Development boundary delimiting method considering urban three-dimensional form

Abstract

The invention relates to the technical field of urban development, and discloses a development boundary demarcation method considering urban three-dimensional morphology, which comprises the following steps: according to urban land utilization data, constructing scenes including natural development, economic priority, ecological expression and coordinated development, and utilizing a multi-objective planning model to predict land utilization requirements under different scenes; setting an evaluation unit according to the target distance, and constructing land utilization simulation driving factors including natural environment factors, human activity factors and urban form factors; on the basis of land utilization requirements and land utilization simulation driving factors, a development boundary stipulation model is constructed in combination with a PLUS model and an iterative mathematical morphology algorithm, and land utilization simulation and urban development boundary demarcation are carried out. According to the method, a PLUS model and an iterative mathematical morphology method are combined, a development boundary demarcation model integrating multi-source features is constructed, and a decision basis is provided for urban planning and management, urban sustainable development and the like.

Description

Technical Field

[0001] This invention relates to the field of urban development technology, and more specifically, to a method for delineating development boundaries that takes into account the three-dimensional form of a city. Background Technology

[0002] Since the beginning of the 21st century, the problems brought about by rapid urban development have become increasingly prominent, such as land resource shortages and ecological degradation. In order to effectively curb the disorderly sprawl of cities and improve land use efficiency, the concept of Urban Growth Boundary (UGB) has been proposed. It can also be called urban development boundary or development boundary. It clearly defines the buildable areas and protected areas of cities through legally defined control boundaries, which can effectively solve problems such as farmland loss, traffic congestion and environmental pollution. GB is now widely used in urban planning and management in various countries. The development of UGB in China is relatively late. In 2006, the government first clearly defined UGB as an important policy tool. In 2019, it formally proposed that urban development boundary be used as one of the three control lines of national land spatial planning to guide and constrain future urban development, concentrated urban development and construction, and improvement of urban functions.

[0003] Land use simulation, also known as spatial simulation, is the foundation for the scientific and rational delineation of UGB (Urban Use Block). It predicts land use types over a specific period. Spatial simulation, based on geographic simulation and spatial prediction methods, effectively integrates spatial growth probabilities with the interactions between local units. Cellular automata (CA) models, based on bottom-up principles, are among the most widely used intelligent models. These models analyze the spatiotemporal evolution of land use and its driving factors by defining spatial neighborhood rules, enabling spatiotemporal dynamic simulation of complex urban land use systems. Building upon the CA model and artificial neural networks (ANNs), researchers have developed the FLUS (Future Land Use Simulation) model, based on an adaptive inertial competition mechanism using roulette wheel selection. This model effectively obtains the suitability probabilities of various land use types, improving the accuracy of land use simulation results. Furthermore, researchers have introduced the random forest algorithm to mine the characteristics and driving factors of various land use expansions. By integrating land expansion analysis strategies with multi-type random patch seeding mechanisms, they have developed and proposed PLUS (Patch-generating Land Use). Simulation models can better simulate patch-level changes in multiple land use types. To convert the simulation results from patch-level or grid-level results into implementable and manageable UGB vector boundaries, it is necessary to merge neighboring patches and eliminate areas with low compactness and small area, such as through mathematical morphology algorithms, to achieve an effective conversion of simulation results to UGB.

[0004] The selection of driving factors is crucial and central to spatial simulation models. The initial stage of factor selection primarily considers natural and human factors such as topography, land adaptability, transportation location, human activities, and economic development. With the rapid development of geographic big data and related technologies, data representing the intensity and characteristics of human activities, such as Points of Interest (POIs), Weibo check-ins, and mobile phone signaling, have emerged and are widely used in land use simulation and UGB (Urban Geographical Indication) delineation studies. Urban morphology refers to the physical structure and morphological characteristics of a city in space, including building distribution, density, and shape. As cities grow and expand vertically, buildings of different heights and volumes are distributed in different combinations, constituting the city's three-dimensional morphology. Changes in urban space utilization efficiency by this three-dimensional morphology influence urban growth patterns and development potential, thus playing a significant role in UGB delineation. Urban three-dimensional morphology indicators combine information on the height of buildings and vegetation, and commonly include building height, building three-dimensional morphology, and three-dimensional landscape indicators.

[0005] However, urban three-dimensional morphological information has not been fully integrated into land use simulation studies, which may lead to a disconnect between UGB delineation results and the actual spatial layout of the city. At the same time, most existing UGB delineation studies use two-dimensional planar features and rarely consider urban three-dimensional morphological features, and their impact on UGB delineation lacks systematic research.

[0006] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0007] In response to the problems in related technologies, this invention proposes a method for delineating development boundaries that takes into account the three-dimensional morphology of cities, so as to overcome the aforementioned technical problems existing in the existing related technologies.

[0008] Therefore, the specific technical solution adopted by the present invention is as follows: A method for delineating development boundaries that takes into account the three-dimensional morphology of the city includes: Step 1: Based on urban land use data, construct scenarios that include natural development, economic priority, ecological considerations, and coordinated development, and use a multi-objective programming model to predict land use demand under different scenarios; Step 2: Set up evaluation units according to the target distance, and construct land use simulation driving factors that include natural environmental factors, human activity factors and urban morphology factors; Step 3: Based on land use demand and land use simulation driving factors, construct a development boundary specification model by combining the PLUS model and iterative mathematical morphology algorithm, and conduct land use simulation and urban development boundary delineation.

[0009] Preferably, in step 1, based on urban land use data, a scenario is constructed that includes natural development, economic priority, ecological considerations, and coordinated development. A multi-objective programming model is then used to predict land use demand under different scenarios, including: A transition probability matrix is ​​generated based on urban land use data, and a Markov chain is used to predict the transition probability matrix, outputting the land use status of the target period under the natural development scenario. Based on the land use economic benefits of cultivated land, forest land, grassland, water area, construction land, and unused land in urban land, the grey model is used to predict the land economic benefit coefficient within the target period and obtain the maximum land economic benefit under the economic priority scenario. Based on the ecosystem service value coefficient and ecological carrying capacity coefficient of urban land, an estimation function is constructed and its expression is optimized to obtain the ecosystem service value and ecological carrying capacity under the ecological manifestation scenario. Based on the maximum economic benefits of land, the value of ecosystem services, and the ecological carrying capacity, an optimization function that takes into account both ecological manifestation and economic effect is generated, and the land use unit area coefficient under the coordinated development scenario is obtained. Based on the constraints set for land use status during the target period under the spatial planning and natural development scenario, and using a non-dominated sorting genetic algorithm to generate Pareto solutions according to the optimization function and constraints, the land use area under the scenarios of economic priority, ecological embodiment and coordinated development is obtained.

