristics unique to this region.

For the accurate targeting of the analysis within the small towns, town government coordinates linked with Gaode Maps and OpenStreetMap were obtained, serving as the central points and boundaries for the study area. OpenStreetMap (OSM) is a global mapping community and online geographic information system that plays an increasingly important role in various academic studies. It provides free, high-quality data on global street networks and other urban infrastructure. Users can directly access the OSM database to download, edit, and use these map data [32,33]. This study processes and analyzes the data using Python and Jupyter Notebook.

There are a number of publicly available Earth observation image datasets throughout the world. Google Earth provides high-resolution satellite images in the form of tiles, with each tile representing a specific area. These tiles are integrated from high-resolution composite images sourced from various satellites, such as Maxar, Airbus, Terrametrics, QuickBird, and WorldView. Various approaches can be used to download these data. Google Earth Pro can directly download the images at maximum resolution, while third-party open tools such as SAS Planet facilitate data extraction from the Google Earth portal. SAS Planet is a free program, widely used in research, that allows the download of georeferenced images (or maps) from systems such as Google Earth, Bing Maps, and ESRI. Cheng et al. [34] used SAS Planet to obtain high-resolution Google Earth image tiles for peach orchard segmentation. Murillo-García and Alcántara-Ayala [35] used SAS Planet to download georeferenced images from systems such as Google Earth and Bing Maps, aiding in their creation of a multi-temporal landslide inventory map. Vasavi et al. [36] used SAS Planet to acquire high-resolution satellite images to train a U-Net- and ResNet-based model to classify buildings in Nashik. To obtain data relevant to this study, the SAS Planet software(v.230909) was used to download Google Earth image tiles at zoom level 19 with a spatial resolution of 0.6 m. Since our study area focused on the small towns of Shangluo City, the volume of the downloaded data did not qualify as a “large-scale data download” and thus did not violate the data usage guidelines.

Due to the lack of suitable datasets for small towns, a dataset was manually created. This dataset comprised 16,128 manually annotated training images, sourced from high-resolution Google Earth imagery. The specifically selected U-Net3+, known for its successful implementation in image segmentation [37], was used to precisely extract building footprint data, allowing for the identification of the outlines of structures within the small towns. The combination of geographic information from Gaode Maps and OpenStreetMap with U-Net3+ analysis enabled the capturing of numerous detailed urban forms from different sources.

The next step involved using OpenCV for data optimization and processing. This step was aimed at clarifying the boundaries of the buildings to increase the accuracy of the subsequent analysis. As an open-source library, OpenCV has powerful image processing capabilities and can effectively support the optimization and processing of images [38]. The optimized data were processed using the DBSCAN algorithm to determine the town’s district boundaries. As a density-based spatial clustering algorithm, DBSCAN can identify areas with similar densities, thereby effectively delineating the areas of the small town.

At the same time, this study also adopted methods from biology and the method of cell morphology measurement, and through iteration calculation and the concave hull algorithm, it accurately obtained the small town’s boundaries. With a series of indicators, the boundaries of the small-town and their characteristics were analyzed. We conducted a comprehensive analysis of the small town’s spatial characteristics and the composition of its structure. The measurement method was inspired by the measurement and classification of cell and organism forms in biological morphology. In urban form analysis, the use of this method also contributes to interdisciplinary innovation [37].

This study conducted detailed measurements and calculations of the urban morphology of the small towns through the aforementioned data processing and analysis methods, and it performed a clustering analysis based on the morphological characteristics.

2.3. Morphometric Characteristics

In assessing urban morphology, researchers have identified and applied various metrics to capture the complexity and evolution of urban forms. Basaraner and Cetinkaya [39] refined the analysis of building footprints in GIS by employing shape indices such as circularity, convexity, and rectangularity and introducing new indices such as the Equivalent Rectangular Index and Roughness Index to enhance the classification schemes. Song et al. [40] applied indicators such as the fractal dimension, compact ratio, and shape factor to examine the urban morphology at different scales, providing insights into both the overall and localized urban characteristics. Additionally, Triantakonstantis and Stathakis [41] used spatial metrics to track urban sprawl across Europe, noting a substantial increase in urban areas and identifying trends toward simpler, more circular urban forms. These studies underscore the utility of various metrics in detailing the structural complexities of urban environments. The field of urban morphology research is continually advancing with the development of innovative technological tools, which significantly enhance the methods used to analyze urban forms. Serrano et al. [42] utilized GIS techniques to classify European urban settlements, demonstrating the detailed delineation of the urban form from high-density clusters to small towns. Zhang et al. [43] utilized remote-sensing and segmentation techniques for the mapping of urban informal settlements. The integration of open-source tools such as Python and OpenStreetMap has significantly advanced the methodologies used for the analysis of urban forms. Ma et al. [44] leveraged OpenStreetMap data to develop the OSMsc framework, creating semantic 3D city models that enhance urban analysis in fields such as morphology and microclimates.

