Construction of high-precision DEMs for urban plots

ABSTRACT High-precision digital elevation models (DEMs) are the basic data for constructing digital cities. With the acceleration of urbanization, the topography of urban plots is constantly transformed by human activities, so that surface morphology shows the characteristics of diversification and discontinuity. Existing modelling methods focus on the expression of continuous terrain. Constructing high-precision DEM in urban plots is still challenging. A block-based modelling method that considers the morphological characteristics of urban plot elements was proposed. The Jinzhai County urban area was selected as the research area. The elements of urban plots were classified into six types, in which the boundaries and elevation information were extracted with real sense 3D models, Digital Orthophoto Maps (DOMs) and dense matching point cloud data. The DEMs of the 6 types of elements were generated separately with different methods, that are fused to complete the DEM of urban plots. The DEM obtained using the method in this manuscript was consistent with the reality in terms of topographic relief within each element and clarified the boundary of each element. The accuracy assessment showed that the RMSE results of roads, slopes, other terrains and natural terrains are approximately 0.05 m, which meets the elevation accuracy requirements of the 1:1000 large-scale mapping.


Introduction
With the development of smart and digital city, the refinement of urban management is constantly improving, and the application demand for high-precision digital elevation model (DEM) is increasing in all urban industries. As the foundation data of the construction of a digital city, high-precision DEM provides indispensable support for urban planning and design, city meteorological disaster warning, urban heat island effect studies and fine-scale urban waterlogging simulation (Chen et al. 2021;Chengcai et al. 2017;Yuan et al. 2017;Zhang and Yong-Xin 2017).
Usually, urban DEM modelling is completed by the interpolation of elevation data obtained from field measurement (Yonezawa 2009;Guonian et al. 2017;Li et al. 2022;Xiong et al. 2022), digitization of topographic maps (Chi and Song 2004;Wenshuang, Haili, and Fei 2008), LiDAR point clouds (Cui et al. 2013;Xiaoxia 2021;Xiaochun 2020a;Du et al. 2021), photogrammetry and remote sensing and multi-source data (Minqiu, Wei, and Wei 2009;Wang, Sun, and Xiaojuan 2016;Fachang and Wangmin 2019). Research of high-precision urban DEM modelling focuses on the data acquisition and process, and then the methods of generating TIN or interpolating DEM are still adopted. The first three kinds of data acquisition have their disadvantages, such as being time consuming, laborious and high cost. The fourth data acquisition of generating DEM by digital automatic photogrammetry has high automation, fast processing speed, and high map accuracy. This kind of production method is more extensive and the technological route is more mature and the cost is also lower. The unmanned aerial vehicle (UAV) photogrammetry technology is one of the digital photogrammetric methods, and greatly reduces the manual field workload, improves the efficiency of acquiring geographic information data and makes it possible to acquire high-precision terrain data in the region quickly. High-resolution Digital Orthophoto Maps (DOMs), dense point clouds and real sense 3D models based on image-intensive matching data can be obtained by UAV aerial survey technology, which has been used increasingly in the research of digital elevation model construction (Xiaoyi and Luhe 2017;Jing et al. 2022;Zhuohao 2022).
When urban DEM is produced by the interpolation method, urban is regarded as a whole area. Actually, the surface of the urban plot has been modified by humans, and the topography in urban plots presents a phenomenon of interweaving between the continuously changing natural and severely fragmented artificial topographies, the natural and artificial landforms interweave together, with diverse landforms and strong spatial heterogeneity. Therefore, in urban plots with complex natural and artificial landforms, the global interpolation methods adopted to acquire high-precision DEM are unreasonable. It causes flat places to become undulating terrain and smoothes out uneven natural terrain. It is necessary to classify the plots for high-precision DEM modelling of urban plots.
The traditional urban land classification of most countries emphasizes the division of land utilization mode rather than urban terrain morphology, which uses a secondary classification system, thereby making every land type a land plot (undefined). With the development of the economy, the traditional land function division has been transformed into a multiform division. The dimensions of ecological protection objectives (Baoying et al. 2002;Liuke, Xinxiang, and Shuying 2003;Lin and Jingjing 2016), policy objectives (Jie 2012), and development and management objectives (Association, A.P) have replaced the traditional dimension of land use and have become the main classification methods of land use planning. Therefore, the functional classification of urban land, which lacks descriptions of surface morphology and topographic semantic feature, has minimal work for the construction of urban highprecision DEM. In the Specification for feature classification and codes of fundamental geographic information (GB/T 13,923-2006) of China, the entity object is introduced and the classification criterion of geographic information elements is formulated (General Administration of Quality Supervision 2006). Based on this standard, an object-oriented, high-precision DEM modelling method for urban plot classification is proposed from the geometric and semantic perspectives (Cancan et al. 2017). In Yang's study, the city is divided into urban roads and urban plots while the elements in urban plots are divided into basic and thematic elements (Table 1). The Classification of Yang is an element classification method considering come element characteristics for urban terrain modelling. But the topographic features are not considered in this classification strictly. For example, the railway, flat area and other hardening areas have the same topographic characteristics, but divided into three categories.
In conclusion, to acquire high-precision DEM of urban plots, the various semantic morphological characteristics of surface elements inside the urban plots should be considered. A new classification of elements in urban plot will be studied. After analysing the topographic characteristics of various elements, appropriate modelling methods are proposed, and a complete urban plot DEM is formed by merging.