[0010] Preferably, the natural environmental factors in step 2 include slope, elevation, average annual temperature, and vegetation coefficient; Step 2 includes human activity factors, socioeconomic factors, and accessibility factors; Among them, human activity factors include population density and GDP per capita; socioeconomic factors include point of interest density and housing rent; accessibility factors include distances from urban buildings to main roads, rail transit and water bodies, and road network density. In step 2, urban morphology factors include building height factors, building spatial distribution factors, building spatial pattern factors, and neighborhood spatial pattern factors.

[0011] Preferably, the building height factor includes the average height of urban buildings, the standard deviation of urban building height, the coefficient of variation of urban building height, and the proportion of mid-rise and high-rise buildings in the city. The standard deviation of urban building height represents the dispersion and statistical characteristics of urban building heights within the evaluation unit; the coefficient of variation of urban building height is the ratio of the standard deviation of urban building height to the average height within the evaluation unit. Building spatial distribution factors include urban building footprint, urban building floor area ratio, and urban building sky visibility factor. The urban building footprint is the ratio of the base area of ​​urban buildings within the evaluation unit to the total area of ​​the evaluation unit; the urban building volume ratio is the ratio of the total building area of ​​urban buildings within the evaluation unit to the total area of ​​the evaluation unit.

[0012] The preferred formula for calculating the average height of urban buildings is: ; The formula for calculating the floor area ratio of urban buildings is: ; In the formula, n This indicates the number of urban buildings within the evaluation unit. S i Represents urban buildings i The base area, H i Represents urban buildings i height, S Indicates the total area of ​​the evaluation unit. F i Represents buildings i The number of floors is estimated based on the building's height. BH Indicates the average height of buildings in the city. FAR This indicates the building volume ratio in a city.

[0013] Preferably, the urban building sky visibility factor uses the center point of the evaluation unit as the observation point. It adopts open source libraries and just-in-time compiler libraries in Python, and generates search paths in 16 uniformly distributed directions through the Bressenham line algorithm. The performance of the calculation process is optimized by using Numba's just-in-time compilation function. By calculating the sine average of the maximum elevation angle in each direction, multi-directional terrain shading analysis of the observation point is realized within a 5×5 window to quantify the degree of sky shading by urban buildings, terrain, etc.

[0014] Preferably, architectural spatial pattern factors include urban architectural Shannon diversity, urban architectural aggregation, and urban architectural sprawl. Urban architectural Shannon diversity is based on the proportion of buildings of different height categories within the evaluation unit, used to reflect the complexity of the three-dimensional spatial form of the city; urban architectural aggregation is obtained by extracting all urban building pixels with a height of 30 meters within the evaluation unit and quantifying the degree of aggregation, used to reflect the degree of aggregation and dispersion of architectural space; urban architectural sprawl is used to quantify the aggregation and sprawl trend of urban buildings. The neighborhood spatial pattern factor uses 750×750 meters as a new evaluation unit to construct three indicators: regional Shannon diversity, regional building aggregation, and regional sprawl. The calculation results are then assigned to the evaluation unit to capture neighborhood interactions and local spatial structure characteristics.

[0015] Preferably, step 3, based on land use demand and land use simulation driving factors, combines the PLUS model and iterative mathematical morphology algorithm to construct a development boundary determination model, and performs land use simulation and urban development boundary delineation, including: The Gini index of land use simulation driving factors at the splitting of nodes in a random forest is analyzed, and the sum of the changes in the Gini index of all trees and nodes is used as the contribution of simulation driving factors to the expansion of each land use type, so as to obtain the development potential of each land use type. Land use demand is used as a total constraint, and the iterative simulation process is driven by neighborhood weight parameters. Based on the simulation results, a patch generation mechanism based on random seeds is introduced to randomly generate new development seeds in potential development areas. By analyzing the diffusion process of newly developed seeds and the decay threshold and expansion probability parameters of generated patches, continuous and compact land use patches are obtained, and land use simulation results at the patch level are acquired. The land use simulation results are subjected to closed-open operations using a multi-scale structuring element iteration method to generate construction land raster data, and urban development boundary delineation is carried out in conjunction with a line smoothing tool.

[0016] Preferably, the land use simulation results are subjected to closed-open operations using a multi-scale structuring element iteration method to generate construction land raster data, and urban development boundary delineation is carried out in conjunction with a line smoothing tool, including: Using 3×3, 5×5, and 7×7 structural elements sequentially according to the set maximum iteration depth, iterative closed-open operations are performed on the land use simulation results. During the iterative operation, the rate of change of the construction land grid is monitored in real time. Based on the cyclically increasing structural elements, the boundary is gradually optimized to eliminate irregular construction land patches while ensuring the stability of the main structure. Based on the results of the closed-open operation, construction land raster data is generated. At the same time, the vector-raster conversion tool and the line smoothing tool are used to convert the construction land raster data into vector urban development boundaries, and vector urban development boundary patches with an area of ​​less than 0.5 square kilometers are deleted to carry out the urban development boundary delineation operation.

[0017] The beneficial effects of this invention are as follows: This invention aims to construct a UGB delineation model that takes into account the three-dimensional morphological characteristics of cities. Based on multi-source geographic data such as building outlines and building heights, it proposes characterization indicators for the three-dimensional morphology of cities. Combining the PLUS model and iterative mathematical morphology methods, it constructs a development boundary delineation model that integrates multi-source features and evaluates the impact of the three-dimensional morphological indicators of cities on the results, providing a basis for decision-making in urban planning and management, and sustainable urban development. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of a development boundary delineation method that takes into account the three-dimensional morphology of a city according to an embodiment of the present invention; Figure 2 This is a flowchart of iterative mathematical morphology operation in a development boundary delineation method that takes into account the three-dimensional morphology of a city, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of some driving factors in a development boundary delineation method that takes into account the three-dimensional morphology of a city, according to an embodiment of the present invention. Figure 4 This is a schematic diagram of land use simulation results under different scenarios in 2030 in a development boundary delineation method that takes into account the three-dimensional morphology of the city according to an embodiment of the present invention. Figure 5 This is a schematic diagram of the development boundary delineation result of a city in a development boundary delineation method that takes into account the three-dimensional morphology of the city according to an embodiment of the present invention; Figure 6 This is an indicator contribution analysis diagram in a development boundary delineation method that takes into account the three-dimensional morphology of a city, according to an embodiment of the present invention. Detailed Implementation

[0020] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0021] According to an embodiment of the present invention, a method for delineating development boundaries that takes into account the three-dimensional morphology of a city is provided.