In this study, a comprehensive set of morphological indicators was adopted. This system not only covered the dimensions and shape characteristics of the town district but also included a detailed analysis at the level of tessellation cells, defined by Martin Fleischmann et al. [45] as distinct spatial units formed via Voronoi-based spatial partitioning techniques and buildings. Notably, our selection of indicators was greatly inspired by the field of biology and cell morphology studies. Progress in cell morphology analysis highlights the need for standardized morphological indicators, including the cell area, aspect ratio, convex hull perimeter, convex hull area, roundness, and ellipticity, to assess the significance of the cell morphology in the context of regenerative medicine. These indicators, while evaluating the morphology of biological cells, also provide us with new perspectives and tools for the assessment of the spatial forms of small towns. A range of morphological feature indicators was utilized to conduct the detailed measurement and analysis of the urban morphology of the small towns. These indicators ranged from the whole town district to specific buildings, aiming to fully capture and illustrate the spatial structure and morphological characteristics of the small towns.

Fleischmann et al. [15] considered morphological aspects in urban research that were quantifiable in nature, such as the shape of the building and its basic dimensions. Dibble et al. [46] analyzed morphological urban evolution by measuring the building and spatial shape and distribution, where the best urban morphological indicators seemed to be the features of the shape and dimension. In this context, Wentz et al. [47] illustrated six basic features conceptualizing a multidimensional urban form, eventually including the characteristics of the spatial distribution and shape of buildings, thus addressing the need for such categorizations. This shows the importance of measures that describe the properties and dimensions, such as the area and perimeter; those that describe the scale, size, and shape, such as the circular compactness and number of corners; those that describe the geometric features of buildings and their intensity, such as the coverage area ratio and density; and those that describe the distribution density and intensity of buildings in space. Through a holistic analysis of such features, it is possible for the spatial structure and the morphological evolution of urban areas to be more effectively characterized and understood.

A range of morphological feature indicators were utilized to conduct the detailed measurement and analysis of the urban morphology of the small towns. These indicators ranged from the whole town district to specific buildings, aiming to fully capture and illustrate the spatial structure and morphological characteristics of the small towns. As detailed in

Table 1. Morphological feature indicators for small towns’ urban forms in the Qinba Mountain Area of Southern Shaanxi.

Index	Element	Level	Category
Area	Town district	L	Dimension
Perimeter	Town district	L	Dimension
Fractal Dimension	Town district	L	Shape
Longest Axis Length	Town district	L	Shape
Circularity	Town district	L	Shape
Centroid–Corner Mean Distance	Town district	L	Shape
Hull Perimeter	Town district	L	Dimension
Aspect Ratio	Town district	L	Shape
Nucleus Area	Tessellation cell	M	Dimension
Nucleus Buildings Count	Tessellation cell	M	Dimension
Nucleus Area Ratio	Tessellation cell	M	Intensity
Building Count	Building	S	Dimension
Area	Building	S	Dimension
Coverage Area Ratio	Building	S	Intensity

, these indicators were categorized into three levels: the town district, the tessellation cell, and the building. Each level was further divided into three categories, dimension, shape, and intensity, enabling a more systematic and comprehensive analysis of the spatial features of the small towns.

At the town district level, indicators such as the area, perimeter, fractal dimension, length of the longest axis, roundness, average distance from the centroid to corner points, shell perimeter, and aspect ratio are included to describe the overall size and shape of the town. The tessellation cell level focuses on the town’s core district, using indicators such as the core district size, number of core buildings, and core district ratio to depict the characteristics of the town’s internal spatial units. The building level considers individual buildings and their clusters, with indicators such as the number of buildings, the building area, and the ratio of covered areas, reflecting the town’s building distribution and density.

2.4. Morphological Measurement of Small Towns in Shangluo City, Qinba Mountains, Southern Shaanxi

2.4.1. Small-Town District Identification

In the process of identifying small-town districts, machine learning algorithms such as DBSCAN (Density-Based Spatial Clustering of Applications with Noise) offer an innovative approach. This method not only effectively identifies the boundaries of towns but also explores the spatial structures and functional areas within them. By analyzing geospatial data, this approach can reveal the morphological characteristics of small towns, thus providing a new perspective for a deeper understanding of towns’ features [48]. Research by Cetinkaya et al. [49] further demonstrates the utility of DBSCAN in urban blocks, highlighting its ability to effectively distinguish building groups based on proximity.