Study area
The urban area of Jinzhai County, Anhui Province, was selected as the study area, which is surrounded by four main roads (Figure 1). It has a longitude of 115°55'44"−115° 56'38" and latitude of 31°42'37"−31°43'20". The area is about 1.4 km 2 and elevation is between 56 m and 119 m. Inside the study area, houses, squares, roads, grass, water, embankments, playground and other elements are distributed. Continuous variation natural landforms and scattered distributed artificial landforms exist. The study area has the typical surface features of urban plot and is an ideal area for high-precision urban plots DEM construction research. The southeast part of the study area (in the red box of Figure 1) is the key area, which was used for element classification and modelling experiments.

Data
The dJI M300 UAV was worked for the data collection in a sunny day, an average altitude of 127 m and a flight speed of 12.5 m/s. A total of 32 image control points were evenly distributed in the study area ( Figure 2). The heading overlap degree of the image was 80%, and the side overlap degree was 70%. Real sense 3D model, DOM and dense point cloud were produced using Context Capture software and was used in this manuscript.

Real sense 3D model
The real 3D model has accurate 3D geometric information, rich terrain elements and accurate spatial relations that can express the ground object elements in real world at multiple levels of detail as required. High-precision and largescale digital line graphic (DLG) data can be obtained by 3D mapping real sense 3D model in computer. It greatly reduces the work of field measurement and improves the accuracy and efficiency of data acquisition. Figure 3 shows the real sense 3D model of the key sample area. The plane median error is 0.04 m, the elevation median error is 0.059 m and the ground resolution is 2 cm.

DOM
DOM produced by UAV contains rich geometric features and high-resolution texture information, which is intuitive and realistic. The obvious edges of feature inner plots can be shown clearly in the DOM. The clear texture features help to quickly distinguish the elements inside the plot. The orthographic image of the key sample area has a resolution of 5 cm, and features such as houses, roads, playgrounds and steps are clearly displayed.

Dense matching point cloud
The point clouds of key sample area produced by UAV have different density for various ground elements. The points of the building are relatively dense, up to 2100/m 2 , whereas the points of vegetation and other areas are relatively sparse, and the point cloud density is nearly 450/m 2 .