[0022] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, the development boundary delineation method considering the three-dimensional morphology of the city according to an embodiment of the present invention includes: Step 1: Based on urban land use data, construct scenarios that include natural development, economic priority, ecological considerations, and coordinated development, and use a multi-objective programming model to predict land use demand under different scenarios.

[0023] In one embodiment, based on urban land use data, a scenario is constructed that incorporates natural development, economic priority, ecological considerations, and coordinated development. A multi-objective programming model is then used to predict land use demand under different scenarios, including: A transition probability matrix is ​​generated based on urban land use data, and a Markov chain is used to predict the transition probability matrix, outputting the land use status of the target period under the natural development scenario. Based on the land use economic benefits of cultivated land, forest land, grassland, water area, construction land, and unused land in urban land, the grey model is used to predict the land economic benefit coefficient within the target period and obtain the maximum land economic benefit under the economic priority scenario. Based on the ecosystem service value coefficient and ecological carrying capacity coefficient of urban land, an estimation function is constructed and its expression is optimized to obtain the ecosystem service value and ecological carrying capacity under the ecological manifestation scenario. Based on the maximum economic benefits of land, the value of ecosystem services, and the ecological carrying capacity, an optimization function that takes into account both ecological manifestation and economic effect is generated, and the land use unit area coefficient under the coordinated development scenario is obtained. Based on the constraints set for land use status during the target period under the spatial planning and natural development scenario, and using a non-dominated sorting genetic algorithm to generate Pareto solutions according to the optimization function and constraints, the land use area under the scenarios of economic priority, ecological embodiment and coordinated development is obtained.

[0024] It should be noted that the research data in this embodiment includes land use data, natural environment data, human activity data, and building data. The data is primarily sourced from 2020, as detailed below: (1) Land use data: China land use remote sensing monitoring dataset with a resolution of 30m for 2010, 2015 and 2020, which is sourced from the Resource and Environment Science Data Platform (RESDC) of the Chinese Academy of Sciences, including six categories: cultivated land, forest land, grassland, water area, construction land and unused land.

[0025] (2) Natural environment data: Digital elevation data (DEM) with a resolution of 30m from the Geospatial Data Cloud; annual average temperature data with a resolution of 1km from the Earth Resources Data Cloud Platform; and 2020 China 30m Normalized Difference Vegetation Index (NDVI) data provided by RESDC.

[0026] (3) Human activity data: Population density and GDP spatial distribution data of 1km grid are obtained from the Worldpop dataset and RESDC, respectively; Point of Interest (POI) data are crawled from Baidu Maps and Dianping, including different types such as life services, leisure and entertainment, and commercial offices; Weibo check-in location data in July 2020 are obtained by crawling technology; residential rental information in September 2021 is crawled from Anjuke, and shop rental information is crawled from 58.com, and spatial location information is determined based on the property name, etc.; Road data at all levels are obtained from OpenStreetMap; The above-mentioned crawled geographic big data is preprocessed by data cleaning, coordinate correction and manual correction to ensure data reliability and accuracy.

[0027] (4) Building outline and height data: The building outline vector data of Zenodo database in 2020 includes the corresponding building height information. At the same time, the building height raster CNBH data product with a resolution of 10 meters from the National Earth System Science Data Center was selected to verify and complete the building height information.

[0028] like Figure 1 As shown, this embodiment proposes a development boundary delineation method that takes into account the three-dimensional morphology of the city. It predicts the land use demand in 2030 under different scenarios based on the multi-objective programming (MOP) model; and constructs three types of driving factors, namely natural environment, human activities, and urban morphology, with 150 meters as the evaluation unit. Combining the PLUS model and iterative mathematical morphology algorithm, a development boundary delineation model is constructed to simulate and delineate the land use in 2030.

[0029] The MOP (Multi Objective Programming) model is suitable for finding the optimal solution set when there are multiple evaluation indicators or objective functions. It helps to solve the problem of conflicting objectives in complex land systems. MOP seeks the best solution for each land use type under constraints and is widely used in land use simulation. The model consists of decision variables, objective functions and a series of constraints.

[0030] This embodiment designs four scenarios to assess the area of ​​each land use type in 2030: Natural Development Scenario (BAU), Economic Priority Scenario (RED), Ecological Priority Scenario (ELP), and Coordinated Development Scenario (EEB), as detailed below: (1) BAU Scenario: Based on the historical development trend of land use, Markov chains are used to predict the scale of each land use type in the study area in 2030. The transition probability matrix is ​​obtained based on land use data from 2010 and 2020. ,in k 10 andk 20 This represents the different land use types (arable land, forest land, grassland, water area, construction land, and unused land) in 2010 and 2020, and then... S ( t Setting the land use status to 2020, we obtain the predicted land use status for 2030. .

[0031] (2) RED scenario: Based on the total output value of agriculture, forestry, animal husbandry and fishery in the statistical yearbooks from 2010 to 2020, estimate the economic benefits of cultivated land, forest land, grassland and water area; set the economic benefits of unused land to 0; estimate the economic benefits of construction land based on the GDP of the secondary and tertiary industries, and predict the economic benefit coefficients of various types of land in 2030 through the grey model GM(1,1). In order to obtain the greatest economic benefits , x 1 to x 6 represents the area of ​​each land use type, including cultivated land, forest land, grassland, water area, construction land, and unused land (unit: km²). 2 ).

[0032] (3) ELP Scenario: Constructing estimation functions for ecosystem service value (ESV) and ecological carrying capacity (EC) f 2( x )and f 3( x ), through function optimization To maximize ecological benefits, the ESV is estimated using an improved unit area value equivalent factor method, and its estimation function is as follows: , Esv k Ecosystem service value coefficients for various types of land (unit: 10,000 yuan / km2).