By applying the DBSCAN algorithm to define the vector edges of structures, the recognition of the ranges of small-town areas can be automated. By excluding the neighboring villages, it is possible to determine the study subjects more precisely. This enables us to obtain clustering results reflecting the small-town regions. After calculating them on a map, it is also possible to identify the main spatial zones of these study subjects, providing useful information for further research.

Figure 3 depicts the results of the clustering with the DBSCAN algorithm and the visualization of these results on a map. It clearly marks the boundaries of the small towns, showing the automatic clustering process after converting the building vector boundaries into points, effectively distinguishing the town areas from the surrounding village areas.

2.4.2. Small-Town Boundary Identification

In traditional methods of determining the boundaries of small towns in research, the administrative boundaries formulated by the government are always emphasized. This is an essential part of national spatial planning. However, data collection for small towns in mountainous areas with complicated terrain is challenging, and it is essential for the town boundaries to be calculated using geospatial data and computational geometry.

The convex hull and concave hull represent the two central concepts associated with describing the shape of a set of points. The convex hull is the smallest convex polygon encapsulating the set of points, whereas the concave hull is a non-convex polygon that closely fits around the shape of the set of points. The definition and algorithms of the convex hull have been extensively studied. Edelsbrunner et al. [50] proposed an algorithm based on the shape of planar point sets, which has significant applications in information theory. Convex hulls are widely used in image processing, geographic information systems (GIS), and computer graphics due to their simplicity and efficiency. However, it has been noticed that convex hulls fail to accurately describe point sets with complex boundaries. As a result, researchers proposed the concept of the concave hull. Duckham et al. [51] proposed that a simple polygon generated by an efficient algorithm can capture the shape of the planar point set more accurately. Therefore, this method provides an effective solution for the generation of a concave hull due to the balance between computational efficiency and the accuracy of shaping.

By iteratively determining the locations of small towns’ boundaries using the convex hull and concave hull algorithms, this study is able to increase the accuracy of boundary recognition and better represent a real geographical small town. By exploring the possibility of identifying the boundaries of the small towns in the Shangluo City region within the Qinba Mountains of Southern Shaanxi, this research introduces a novel approach to boundary recognition based on concave hull algorithm calculations. Not only does it consider the continuity and integrity of the geographical space of a small town, but it also overcomes issues related to data acquisition in disadvantaged mountainous areas, contributing a novel solution for the accurate recognition of small towns’ boundaries.

With the advent of powerful computing tools, the calculation of convex and concave hulls has become more accessible and efficient. Python, in particular, offers a range of libraries that simplify the computation of these geometric shapes. This study uses the shapely [52] library in Python to compute the convex hull and the alphashape [53] library to compute the concave hull, providing a robust framework for boundary recognition in geographical data analysis. Additionally, the relevant dataset and codes used in this study are publicly available. The convex hull algorithm generates the smallest convex polygon that can enclose all points. This provides a simple yet effective way to outline the general shape of a set of points, forming the foundation for boundary recognition. The algorithm first extracts all of the points from the provided GeoDataFrame and then uses the MultiPoint class from the shapely library to combine these points into a MultiPoint object, computing the convex hull by adopting the method that generates the smallest convex polygon that can enclose all of the points. The concave hull algorithm extends this concept by allowing the boundary to follow the actual contours of the points more closely, capturing the nuances of the geographical shape. The iterative approach ensures that the algorithm fine-tunes the boundary to avoid splitting it into multiple parts, thus maintaining the integrity of the geographical space. The algorithm extracts all points from the provided GeoDataFrame, initializes the parameters with an initial alpha value (controlling the shape of the concave hull) and other iteration parameters, and then iteratively calculates the alpha shape (an approximation of the concave hull) for the current alpha value using the alphashape function. If the resulting shape is a valid polygon, it is saved as the last valid concave hull, and the alpha value is incremented by a certain factor to gradually adjust the shape. This process continues until the shape is split into multiple parts or the maximum number of iterations is reached.

By applying these algorithms to the Shangluo City region within the Qinba Mountains of Southern Shaanxi, this research demonstrates a novel approach to boundary recognition. The combination of convex and concave hull calculations enhances the accuracy of delineating small towns’ boundaries, addressing the challenges related to data acquisition in mountainous areas.