Method
The work flow is presented as follows ( Figure 4): (1) Select the study area; (2) produce data, including field trips to take photographs and indoor modelling; (3) classify elements of urban plots using various DEM construction methods for different elements; (4) extract elements; (5) construction a DEM for each element; (6) merge the modelling results; (7) evaluate the precision of high-precision DEM of urban plot.
As an area of human life, the overall elevation changes gently in the city. Natural and artificial terrains exist inside the urban plot. The natural topography is undulating and uneven, with local slight changes in elevation. On the basis of natural terrain, artificial terrain is reshaped by human beings and presented as segmented patches without elevation changes in the plot. Land use and geographical element attributes are the key contents of the existing methods of urban plot classification, which lack the morphological characteristics of geographical elements within the plot and is unsuitable for the DEM modelling of urban plot with complex topography.

Element classification
Due to urban planning and construction, various elements are found in the urban plot. The most common elements include natural terrain, buildings, roads and squares, as well as water and slopes distributed within the plot. Based on the morphological characteristics, the elements inside the urban plot can be divided into artificial and natural terrains. On the basis of urban elements classification of Yang (Cancan et al. 2017), the artificial terrain can be subdivided into roads, building bases, waters, slopes and other terrains. Special elements that do not fit the ground, such as underground parking lots and bridges, are not included in this classification. Figure 5 and Table 2 show the element classification and their morphological characteristics.

DEM construction of elements
(1) Building bases According to the morphological characteristics of the building base, the building base is a flat polygon after the building be removed. Therefore, the DEM of the building area only needs to consider the elevation of ground, that is, the elevation of the building base line, without considering the height of the building itself. The boundary of building base can be obtained by 3D mapping with real sense 3D model in DP-Mapper software, while the average elevation of all nodes on the boundary is used as the elevation of building base and building DEM can be built by turning vector surface into grid and by assigning an elevation value.
(2) Waters In lakes, ponds, ditches, outdoor swimming pools and other water areas, the boundaries were mapped by 3D mapping with 3D real sense model. The elevation of water surface was considered rather than underwater terrain. Due to the slight difference in elevation between upstream and downstream of the water in the urban plot being negligible, the highest elevation of points on water boundary is used as the elevation of water area.
After extracting the boundary between the building bases and waters, the remaining element boundaries were segmented by the multi-resolution segmentation method. Multi-resolution segmentation is a common and effective method in feature extraction based on highresolution image (Daoshuang, Lin, and Zhang 2019; Nazmfar and Jafarzadeh 2019; Shukla and Jain 2020; Wojtaszek et al. 2021). The three parameters, namely, segmentation scale, shape heterogeneity factor and compactness factor, are the key to multi-resolution segmentation and several attempts are needed to find the best parameter value. With the help of eCoginition software, the optimal scale of image segmentation is determined by trial-and-error method. The shape and compactness factors were fixed at 0.5, and the scale parameters were set within 50-600. The image was segmented incrementing with 50 to determine the optimal segmentation scale parameters. When the segmentation scale parameter is 500, the boundary between natural and artificial features can be  segmented more carefully. Then, the segmentation scale parameter was fixed at 500, and the optimal parameters of the shape and compactness factors were determined by adjusting their sizes. Through several experiments, the segmentation results were visually interpreted and compared, and the optimal segmentation scale parameters of the natural terrain elements were determined as follows: segmentation scale 500, shape factor 0.4 and compactness factor 0.6. In the end, the extracted building base line and water boundary line are used as vectors to participate in  The paved roads, including the entrance to the underground parking.

Building bases
A flat regular plane, no change in the elevation of a single building base.
The base of building.

Waters
The height of water surface in the model is taken as the water elevation.
A lake, pond, ditch, outdoor swimming pool, etc.