[0033] EC The estimation function is Ecological carrying capacity coefficient Ec k Through equivalent factors Q k With yield factor Y k The calculation shows that 12% of bioproductive land should be reserved for biodiversity conservation, and therefore it is deducted when calculating EC.

[0034] (4) The EEB scenario takes into account both ecological and economic benefits, and its optimization function is expressed as: number of objective functions f 1( x ), f 2( x )andf 3( x The economic and ecological benefit coefficients per unit area for each land category are calculated and shown in Table 1. Table 1: Unit Area Coefficient for Different Types of Land Use Based on spatial planning and existing land use conditions, a series of constraints are set for socio-economic development and ecological environment. According to the three constructed optimization functions and constraints, the Pareto solution of MOP is obtained using the NSGA-II genetic algorithm. The decision variable values ​​of the objective function under the three scenarios of RED, ELP, and EEB can be obtained, which are the areas of various land use types in 2030. Specifically, the pymoo library in Python is used to solve the multi-objective optimization problem of the NSGA-II genetic algorithm. By defining the optimization problem containing decision variables and objective functions, and combining inequality constraints, the automatic search of the Pareto optimal front is realized, and finally the solution set that satisfies all constraints is obtained.

[0035] The specific constraints are as follows: (1) Total area: The sum of the total areas of each land type is the total area of ​​the region; (2) Landscape diversity constraints: In order to maintain landscape diversity and reserve space for urban development, the combined area of ​​grassland and unused land shall be greater than 1% of the total area; (3) Cultivated land x 1. Area: The upper limit is the area in 2020, and the lower limit is the area predicted by Markov in 2030; (4) Forest x 2. Coverage Constraints: Using an ecological green equivalent method, the photosynthetic and key ecological functions provided by different ecological land uses such as arable land, forest land, and grassland are uniformly converted into the equivalent forest area; based on the conversion coefficients obtained from existing research, such as 0.46 for arable land, 1.00 for forest land, and 0.49 for grassland, a lower limit for forest coverage is set. (5) Grassland x 3. Area: The upper and lower limits are the maximum and minimum areas from 2010 to 2020; (6) Water area x 4. Area: The lower limit is the area in 2020, and the upper limit is the area predicted by Markov in 2030; (7) Construction land x 5. Area: The lower limit is the area in 2020, and the upper limit is the area in 2030 as predicted by Markov, with an upward adjustment of 10%. (8) Unused land x 6. Area: The upper limit is the area in 2020.

[0036] Step 2: Set up evaluation units according to the target distance, and construct land use simulation driving factors that include natural environmental factors, human activity factors and urban morphology factors.

[0037] It should be noted that the driving factors of land use simulation include natural environmental factors, human activity factors, and urban morphology factors.

[0038] Natural environmental factors include topographic factors and environmental factors. Four indicators were selected: slope (A1), elevation (A2), average annual temperature (A3), and NDVI (A4). These indicators can reflect the topography, climate conditions, and ecological environment of the region, and have a significant impact on the spatial distribution and expansion of urban land use.

[0039] Human activity factors include three types: human activity factors, socio-economic factors, and accessibility factors. Socio-economic factors include two indicators: population density (B1) and GDP per capita (B2). Human activity factors involve the impact of human behavior on the environment and society, and three indicators are selected: Weibo check-in (B3), POI density (B4), and housing rent (B5). For these point-like data, the grid density value or attribute mean is generally extracted as the indicator. Accessibility factors are the transportation and infrastructure construction of a region, and four indicators are selected: distance to main roads, rail transit, and water bodies (B6, B7, B9), and road network density (B8). The distance to roads and water bodies is calculated using the ArcGIS Euclidean distance module as the accessibility factor.

[0040] Urban morphology factors include four categories: building height factors, building spatial distribution factors, building spatial pattern factors, and neighborhood spatial pattern factors.

[0041] (1) The building height factor expresses the characteristics of the building in the vertical direction and is also an intuitive indicator for measuring the upward development of buildings in a region. In this embodiment, three indicators were selected: the average height of urban buildings (C1), the standard deviation of height (C2), the coefficient of variation of height (C3), and the proportion of mid-rise and high-rise buildings (C4).

[0042] Average Height: To reflect the impact of different building areas on the indicators within the evaluation unit, an area-weighted average building height is used to characterize the average building height information. The specific calculation formula is as follows: ; In the formula, n Indicates the number of buildings within the evaluation unit. S i Represents buildings i The base area, H i Represents buildings i The height.

[0043] Height standard deviation: reflects the dispersion and statistical characteristics of urban building heights within the evaluation unit; standard deviation σ The larger the value, the greater the difference in building height within the evaluation unit.

[0044] Coefficient of variation in height: refers to the standard deviation of building height in a spatial evaluation unit. σ The ratio to the average height. It reflects the relative difference in building height in the vertical direction and characterizes the efficiency of three-dimensional space utilization.

[0045] Proportion of mid-rise and high-rise buildings: This index reflects the proportion of mid-rise and high-rise buildings in a city and can characterize the city's building structure. Mid-rise and high-rise buildings are defined as buildings with a height of more than 24m.

[0046] (2) The building space distribution factor expresses the spatial distribution of the building. In this embodiment, three indicators are selected: building footprint (C5), floor area ratio (C6), and sky visibility factor (C7).

[0047] Building footprint ratio: refers to the ratio of the building footprint area in the evaluation unit to the total area of ​​the evaluation unit, which represents the density of land cover and land use efficiency in the horizontal direction.

[0048] Floor area ratio (FAR): This refers to the ratio of the total building area of ​​buildings in a spatial evaluation unit to the total area of ​​the evaluation unit. It reflects the overall development intensity of buildings and characterizes the spatial utilization capacity of land. The specific calculation formula is as follows: ; In the formula, n Indicates the number of buildings within the evaluation unit. S i Represents buildings i The base area, S This represents the total area of ​​the evaluation unit (150×150 meters). F i Represents buildings i The number of floors is estimated based on the building's height.