Figure 4 displays the process of iteratively identifying the boundaries of small towns using the concave hull algorithm, where image (a) shows the convex hull boundary and the generated compact concave boundary, while image (b) details the method of identifying the concave boundary through the iterative process. The key aspect of this method is that it begins with an initially small alpha value and gradually increases this value, iterating the calculation until the concave hull begins to split into multiple parts, thereby identifying the final effective concave boundary. This process effectively captures the true geographical boundaries of small towns.

2.4.3. Morphological Measurement

In this section, the unique morphological features of the small towns in mountainous areas were demarcated and assessed through quantitative measurement. Given that the morphology of these small towns tends to be more organic, morphometric methods used in cell biology and ecology were applied.

The metrics measured included the area and perimeter of the town region, the fractal dimension, the length of the longest axis, the roundness, the average distance from the centroid to the vertices, the perimeter of the convex hull, the aspect ratio, the core area of the tessellation units, the number of core buildings, and the core area ratio, among others. To estimate the longest axis, the Minimum Bounding Rectangle (MBR) is used, which encompasses the shape and aligns with the shape’s main direction. The length of the longest axis is then equal to the length of the longest side of this rectangle. These indicators cover not only dimensions and shapes but also aspects such as density and intensity, providing a comprehensive description of the small town’s morphology. One of the metrics included in the calculation of various indicators is circularity, which is calculated as follows.

$$\mathrm{Circularity}=\frac{4\pi \times \mathrm{Area}}{{\mathrm{Perimeter}}^2}$$

(1)

where $\pi$ is the constant Pi; Area represents the area of the town region; and Perimeter is the perimeter of the town region.

Following this, the calculation methods for the fractal dimension and indicators related to the tessellation cell part (i.e., the nucleus part) are also detailed. The application of the concept of the fractal dimension to the demarcation of small-town boundaries is inspired by insights gained in the measurement of organisms and cell morphometry. By viewing geospatial data as analyzable morphological structures, a similar approach can be adopted to explore the spatial complexity and structural characteristics of small towns. The fractal dimension quantifies the complexity of spaces or structures. Although there are several techniques for its calculation, the box-counting algorithm emerges as the predominant method [54]. The pivotal formula in this calculation is the computation of the fractal dimension, which is ascertained through the slope of the linear regression, as calculated according to the formula described below.

$$D=\underset{\epsilon \to 0}{lim}\frac{log(1/\epsilon )}{logN\left(\epsilon \right)}$$

(2)

where D is the fractal dimension; $ϵ$ is the size of the box used in the grid; and $N\left(ϵ\right)$ is the number of boxes of size $ϵ$ that contain part of the shape.

The fractal dimensions of 89 towns were calculated, and, for a comprehensive case study, a particular focus was placed on Rencun Town, Tiechang Town, and Shimen Town. Their fractal dimensions are 1.223, 1.406, and 1.57, which means that, in these towns, there is a difference in the complexity and self-similarity of the spatial forms. The complexity increases with higher values of the fractal dimension and a highly fragmented urban form, while a simple urban form is characterized by a low value for the fractal dimension.

Figure 5 demonstrates the three distinct phases of fractal dimension calculation by superimposing grids of varying sizes onto a map. The dimensions and arrangement of these grids intuitively display the shifts in spatial scale associated with the application of the box-counting algorithm, as well as the interactions between the town boundaries and these grids.

Nuclear morphology analysis and classification methods were adopted to discern the features of the central regions in the small towns, analogous in concept to the “nuclei” of biological cells. The principal methodology was inspired by the concept of enclosed tessellation, as proposed by Martin Fleischmann et al. [45], defined as specific spatial units created through Voronoi-based spatial partitioning techniques. The morphological and functional attributes of these enclosed tessellation units were assessed within their respective spatial contexts. To generate tessellation cells, the momepy library [55], an open-source toolkit tailored to urban form measurements, was utilized. These tessellation cells were then categorized via cluster analysis.

Having calculated the coverage area and radius of proximity for the enclosed tessellation cells, and using the natural breaks method of spatial classification, the above approach allowed us to identify core regions in the small towns with distinctive spatial-related peculiarities for the further study of their structure and form. Figure 6 presents the results of our methodology’s application, where, after the detailed investigation of the enclosed tessellation units, a comparison not only of the number of core regions in the small towns but also of their abundance and shape across different towns is possible. This enables a more in-depth consideration of the spatial structures and unique urban morphologies of each small town.