Slopes
Single inclined plane or curved surface, discontinuous, with elevation varies by the slope.  segmentation and obtain the initial image segmentation results (Figure 6(a)). The elevation information of remaining elements can be obtained from filtered dense matching point cloud. Ground point elevation information needs to be obtained by filtering. Among many point cloud filtering algorithms, the progressive TIN densification filtering algorithm is very mature and can be applied to the dense matching point cloud filtering Xiaochun). First, the test area is segmented according to a certain size, and the size of the grid is affected by the size of the largest building in the test area. Second, the grid index is established, and the lowest point in each grid is selected as the seed point, which is used to build the irregular triangular network model. Third, the grid index is established, and the lowest point in each grid is selected as the seed point, which is used to build the irregular triangular network model. The calculated distance and included angle parameters are compared with the set threshold value. If the value is smaller than the set threshold value, then the fixed point is classified as the ground point and added to the initial triangular network to reconstruct the model. Otherwise, it is a non-ground point. Finally, iteration is performed until no ground points exist.The point cloud filtering result is shown in Figure 7. In other terrains and natural terrains where there are many vegetation point clouds, the non-ground points can be removed effectively and the surface points be reserved by using the progressive TIN densification filtering algorithm.
(3) Natural terrains The interior of the natural terrain is dominated by grassland and vegetation, which is closely related to green and blue bands in colour aerial images (Yongbing and Yongqing 2016;Longfei et al. 2021). Based on the results of multi-resolution segmentation method, the area of natural terrain can be automatically extracted according to the spectral information of DOM. Through experiments, the mean of the blue wave segment in the DOM image can extract natural terrain elements better. The mean value of the blue wave range is 29-63, which can obtain relatively complete vegetation area, that is, natural terrain areas (Figure 6(b)).
The DEM of natural terrains was generated from TIN which is constructed by filtered point cloud and turned to GRID.
(4) Roads Roads were classified manually based on the segment results.
Existing road modelling methods include direct method, indirect method and plane modelling method (Tao et al. 2020;Susu et al. 2021). The direct method adopts unified mathematical surface modelling for road, which lacks consideration of road morphological characteristics. The indirect interpolation method aims to construct Delaunay triangle network directly from the original road elevation points, and then convert the Delaunay triangle DEM into a regular grid DEM. The road DEM generated by this method produces many triangle phenomena, which are inconsistent with the field, thereby causing distortion of road form and simulation analysis of surface.
This study used the plane modelling method. The plane modelling method (Figure 8) uses the points in the road within 10 cm from the road boundary and map their elevation vertically to the road centre line and the boundary on both sides of the road. Then, encryption is carried out vertically and horizontally, and the inverse distance weighted (IDW) interpolation method is finally used to model the road DEM. The plane modelling method considers the geometric and semantic constraints of the road, and has good effect on strip and cross roads, which were adopted to the road modelling in this manuscript.
(5) Slopes The slope areas were classified manually based on the segment results.
Considering the morphological characteristics of the slope is oblique flat surface, the plane modelling method was also used for slope modelling. The points in the slope and within 10 cm from the bottom and top of the slope boundary line were selected. By linear encryption with equal spacing horizontally and vertically, the points are enough to construct a smooth slope DEM by interpolation. (6) Other terrains Playground and squares are found in urban plots, where the uneven surface appear after point cloud filtering. IDW and Kriging interpolation methods cannot satisfy the terrain modelling of these areas. Therefore, the firstorder linear trend surface interpolation method used in this manuscript can obtain the DEM of playground and squares, which have flat terrain morphological characteristics. Stairs, which need to extract and model using TIN to Grid, also exist in urban plot.
(7) DEM merger of six types of elements Taking the DEM of natural terrain as the reference, the DEM of the building base was linearized and embedded into the DEM of the natural terrain using the Mosaic tool in ArcGIS. The result is taken as the base model of the next element Mosaic. The DEM of water, slope, road and other artificial factors were embedded into the above results by repeating the aforementioned embedding steps in sequence. In the process of data fusion, zigzag gaps may appear in the DEM after Mosaic. In this case, the element surface need buffer by the size of a cell before mosaic, and then the DEM models of each element are extracted by masking. The Mosaic method can be used to achieve a seamless DEM of urban plot.

Classification result of key area
According to the element classification and extraction methods in Section 2.2, the classification results of six types of elements in the key area were shown in Figure 9. The multi-scale segmentation result based on high-resolution images is not the final classification result. It still needs to be combined with manual interpretation to merge some tiny patches into adjacent elements, such as street trees and tiny buildings.