[0049] Sky visibility factor: Taking the center point of the evaluation grid as the observation point, the vertical elevation angle of the highest point blocked by buildings in different directions starting from the observation point is measured, quantifying the proportion of the visible sky and reflecting the degree of occlusion of the hemispherical space above this point by surrounding buildings, terrain, etc. Specifically, the GDAL library and Numba library in Python are used. The Bresenham line algorithm is used to generate search paths in 16 uniformly distributed directions, and the just-in-time compilation function of Numba is used to optimize the performance of the core calculation process. At the same time, by calculating the average value of the sine of the maximum elevation angle in each direction, multi-directional terrain occlusion analysis of each center point within a 5×5 window is realized to accurately quantify the degree of occlusion of the sky by buildings, terrain, etc.

[0050] (3) The building spatial pattern factor expresses the differences and diversities of building groups and reflects the three-dimensional spatial structure and form of the city, including three indicators: building Shannon diversity (C8), building aggregation degree (C9), and sprawl degree (C10). Before calculating these indicators, the building contour vector data needs to be converted into raster data with a resolution of 30m first.

[0051] Building Shannon diversity: It is used to quantify the heterogeneity and distribution uniformity of building heights in the study area. The raster data is reclassified into 4 categories according to height: low-rise buildings (h ≤ 10m), mid-rise and high-rise buildings (10m < h ≤ 24m), high-rise buildings (24m < h ≤ 50m), and super high-rise buildings (h > 50m). The proportion distribution of buildings in different height categories within the evaluation unit is statistically analyzed to reflect the complexity of the three-dimensional spatial form of the city. The specific calculation formula is as follows: ; In the formula, p j represents the proportion of the base area occupied by the j th type of building, O represents the number of different height categories within the evaluation unit.

[0052] Building aggregation degree: All 30-meter building pixels within the evaluation unit are extracted to quantify their aggregation degree, reflecting the aggregation and dispersion degree of the building space. It is the ratio of the number of adjacent boundaries between building pixels within the evaluation unit to the maximum number of intra-class adjacent boundaries that could be formed when all building pixels are completely aggregated theoretically.

[0053] Building sprawl degree: It is used to quantify the aggregation and sprawl trends of the urban landscape. The higher its value, the better the connectivity of the dominant patch type and the more aggregated distribution; on the contrary, it indicates strong landscape heterogeneity and scattered patches. To focus on the expansion pattern of the building space, all 30-meter pixels within the evaluation unit are clustered into building patches and non-building patches.

[0054] (4) Neighborhood Spatial Pattern Factors: The spatial distribution of buildings in the evaluation unit is influenced not only by its own planning but also by the surrounding area. Therefore, this embodiment improves the above-mentioned spatial pattern factors to assess the degree of influence of the evaluation unit on its neighborhood. For each 150×150 meter evaluation unit, its surrounding 5×5 neighborhood range is used as the new evaluation range, i.e., 750×750 meters. Using the same index calculation method, three indicators are constructed: regional Shannon diversity (C11), regional building aggregation (C12), and regional sprawl (C13). The calculation results are assigned to the evaluation unit. By analyzing the spatial pattern of the evaluation unit and its neighborhood, neighborhood interactions and local spatial structure characteristics can be captured. Compared with the direct attribute measurement of building spatial pattern in a single grid, these indices can better reflect the spatial structure and characteristics of the region.

[0055] Step 3: Based on land use demand and land use simulation driving factors, construct a development boundary specification model by combining the PLUS model and iterative mathematical morphology algorithm, and conduct land use simulation and urban development boundary delineation.

[0056] In one embodiment, step 3, based on land use demand and land use simulation driving factors, combines the PLUS model and iterative mathematical morphology algorithm to construct a development boundary specification model, and performs land use simulation and urban development boundary delineation. This includes: analyzing the Gini index of land use simulation driving factors when a single tree node in a random forest splits, and using the sum of the changes in the Gini index of all trees and nodes as the contribution of the simulation driving factors to the expansion of each land use type, thus obtaining the development potential of each land use type; using land use demand as a total constraint, combined with neighborhood weight parameters to drive the iterative simulation process, and introducing a patch generation mechanism based on random seeds according to the simulation results, randomly generating new development seeds within the potential development area; obtaining continuous and compact land use patches through the diffusion process of new development seeds and the attenuation threshold and expansion probability parameters of generated patches, thus obtaining land use simulation results at the patch level; using a multi-scale structuring element iteration method to perform closed-open operations on the land use simulation results to generate construction land raster data, and combining line smoothing tools to implement urban development boundary delineation operations.

[0057] In one embodiment, the land use simulation results are subjected to closed-open operations using a multi-scale structuring element iteration method to generate construction land raster data, and urban development boundary delineation is performed using a line smoothing tool, including: Using 3×3, 5×5, and 7×7 structural elements sequentially according to the set maximum iteration depth, iterative closed-open operations are performed on the land use simulation results. During the iterative operation, the rate of change of the construction land grid is monitored in real time. Based on the cyclically increasing structural elements, the boundary is gradually optimized to eliminate irregular construction land patches while ensuring the stability of the main structure. Based on the results of the closed-open operation, construction land raster data is generated. At the same time, the vector-raster conversion tool and the line smoothing tool are used to convert the construction land raster data into vector urban development boundaries, and vector urban development boundary patches with an area of ​​less than 0.5 square kilometers are deleted to carry out the urban development boundary delineation operation.

[0058] It should be explained that the boundary delineation model is a coupling of the PLUS model and mathematical morphology methods. The PLUS model is used for land use simulation, while mathematical morphology is used for delineating UGB vector boundaries. The PLUS model is an open-source and widely used future land use change simulation model. Driving factors are the core of the PLUS model. This embodiment constructs three major categories of driving factors, including natural environment, human activities, and urban morphology, comprising nine types of driving factors and 26 indicators. Through its innovative patch generation mechanism, the PLUS model can dynamically generate land use patches with specific morphologies based on pixel transformation, thereby enabling precise simulation and presentation of spatial pattern changes of various land uses at the patch level. The PLUS model includes two modules: (1) Based on the transformation rule mining framework of the Land Expansion Analysis Strategy (LEAS), the Random Forest (RF) algorithm is used to analyze the influence mechanism of driving factors and land use change. That is, the importance of driving factors is measured by calculating the average reduction of Gini index when the node of a single tree in the RF. The sum of the changes in Gini index of all trees and nodes is calculated as the contribution of each driving factor to the expansion of different land use types, thereby obtaining the development potential of each land use type.