3. Results

3.1. Building Footprint Extraction Utilizing Open EO Data in the Qinba Mountain Area, Shangluo City

This study, conducted in the Qinba Mountain Area of Shangluo City, has led to significant advancements in the extraction of building footprints and town boundaries using open EO data. The U-Net3+ network was utilized to train deep learning models on high-resolution image data acquired through remote sensing. With the trained model, 31,799 buildings were successfully recognized. The redesigned full-scale skip connection mechanism in the U-Net3+ architecture notably enhanced the multi-scale feature aggregation and deep learning supervision. The novel mechanism could better promote the learning of hierarchical representations [56,57]. OpenStreetMap and Gaode Maps were used to obtain the town center points and the extent of the towns in the study area. We applied for a free API from Gaode Maps, which can be accessed at (https://lbs.amap.com/api/webservice/summary). Then, the optimization of the extracted building footprints was carried out with OpenCV, aiming to improve the clarity and accuracy of the outlines of the buildings. The purpose of this step was to delineate the building outlines obtained from the remote sensing imagery so that they corresponded more precisely and unambiguously to their actual forms. The quality of this information was vital to the accuracy of the subsequent analysis. Subsequently, the concave hull algorithm was iteratively applied to accurately describe the boundaries of the town forms.

In Figure 7, the results of building footprint and boundary extraction are illustrated. The superimposition of various small-town forms onto the map of the Shangluo area reveals the rich morphological diversity present within the district. The detailed examination of six representative towns, each situated in different landscapes ranging from mountains to plains, underscores the importance of recognizing and understanding the unique characteristics and diversity of small towns’ forms.

3.2. Morphological Measurement of Small Towns in Shangluo City, Qinba Mountain Area

Morphological Clustering

When performing hierarchical cluster analysis on the 12 characteristic indicators of the 89 towns, three of the most important clustering evaluation metrics—the Davies–Bouldin Index, the Calinski–Harabasz Index, and the Silhouette Score—were calculated to find the optimal number of clusters. These three indices adopt different calculation methods and offer different perspectives in measuring the effectiveness of clustering, so they provide a scientific and rational basis for determining the optimal number of clusters. Additionally, limitations in computational resources and software capabilities also led us to adopt these three easily computable and widely used indices. Python has several convenient libraries, such as scikit-learn, that can be used to calculate these indices, enabling us to efficiently perform a clustering analysis and evaluation.

The Davies–Bouldin Index calculates the cluster cohesion and separation, where lower scores indicate tightly grouped clusters that are clearly differentiated from others, signaling effective clustering [58]. As depicted in Figure 8, our analysis found that a cluster count of eight yielded a relatively low Davies–Bouldin Index, marking it as a judicious choice. The Calinski–Harabasz Index assesses a cluster’s compactness relative to the spread between clusters at any given count, which is why a higher score means a more defined cluster and independent delineation between two distinct canopies. At the same time, the Silhouette evaluates the difference between the similarity of a sample to the samples in its own cluster and the similarity of a sample to the samples in the nearest other cluster. Considering the classification results obtained, eight was selected as the best cluster number because it enabled a positive trade-off between the intra-cluster similarity and inter-cluster dissimilarity.

The hierarchical clustering method was used to study the morphological features of 89 towns. These algorithms progressively combine smaller clusters into larger ones based on the similarity in the length or correlation between samples, continuing this process until all samples are paired, thereby creating a clustering structure that resembles a tree [59].

As shown in Figure 9, the data were first standardized to eliminate the differences between the scales of various features. The “Ward” method of hierarchical clustering was used, which is optimal in the sense that it minimizes the increment in within-cluster variance as the criterion for merging, and it can thus effectively identify clusters with significant structural differences [60]. A dendrogram is a tree-like diagram that shows the merging of clusters. At each fusion event in hierarchical clustering, a vertical line represents the distance between the two clusters being merged. The length of this vertical line indicates the magnitude of the difference between the two clusters. By examining the dendrogram and setting a threshold line, shown as the red dashed line in Figure 9, a reasonable number of clusters can be determined based on the distance threshold.

Based on the hierarchical classification of the small towns in the Qinba Mountain Area of Southern Shaanxi, the towns themselves were segregated into eight distinguishable categories with different morphological characteristics. A general summary of each cluster is provided in

Table 2. Summary of each cluster’s characteristics based on its geographical and architectural features. Clusters are analyzed to provide insights into the underlying patterns of the dataset.