DEMs of key areas
The high-accuracy DEMs with 0.1 m resolution of different elements were using various methods. The DEM of urban plot is completed by merging and mosaicking the modelling results of six elements (Figure 10(a)). Meanwhile, the DEM with common indirect method was also generated (Figure 10(b)).
The results in the comparison of the two methods show that the DEMs generated by indirect method are not smooth enough, especially in water area and road interior, and do not conform to the actual factor characteristics. The DEM obtained using the method in this manuscript was consistent with the reality in terms of topographic relief within each element. It also clarifies the boundary of each element, thereby reflecting the terrain characteristics of the combination of artificial and natural terrains, and the interlacing of abrupt and gradual terrains inside the urban plot. The slope and hillshade were extracted from the urban plot DEM model to check whether the morphology characteristics of various elements was correct ( Figure 11). From the figures, DEM generated by indirect method can roughly reflect the composition of elements inside the plot, but the boundary of elements is fuzzy, and there are slope changes in buildings and water. Therefore, the proposed method can be considered a better method for constructing DEM consistent with actual urban plot characteristics. The final DEM of Jinzhai County urban area is constructed by the proposed method ( Figure 12).

Accuracy analysis
Elevation accuracy is an important part of DEM quality. Six types of elements were evaluated using root mean square error (RMSE) and mean error (ME) by field measured elevation points. The RMSE reflects the elevation deviation between the constructed DEM and the reference data. The ME describes the average values of the elevation difference between the reference data and the constructed DEM. The formulas of the two evaluation factors are presented as follows: RMSE ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi P n i¼1 ε 2 i n r ; (1) Where ε is the error between the measured value and DEM elevation, n is the number of checkpoints. The 32 control points used to construct the real 3D model were used as reference data. These points are not distributed in buildings and water, and building base and water are horizontal surface, wherein the elevation is equal to the elevation on the boundary line. Thus, the elevation error of these two elements is not calculated. The elevation error statistics results are shown in Table 3. Compared to elevation error of the DEM generated by indirect method, the RMSE of roads, slopes, other terrains and natural terrains from the DEM generated by the proposed method are approximately 0.05 m, which is higher precision and meets the elevation accuracy requirements of the 1:1000 large scale mapping.

Conclusions and discussions
A classification of urban plots is proposed according to the analysis of the morphological characteristics of different elements inside the urban plot. This classification summarizes the morphological characteristics of six elements in the plot, including roads, building bases, slopes, waters, other artificial terrains and natural terrain, which can better present the basic elements and the morphological characteristics of the elements in the urban plots. A high-precision DEM modelling method for urban plot is also proposed, and different modelling methods are used for roads, building bases, waters, slopes, natural terrains and other artificial terrains in the plots. The urban area of Jinzhai County was taken as the study area, in which the DEM model of the urban plot was constructed by using the real 3d model, DOM and dense matching point cloud obtained by UAV. Compared with DEM generated by indirect method, the DEM constructed by element classification, DEM construction and DEM fusion can express the topographic characteristics of actual urban plots better.
By comparing with the indirect modelling method, the DEM obtained by the proposed method can reflect the morphological characteristics of elements better and express the frame structure of urban plot elements clearly. The geometric and semantic characteristics of single horizontal elevation and gradual vertical elevation of roads are reflected without the phenomenon of uneven roads. The accuracy verification result showed that the RMSE results of roads, slopes, other terrains and natural terrains are approximately 0.05 m, which meet the elevation accuracy requirements of the 1:1000 large-scale mapping.
On the other hand, limited by the data structure of DEM, suspended ground elements, such as steps, urban overpasses and air corridors between buildings, cannot be expressed well. Moreover, water modelling only represents the boundary elevation of water surface, and the modelling idea is relatively simple without considering the underwater topographic features. High-precision urban DEM modelling method in this manuscript is not automated enough; a lot of human interventions are required in elements segmentation, which results in the limited availability of this method in other areas. The details of high-precision DEM modelling for urban plots still need further study.

Disclosure statement
No potential conflict of interest was reported by the authors.