[0059] (2) The CA model (CARS) based on the multi-type random patch seed mechanism uses land use demand (predicted by Markov and MOP algorithms in this embodiment) as the total constraint, combined with the land use transformation matrix from 2010 to 2020, neighborhood weights and other parameters, where the neighborhood weights are obtained based on existing research and the actual situation of the study area (cultivated land = 0.1147, forest land = 0.1051, grassland = 0.033, water area = 0.13, construction land = 0.5493 ​​and unused land = 0.0279) to drive the iterative simulation process; a patch generation mechanism based on random seeds is introduced to randomly generate new development seeds in the potential development area. These seeds further grow gradually through the seed diffusion process according to the attenuation threshold of generated patches (set to 0.5 in this embodiment) and expansion probability (set to 0.1 in this embodiment) and other parameters, and finally form a continuous and compact patch structure.

[0060] This embodiment uses 2020 as the starting year and inputs the predicted area of ​​various land types in 2030 under four scenarios as the end condition for the simulation. This yields 150-meter land use raster data for different scenarios in 2030. The obtained raster data is reclassified into two categories: construction land and non-construction land, for use in subsequent UGB delineation.

[0061] By employing morphological erosion and dilation algorithms, small, isolated noise regions generated in urban simulations can be eliminated, and scattered, discontinuous patches can be integrated and merged to form continuous, compact boundaries, such as... Figure 2 As shown, let A be the construction land area in the input binary map, and B be the structuring element. B x Indicates the translation of a structuring element to a position. x The set after; the erosion algorithm shrinks the target region by eliminating boundary pixels, and its operation is expressed as: The dilation algorithm expands the target region by extending the boundary pixels; its operation is expressed as: Opening and closing operations are morphological operations based on a combination of erosion and dilation. Opening involves erosion followed by dilation, which can be used to smooth irregular boundaries. Closing involves dilation followed by erosion, which can fill small gaps in urban units. In this embodiment, the closing-opening operation is used as the basic processing unit. That is, a closing operation is performed first to connect adjacent regions, and then an opening operation is performed to eliminate scattered and isolated noise units. This composite operation can effectively maintain the morphological characteristics of the main region and optimize the boundary structure.

[0062] This embodiment employs an iterative approach based on multi-scale structuring elements for UGB delineation. Structuring elements at different scales all use a fixed shape with the four corners removed. Each iteration cycle includes three sequentially executed iterative steps: using 3×3, 5×5, and 7×7 structuring elements in turn to perform closed-open operations on the land use simulation results. During the iteration process, the rate of change of the construction land grid is monitored in real time, and optimization automatically stops when the rate of change is less than 0.1%, indicating stability. Simultaneously, the maximum iteration depth is set to 5 cycles to ensure convergence. This method, through cyclically increasing structuring elements, achieves progressive boundary optimization, effectively eliminating extremely small and irregular construction land patches while ensuring the stability of the main structure.

[0063] Using the vector-raster conversion tool and line smoothing tool in ArcGIS, the iteratively generated construction land raster data is converted into vector UGB, and UGB small patches with an area of ​​less than 0.5 square kilometers (about 22 grid scales) are further deleted. This makes the overall boundary smooth and continuous, and also fits the urban area outline well, maintaining the complex edge shape characteristics of the city.

[0064] like Figure 3 As shown in the figure (A represents natural environmental factors, B represents human activity factors, and C represents urban morphology factors), this embodiment constructs 3 categories of factors, 9 categories of factors, and 26 indicators as driving factors for the PLUS model; the sky visibility factor (such as...) is one of the urban morphology factors. Figure 3 As shown in C7), building sprawl and regional sprawl (such as...) Figure 3 The three indicators (C10, C13, etc.) exhibit a trend of low values ​​in the central area and the two sub-cores, rising from the center outwards, due to their inherent physical meaning. Other urban three-dimensional morphology indicators generally show a downward trend from the center outwards, with high-value areas existing in both the east and west sub-cores. The statistical graphs of the indicator values ​​also show a certain degree of normal distribution. It is worth noting that compared to architectural spatial pattern factors (such as...) Figure 3 As shown in C8-10), similar indicators of neighborhood spatial pattern factors exhibit a smoother and more continuous spatial pattern (e.g., Figure 3 As shown in C11-13, the statistical charts also show a smoother trend, indicating that these indicators have stronger explanatory power and can more clearly identify the regional characteristics of urban morphology. At the same time, the indicators constructed in this embodiment also show low correlation and redundancy. In particular, the correlation between the 13 newly constructed urban morphology indicators is less than 0.7, which can be used for subsequent land use scenario simulation and UGB delineation.

[0065] This embodiment takes a certain city as the study area and uses Markov chains and NSGA-II genetic algorithm to obtain the Pareto solution of MOP, predicting the area of ​​different land use types under the BAU scenario and three other scenarios (Table 2). Among them, the construction land area is the highest under the RED scenario, at 1273.38 square kilometers, an increase of 37.7% compared to 2020; under the ELP scenario, the area of ​​ecological land such as cultivated land and forest land is the largest, while the construction land area is the smallest, at 988.89 square kilometers, an increase of only 7.0% compared to 2020; the construction land area is comparable to that under the BAU and EEB scenarios, at approximately 1157.60 square kilometers.

[0066] Table 2: MOP land use demand forecast results under different scenarios (unit: square kilometers) Although the land use area of ​​a certain city in 2030 obtained by PLUS simulation is close to the MOP prediction results in Table 2, there are still some differences. The final land use area is generated by the combined constraints of "top-down" demand and bottom-up geographical conditions. The simulation results are as follows: Figure 4 As shown, cultivated land, forest land, and construction land constitute the basic pattern of land use in this city. The overall pattern is roughly the same in the four scenario simulations. Construction land is mainly concentrated in the central urban area. In the RED scenario, construction land and cultivated land account for 10.8%, and cultivated land accounts for 28.6%, which is the highest proportion among the four scenarios. The ELP scenario preserves ecological land the best, with forest land accounting for 60.8%.