Cluster Number	Shape	Density	Size
1	Irregular	Low	Large
2	Irregular	Low	Large
3	Circular	Moderate	Small
4	Long–Narrow	High	Small
5	Regular	Moderate	Medium
6	Compact	Very High	Very Small
7	Long–Narrow	Low	Large
8	Irregular	High	Medium

. This table differentiates the clusters into multiple groups and describes their most prominent features, including the form of the geographical entities, the concentration of constructions receiving the same measurement, and the total area.

Category 1 towns, notably Zhongcun and Jingcun, featured larger perimeters and areas, irregular shapes, and sparse buildings. They were distributed in the northern and central regions, usually located in relatively flat terrain areas. Category 2 comprised towns such as Bao’an and Shangzhen, which differed from Category 1, with even larger perimeters and areas, a low building density, and higher fractal dimensions. This suggests that the town boundaries are more complex and take on more unique morphologies determined by geography. These towns are primarily concentrated in the central region, with a few located in the northern flat terrain areas. As for Category 3 towns, characterized by Banqiao and Xianghe, the mean perimeters and areas were smaller and the circularity was higher, with little difference between the perimeters and areas. This could point to their closeness to a circle-like shape, and it may indicate more centralized and planned development. These towns are mostly scattered in the northern and southeastern regions. For Category 4 towns, including Xiaoliang, Dongchuan, and Liangling, the geographical entities were narrow and elongated, which could have resulted from the mean perimeters and areas being lower and also the combination of the high aspect ratio and building area to concave area ratio. They are dispersed throughout the entire region. Category 5 towns, such as Yungaisi and Nankuanping, had a medium size and regular shape, which corresponded to a medium geographical scale, regular terrain, and medium building density. These towns are mostly distributed in the southern region. Category 6 towns, such as Sanchahe and Beizhaochuan, were extremely small but also had the highest aspect ratios, which indicates the development of either small or narrow strips with densified buildings. They are primarily located in the southeastern region. Category 7 towns, such as Sanyao and Xingping, show similar mean perimeters and areas but the highest aspect ratio, meaning that the constitutive geographical entities are very long and narrow and likely formed due to a river or valley, exhibiting valley areas with sparse building layouts. These towns have a very distinctive shape and are distributed in the central region. Finally, Category 8 towns, including Fenghuang and Luanzhuang, show a moderate area and building density but an irregular shape, and they are also expected to be located in complex terrain. They are dispersed throughout the entire region. In Figure 10, the overall distribution of the clusters is shown, along with the representative Clusters 1, 2, 7, and 8.

Table A1. List of small towns in Shangluo City within the Qinba Mountain Area of Southern Shaanxi by cluster.

Cluster	Towns
1	Zhongcun Town, Shilipu Town, Jingcun Town, Yongfeng Town, Shimen Town, Yaoshi Town
2	Bao’an Town, Gucheng Town, Shang Town, Dihua Town, Shahezi Town, Qingyouhe Town
3	Shiliping Town, Banqiao Town, Xianghe Town, Xizhaochuan Town, Qingtongguan Town, Gaoyao Town
4	Xialiang Town, Dongchuan Town, Liangling Town, Dangma Town, Beikuanping Town, Daping Town, Yuling Town, Muwang Town, Banyan Town, Manchuanguan Town, Niu’echuan Town, Shipo Town, Hongyansi Town, Caichuan Town, Daren Town, Jinsixia Town, Maping Town, Machihe Town, Majie Town
5	Yungaisi Town, Nankuanping Town, Tumen Town, Yecun Town, Dajing Town, Tianzhushan Town, Xiaoyi Town, Fushui Town, Siping Town, Sier Town, Xiaohekou Town, Zhangjia Town, Hujia Yuan Town, Milang Town, Sehepu Town, Maoping Hui Town, Shim Town, Zhaochuan Town, Tiechang Town, Gaobadian Town, Gaofeng Town
6	Sanchahe Town, Beizhaochuan Town, Tianqiao Town, Xiaoling Town, Yanping Town, Yangyuhe Town, Guofenglou Town, Qingshan Town
7	Sanyao Town, Xingping Town, Yangxia Town, Mu Hu Guan Town, Zhulin Guan Town, Tieyupu Town, Yinhua Town
8	Fenghuang Town, Luanzhuang Town, Xunjian Town, Yangdi Town, Chaiping Town, Wuguan Town, Faguan Town, Luoyuan Town, Shifosi Town, Shipu Town, Shiwen Town, Huapingzi Town, Yingpan Town, Xikou Hui Town, Heishan Town, Heilongkou Town

in the Appendix A details the classification of each small town within these eight morphological clusters.

The boxplots in Figure 11 provide a comprehensive overview of the morphological characteristics of the towns across the eight identified clusters in the Qinba Mountain Area of Southern Shaanxi.

The perimeter feature boxplots suggested that, for towns in Clusters 1 and 2, there is the largest variability in the size of the perimeters. Moreover, towns in Cluster 1 exhibited particularly large perimeters, which could mean that these towns are more irregularly shaped and more sprawling. In contrast, Clusters 3 and 6 exhibited much tighter distributions and smaller values for the perimeters, which implies that they are more compact. Regarding the area, Clusters 1 and 2 were once again the most prominent clusters with larger areas. It can be inferred that their towns occupy more extensive terrain. Meanwhile, Clusters 4 and 6 covered smaller areas but had denser settlements. The fractal dimension is an indicator of boundary complexity, and Clusters 2 and 3 showed the highest median value for this feature. This could mean that their boundaries are more complex and they may exhibit the natural features of the terrain or be structured in a complex pattern due to historical constraints. Clusters 7 and 8 have much smaller fractal dimensions, suggesting towns with more straightforward boundaries. In the case of the aspect ratio, the towns in Cluster 7 had a noticeably higher spread and median. It could be hypothesized that towns stretching along geographical features such as a river or a valley have a large amount of space occupied in a single direction. Clusters 1 and 3 had lower values, meaning that their towns were possibly very expansive in two dimensions, which could imply more regular shapes. The circularity feature also reflects the towns’ shapes, and Clusters 3 and 5 tightly enclosed towns that closely approximated a circular shape, which implies that the towns’ geometries were more centralized. Clusters 1 and 8, especially the latter cluster, with the most extensive spread, are towns of different shapes that vary from a standardized geometry, from round to square or between these two, and they represent towns that have been shaped by very different influencing factors. The building area/concave area ratio boxplot reveals that Cluster 6 has the town with the highest median ratio, which implies that it is very densely built.

4. Discussion

This study utilizes Earth observation data, addressing the data scarcity challenge typically encountered in small-town research. In most cases, urban morphology research data are acquired from government-provided cartographic information. This information is relatively easily accessible for large- and medium-sized cities. For instance, Jiménez-Espada et al. [61] utilized geographic information systems and aerial images provided by official sources like the National Statistics Institute, the City Council, and the National Geographic Information Center while studying the medium-sized World Heritage City of Cáceres in Spain. However, data scarcity is a common challenge for small towns. Gu et al. [62] demonstrated that while small towns are essential to the Chinese urban system, data collection and analysis are challenging due to the complicated and diverse functions and changing roles of these towns in urban–rural relations. Our approach uses Earth observation data and the deep learning model of U-Net3+ for extracting the building footprints in small towns lying in mountainous areas with complex terrain. Informed by Earth observation data, our research straddles the limitations of traditional data sources and provides new data references and approaches that contribute to the study of small towns.

Defining the boundaries and scope of small towns has been a persistent challenge due to the lack of precise boundary data. This study addresses this issue through several innovative approaches. Firstly, the DBSCAN algorithm, which has been previously applied in urban analysis research, such as Cetinkaya et al.’s work on building proximity grouping [49], is innovatively employed to determine the scope of small towns. By combining geospatial data with the DBSCAN algorithm, a more precise differentiation between towns and surrounding rural districts is achieved, effectively separating towns from their rural surroundings and enhancing the accuracy of the analysis. Secondly, an iterative computation that embeds both convex and concave hull algorithms is introduced to increase the accuracy in delineating complex boundaries of small towns. Ogle et al. [63] employed the convex hull algorithm to assess urban compactness in Pocatello. Despite having low computational complexity, the convex hull algorithm cannot process complex shapes with many concave boundaries. This paper incorporates the concave hull algorithm to resolve this limitation. The concave hull algorithm has the advantage that it captures irregular boundaries and hence makes up for the deficiencies of the convex hull algorithm, though it is computationally more complex. By integrating these two algorithms, a more precise definition of the complex boundaries of small towns can be realized, hence providing a reliable data foundation for further morphological analysis.