[0067] A development boundary delineation model constructed by coupling the PLUS model with morphological methods can transform the 2030 land use simulation results of a certain city into UGB delineation results, such as... Figure 5As shown in the figure (A represents the BAU scenario, B represents the RED scenario, C represents the ELP scenario, and BEE scenario), the results show that under the BAU scenario, the city has obvious external expansion, reflecting the spatial pattern of natural urban evolution in the absence of external policy intervention. In the RED scenario, the city's expansion is biased towards the interior of the built-up area, showing the characteristics of agglomeration in key areas and relatively compact boundaries, while the expansion of some inefficient areas is suppressed. Under the ELP scenario, the overall UGB is relatively contracted, and the expansion direction is restricted by sensitive areas such as ecological red lines and river wetlands, resulting in increased boundary compactness. The EEE scenario achieves a balance between economic development and ecological protection, with a moderate UGB expansion range, taking into account both the needs of reasonable urban expansion and effectively controlling the encroachment on ecological space. The boundary shape is relatively regular and compact, and the spatial layout is more scientific and reasonable. Among the small-area patches in different scenarios, the patches simulated by the BAU scenario are more fragmented; the RED scenario has more small patches, covering existing construction land more comprehensively; the UGB in the small areas of the EEE scenario is more concentrated; and the UGB in the ELP scenario is mainly concentrated in the main urban area and two sub-cores, with the fewest small-scale UGB patches.

[0068] Table 3 shows a comparison between the simulation results and the UGB-defined areas. The RED and EEB scenarios generate more compact urban morphologies, and the UGB area generated after erosion and expansion is larger than the simulated area. The simulated areas of built-up land under the BAU and EEB scenarios are very close, but the defined UGB areas differ by nearly 12 square kilometers. Under the ELP scenario, the UGB area is reduced by 2.3% compared to the simulated area, indicating that the BAU and ELP scenarios generate more scattered and small patches, which are eliminated by the IMA method. Overall, different development goals and control measures affect the UGB... The expansion and morphology of UGB have a significant regulatory effect. Under the natural growth (BAU) scenario, UGB expands rapidly with a relatively loose boundary morphology and localized disorderly sprawl. Under the rapid economic development (BAU) scenario, UGB clusters in economically advantageous areas, with more directional spatial expansion and increased boundary complexity. Under the ecological protection (ELP) scenario, the boundary shrinks overall and becomes more compact, with expansion mainly constrained by ecologically sensitive areas, showing obvious ecological adaptability. Under the economic-ecological coordination (EEB) scenario, a balance is achieved between expansion speed and boundary compactness, and UGB exhibits a relatively regular and scientific spatial pattern.

[0069] Table 3: UGB Delineated Area under Different Scenarios (Unit: square kilometers) Urban morphology is the manifestation of urban spatial layout and structure. Three-dimensional urban morphology indicators quantify the characteristics of vertical building spatial distribution. Applying these factors to the delineation of the Urban Geographical Indicator (UGB) can more rationally guide urban spatial management and land use layout. Using land use data from 2010 and 2015 as starting years, and the Markov prediction of land use area in 2020 as the ending condition, simulations were conducted. The simulation results were then compared with actual land use data from 2020 for accuracy verification. Comparing the improved model (PLUSw) with the original model (PLUSo) without these indicators, PLUSWw showed significant improvements in overall accuracy and Kappa coefficient, reaching over 0.929 and 0.871 respectively. The simulation results with 2010 as the starting year showed improvements of 5.1% and 2.8% in Kappa coefficient and overall accuracy, respectively, while those with 2015 as the starting year showed improvements of 3.8% and 2.1% respectively (Table 4). The improved Kappa coefficient indicates a significant enhancement in the consistency between the model simulation results and the actual land use map, reducing the impact of random consistency and improving the model's overall discriminative ability. The increased overall accuracy suggests a higher proportion of correctly classified pixels among all validation pixels, reflecting an overall improvement in the model's classification ability. In summary, PLUSw's simulation results are more accurate and more similar to actual land use distribution, indicating that the enhanced urban 3D morphology improves the model's ability to fit land evolution patterns and significantly enhances the accuracy of land use simulation.

[0070] Table 4: Accuracy Comparison of PLUS Model Before and After Improvement Compared to traditional spatial simulation models, one of the advantages of the PLUS model is that it can quantify the contribution of driving indicators through the random forest algorithm, providing a clear and measurable basis for understanding the intrinsic mechanism of land use change. Based on the LEAS module of the PLUS model, areas of construction land expansion from 2010 to 2020 were extracted, and the random forest algorithm was used to evaluate the contribution of each driving factor, such as... Figure 6 As shown, the results indicate that compared with traditional driving factors (such as distance from main roads, slope, and population density), the 13 three-dimensional morphological indicators of cities have a higher explanatory power in the contribution ranking, with an overall contribution of 50.2%. The average contribution of these indicators also exceeds the average of the other 13 natural environment and human activity factors. Among them, the regional Shannon diversity index C11, plot ratio C6, and height standard deviation C2 have relatively high contributions, at 10.5%, 7.3%, and 5.5%, respectively, exceeding or approaching traditional indicators such as road accessibility and road network density. This indicates that urban spatial morphological characteristics have a significant impact on urban expansion trends.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for delineating development boundaries that takes into account the three-dimensional morphology of a city, characterized in that, include: Step 1: Based on urban land use data, construct scenarios that include natural development, economic priority, ecological considerations, and coordinated development, and use a multi-objective programming model to predict land use demand under different scenarios; Step 2: Set up evaluation units according to the target distance, and construct land use simulation driving factors that include natural environmental factors, human activity factors and urban morphology factors; Step 3: Based on land use demand and land use simulation driving factors, construct a development boundary specification model by combining the PLUS model and iterative mathematical morphology algorithm, and conduct land use simulation and urban development boundary delineation.

2. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 1, characterized in that, In step 1, based on urban land use data, scenarios are constructed that encompass natural development, economic priority, ecological considerations, and coordinated development. A multi-objective programming model is then used to predict land use demand under different scenarios, including: A transition probability matrix is ​​generated based on urban land use data, and a Markov chain is used to predict the transition probability matrix, outputting the land use status of the target period under the natural development scenario. Based on the land use economic benefits of cultivated land, forest land, grassland, water area, construction land, and unused land in urban land, the grey model is used to predict the land economic benefit coefficient within the target period and obtain the maximum land economic benefit under the economic priority scenario. Based on the ecosystem service value coefficient and ecological carrying capacity coefficient of urban land, an estimation function is constructed and its expression is optimized to obtain the ecosystem service value and ecological carrying capacity under the ecological manifestation scenario. Based on the maximum economic benefits of land, the value of ecosystem services, and the ecological carrying capacity, an optimization function that takes into account both ecological manifestation and economic effect is generated, and the land use unit area coefficient under the coordinated development scenario is obtained. Based on the constraints set for land use status during the target period under the spatial planning and natural development scenario, and using a non-dominated sorting genetic algorithm to generate Pareto solutions according to the optimization function and constraints, the land use area under the scenarios of economic priority, ecological embodiment and coordinated development is obtained.

3. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 1, characterized in that, The natural environmental factors in step 2 include slope, elevation, average annual temperature, and vegetation coefficient. The human activity factors in step 2 include human activity factors, socio-economic factors, and accessibility factors. The human activity factors include population density and GDP per capita; the socioeconomic factors include point-of-interest density and housing rent; and the accessibility factors include the distance from urban buildings to main roads, rail transit, and water bodies, as well as road network density. The urban morphology factors in step 2 include building height factors, building spatial distribution factors, building spatial pattern factors, and neighborhood spatial pattern factors.

4. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 3, characterized in that, The building height factor includes the average height of urban buildings, the standard deviation of urban building height, the coefficient of variation of urban building height, and the proportion of mid-rise and high-rise buildings in the city. The standard deviation of urban building height represents the dispersion and statistical characteristics of urban building heights within the evaluation unit; the coefficient of variation of urban building height is the ratio of the standard deviation of urban building height to the average height within the evaluation unit. The building space distribution factors include urban building footprint, urban building plot ratio, and urban building sky visibility factor. The urban building footprint is the ratio of the base area of ​​the urban buildings within the evaluation unit to the total area of ​​the evaluation unit; the urban building floor area ratio is the ratio of the total building area of ​​the urban buildings within the evaluation unit to the total area of ​​the evaluation unit.

5. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 4, characterized in that, The formula for calculating the average height of urban buildings is as follows: ； The formula for calculating the urban building floor area ratio is as follows: ； In the formula, n This indicates the number of urban buildings within the evaluation unit. S i Represents urban buildings i The base area, H i Represents urban buildings i height, S Indicates the total area of ​​the evaluation unit. F i Represents buildings i The number of floors is estimated based on the building's height. BH Indicates the average height of buildings in the city. FAR This indicates the building volume ratio in a city.

6. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 5, characterized in that, The urban building sky visibility factor uses the center point of the evaluation unit as the observation point. It adopts open source libraries and just-in-time compiler libraries in Python, and generates search paths in 16 uniformly distributed directions through the Bressenham line algorithm. The performance of the calculation process is optimized by using Numba's just-in-time compilation function. By calculating the sine average of the maximum elevation angle in each direction, multi-directional terrain shading analysis of the observation point is realized within a 5×5 window to quantify the degree of sky shading by urban buildings, terrain, etc.

7. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 6, characterized in that, The architectural spatial pattern factors include urban architectural Shannon diversity, urban architectural aggregation, and urban architectural sprawl. The urban architectural Shannon diversity is based on the proportional distribution of buildings of different height categories within the evaluation unit, used to reflect the complexity of the urban three-dimensional spatial morphology; the urban architectural aggregation degree is obtained by extracting all urban building pixels with a height of 30 meters within the evaluation unit and quantifying the degree of aggregation, used to reflect the degree of aggregation and dispersion of architectural space. The urban building sprawl is used to quantify the clustering and sprawl trends of urban buildings; The neighborhood spatial pattern factor uses 750×750 meters as the new evaluation unit to construct three indicators: regional Shannon diversity, regional building aggregation, and regional sprawl. The calculation results are then assigned to the evaluation unit to capture neighborhood interactions and local spatial structure characteristics.

8. The method for delineating development boundaries taking into account the three-dimensional morphology of a city according to claim 1, characterized in that, Step 3, based on land use demand and land use simulation driving factors, combines the PLUS model and iterative mathematical morphology algorithm to construct a development boundary determination model, and performs land use simulation and urban development boundary delineation, including: The Gini index of land use simulation driving factors at the splitting of nodes in a random forest is analyzed, and the sum of the changes in the Gini index of all trees and nodes is used as the contribution of simulation driving factors to the expansion of each land use type, so as to obtain the development potential of each land use type. Land use demand is used as a total constraint, and the iterative simulation process is driven by neighborhood weight parameters. Based on the simulation results, a patch generation mechanism based on random seeds is introduced to randomly generate new development seeds in potential development areas. By analyzing the diffusion process of newly developed seeds and the decay threshold and expansion probability parameters of generated patches, continuous and compact land use patches are obtained, and land use simulation results at the patch level are acquired. The land use simulation results are subjected to closed-open operations using a multi-scale structuring element iteration method to generate construction land raster data, and urban development boundary delineation is carried out in conjunction with a line smoothing tool.

9. A method for delineating development boundaries that takes into account the three-dimensional morphology of a city, as described in claim 8, is characterized in that... The process of using a multi-scale structuring element iterative method to perform closed-open operations on land use simulation results to generate construction land raster data, and then combining this with line smoothing tools to delineate urban development boundaries, includes: Using 3×3, 5×5, and 7×7 structural elements sequentially according to the set maximum iteration depth, iterative closed-open operations are performed on the land use simulation results. During the iterative operation, the rate of change of the construction land grid is monitored in real time. Based on the cyclically increasing structural elements, the boundary is gradually optimized to eliminate irregular construction land patches while ensuring the stability of the main structure. Based on the results of the closed-open operation, construction land raster data is generated. At the same time, the vector-raster conversion tool and the line smoothing tool are used to convert the construction land raster data into vector urban development boundaries, and vector urban development boundary patches with an area of ​​less than 0.5 square kilometers are deleted to carry out the urban development boundary delineation operation.

10. A method for delineating development boundaries taking into account the three-dimensional morphology of a city, as described in claim 9, is characterized in that... The closing-opening operation is based on the combination of erosion and dilation operations in morphology. The erosion operation shrinks the target region by eliminating boundary pixels, and the dilation operation expands the target region by extending boundary pixels. The closing operation is an expansion followed by erosion, and the opening operation is an erosion followed by expansion.

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