Drawing from biological cell morphometry, this study presents approaches and indices to offer a new perspective toward an urban morphology analysis of small towns from multiple dimensions. Fleischmann et al. [18] drew an analogy between this approach and the methods used by early biologists to classify species based on morphological similarities, discussing the effectiveness of morphological methods in understanding complex structures and highlighting the potential applications of these methods in urban structure analysis. The application of specific indicators remains limited in existing research. Most studies have only used fundamental indicators like size and area for in-depth morphological features, and while Basaraner and Cetinkaya [39] calculated several indicators, such as circularity, convexity, and rectangularity in their work about building shapes, very little attention was given to indicators like fractal dimensions, which better reflect the complexity of shape structures. This paper proposes some indicators of the morphology of small towns, including fractal dimension, circularity, and convex hull, from different viewpoints concerning complexity and compactness. In particular, introducing fractal dimensions makes it possible to measure boundary complexity. Based on systematic measurement with 12 indicators of 89 small towns in the Qinling-Daba Mountains, this paper displays the richness of morphological differences among them, including irregular sprawling morphologies, compact high-density morphologies, and elongated strip-like morphologies. These differences reflect the role of unique geographical environment conditions and development paths in shaping mountain towns’ morphology. It is through morphological clustering that eight significantly different small-town types have been identified, thus providing scientific proof for the formulation of town planning strategies under local conditions. This paper has provided a more detailed and in-depth analysis of the morphology of small towns with methodological innovation and large-scale empirical data and enriched the perspectives and methods of research in urban morphology.

This paper focuses on small towns in Qinba mountainous areas, which have complex terrain conditions and unique morphological features. Compared with larger cities, which have consistently been focal points of study, this paper seeks to fill a significant gap in urban morphology studies. Through precise morphometric measurements and classification analysis, the research aims to provide a scientific basis for the development and planning of these areas. This study reveals significant morphological diversity among the small towns in the Qinba Mountain Area. This aligns with the views of Wang et al. [64], who posited that the spatial distribution and morphology of mountain towns are influenced by multiple factors, such as the terrain, level of economic development, and transport accessibility. Through the large-scale extraction of building outlines and the precise delineation of town boundaries, the classification of small-town morphologies was obtained that aligned with the geographical characteristics of the Qinba Mountain Area. This finding supports the assertion made by Shang et al. [30] that the terrain significantly impacts the land use and town layout among mountain areas.

There are still many challenges and unresolved issues in the research on small-town morphology measurement and classification. The morphological characteristics, such as the fractal dimension, building density, and spatial configuration of small towns are interlinked with the geographical environment [65]. For example, understanding and interpreting the relationships between the morphological characteristics of small towns and their ecological environments, as well as how to apply the research findings in small-town planning and management, require further exploration and innovation in future studies. Additionally, the choice of the value of k in clustering can sometimes be subjective, adding another layer of complexity to the analysis.

5. Conclusions

This study performed an in-depth analysis of the urban morphology of small towns in the Qinba Mountain Area of Southern Shaanxi by innovatively integrating Earth observation data and advanced morphometric methods. The use of the U-Net3+ deep learning model to extract the building footprints was quite beneficial in defining the boundaries of the small towns with great accuracy. Such precise delineation allowed a detailed morphological analysis, which was found to be crucial given the complex topographical conditions of the area under study. The hierarchical cluster analysis of 12 morphological indicators in 89 towns made it possible to divide them into eight clusters, each of which differed from the others because of the peculiarities of their spatial features. The clustering results highlighted that the towns exhibited a variety of shapes and distributions, such as large irregular perimeters, compact high-density clusters, and narrow elongated forms. These variations reflect distinct layout patterns unique to each town. The revealed diversity, on a large scale, is caused by various factors, including relief, economic development, and transportation accessibility. This diversity calls for more tailored urban planning strategies rooted in the peculiar geographical and socioeconomic contexts of each city. This study also introduces an innovative interdisciplinary methodology inspired by biological cell morphometry. The possibility of viewing the towns through the lens of morphometric analysis allowed us to obtain new knowledge on the spatial organization, as well as the structural complexity, of the urban forms. In other words, through the analysis of specific data regarding the urban structures of various towns, we were able to point out the core area of the city and capture its morphological characterization at a micro-scale, similar to the nucleus of a biological cell. This extensive analysis will allow a detailed understanding of urban dynamics, contributing to better-informed decision-making regarding urban planning. Additionally, due to the use of data from EO and advanced geometric algorithms in this research, the integration of big data and artificial intelligence technologies should be considered in future studies of the urban morphology. Apart from an increase in the accuracy of this type of morphological measurement, such a data-driven approach also makes the analysis of large-scale spatial patterns possible, enabling a greater contribution to the field of urban studies. The identified morphological clusters provide a scientific basis for the study of similar problems in the design of tailor-made planning strategies that promote sustainable urban development.