1 Introduction

Research on housing prices based on the hedonic model has widely clarified that the properties of houses (square footage, number of bedrooms, house orientation, building age, and so on), the location, and the neighborhood characteristics undoubtedly affect the prices (Goodman, 1978; Rosen, 1974). Typically, these empirical studies state themselves as unique to the experience of a given city and attribute the uniqueness to the distinctive urban spatial structure formed by the interaction between the city’s physical characteristics and the inhabitants’ social needs (Lefebvre, 2003; Lefebvre & Nicholson-Smith, 1991; Lefebvre et al., 1996). However, different case studies in different cities can lead to differences in empirical conclusions. For example, the bid rent model based on monocentric urban form (Alonso, 1964) may have a poor fitting performance for polycentric cities (Wen & Tao, 2015). Likewise, the same kind of urban functional zones in different cities may also affect housing prices differently, such as the impact of hospitals on surrounding housing prices. If hospitals are considered as a type of valuable amenity, then it could increase the commercial values of houses in Shanghai, China Tam et al. ()Tam et al.(2019, 2019), while the negative externalities of hospitals probably depreciate the surrounding housing prices in Bei**g, China (Qiao et al., 2021). Meanwhile, no significant impact has been found in Greater Kuala Lumpur, Malaysia (Teck-Hong, 2012).

Regarding the uncertainty or even the conflicting conclusions in various cities, the comparative research is imperative to explore how the differences are caused by the city’s uniqueness. Limited studies discussed the housing price difference at the city-level market is primarily driven by the city’s economic fundamentals and social demographic structure (Mirkatouli et al., 2018; Waltert & Schläpfer, 2010; Wang et al., 2017; Yi & Huang, 2014). But, as Lynch and Rodwin (1958) Lynch et al. (1958) stated, a well-designed community, a good built environment, and adequate service facilities would not automatically produce the perfect settlements in a city. Houses and their prices are also affected by the city’s organization and arrangement from a larger environment. In this vein, we raise a question that, would the urban form and the urban functional zone distribution affect the housing prices within and between cities? If yes, then to what extent do the urban form and the urban functional zones affect the spatial distribution of housing prices? The empirical evidence could tell whether the effects of urban form and urban functional zones on housing prices were underestimated in previous studies. Also, the findings could support the toolsets to formulate the urban housing policies related to planning human-friendly and affordable settlements when constructing a new town or develo** the suburbs under fast urbanization in China and other regions.

Therefore, we construct three hypotheses for assessing the effects of urban forms and urban functional zones on housing prices. First, urban forms and urban functional zones are significantly different across cities. Second, housing prices vary between cities. Finally, the housing price variation is affected by differentiated urban forms and urban functional zones. This study selects 10 representative extra-large cities in China as comparative cases, namely, Shanghai, Bei**g, Shenzhen, Guangzhou, Chengdu, Hangzhou, Wuhan, Nan**g, Changsha, and **, dining, and recreations, which are vital for sensing the daily living of citizens and capturing the evolving nature of urban functions (Crooks et al., 2015).

Considering the complexity of urban functional zones derived from human activities and interactions (Batty, 2008), the image feature detection method is the traditional and widely used way of extracting and analyzing land use patterns and urban functional zones and relies on remote sensing images with a high spatial resolution (Cao et al., 2020; Wen et al., 2015; Zhang & Du, 2015; Zhang et al., 2017; Zhong et al., 2015). However, although this method specializes in detecting and reflecting the natural properties and features of ground objects, such as land use types, it fails to capture detailed human-involved functional information and socio-economic characteristics (Liu et al., 2015). These limitations are generally overcome by the emergence of big geographic data, such as POIs (Hu et al., 2020; Jiang et al., 2015; Liu & Long, 2016; Liu et al., 2020; Qian et al., 2021; Yao et al., 2017; Yi et al., 2019; Zhai et al., 2019; Zhang et al., 2017, 2019), social media (Du et al., 2020; Gao et al., 2017; Liu et al., 2015; Qian et al., 2021; Tu et al., 2017; Zhang et al., 2019; Zhi et al., 2016; Zhou & Zhang, 2016), mobile phone and floating car trajectory data (Gao et al., 2019; Hu et al., 2021; Qi et al., 2011; Tu et al., 2017; J. Zhang et al., 2021a, 2021b; Zhong et al., 2014), due to the strength of big geographic data to accurately and large-scale capture the human activities. Numerous studies have exemplified the usability and reliability of methods integrated with such data sources in urban functional zones inference, identification, and detection, despite the requirement of meticulous data processing (Li et al., 2016; Niu & Silva, 2020). The methods, data source, and their pros and cons for urban functional zones identification are summarized in Table 1.

Table 1 Five mainstreams for urban functional zones identification
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In recent studies, POI data is the most widely used data source and has four main advantages for urban functional zones identification at a fine-grained scale. First, POI data is highly accessible and available from online map service providers. Second, POI data is highly reliable due to the continuous and multi-source maintenance by commercial map suppliers and volunteer geographical information (Batty et al., 2012). Third, POI data has a fine-grained spatial resolution and a continuous temporal sequence. Lastly, the approximate global coverage of POI data supports large-scale research and global comparative studies. For instance, Jiang et al. (2015) utilized POIs obtained from Yahoo Online and employment data from census data at the aggregate level to identify the land use types at the city block level. Liu and Long (2016), proposed an automatic detection method for urban functional zones by using open resource data, POI data, and road networks from OpenStreetMap.

However, two challenges in using POIs remain (Zhai et al., 2019). First, as the description of POIs has several layers, synonymy and ambiguity are common when directly using these layers’ information. As shown in Appendix Table A1, the bottom layer of food service can be a component in residential or commercial urban functional zones, but the combined semantic signature may be different (such as accommodation service–hotel–food and beverage vs. commercial housing–industrial park–food and beverage). Second, because POI description can only represent the information in the location of the point, redundancy is commonly seen in large plots, like hospitals, parks, airports, or universities. For instance, in addition to one POI with a combined description of tourist attraction–scenic spot–park, the spatial area of a park contains many other ancillary facilities (e.g., ticket office, catering, shop**, sports facilities, and toilets). If only the spatial relationships between these POIs in a given area are considered when inferring the function of the place, redundant POIs would affect the result.

Therefore, we followed the automatic method proposed by Liu and Long (2016) and proposed a hybrid approach to urban functional zones detection to take full advantage of the POI data. The process involves two steps (Fig. 1):

•First, use POI types, which represent single land use, to assign the land use type for urban functional zones.

•Second, use the multi-layer combined descriptions of the POIs reclassified by Sense2VecFootnote 1 to infer the remaining zones with mixed land use.

Fig. 1
figure 1

Flow diagram of detecting urban functional zones

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2.2 Urban form indicators at the city scale

Urban form represents the physical form of a city and comprises activities (Lynch & Rodwin, 1958). The definition and measurements of urban form in the literature are very diverse, mainly relying on the scale of the research (Batty, 2008; Batty & Longley, 1994). Huang et al. (2007) Huang et al. (2007) utilized satellite images of 77 metropolitan areas in Asia, the United States, Europe, Latin America, and Australia to quantify the five dimensions (i.e., compactness, centrality, complexity, porosity, and density) of urban form from the physical characteristics of the urban landscape. Clifton et al. (2008) Clifton et al. (2008) divided the quantitative methods of analyzing urban forms into five categories, namely, landscape ecology, economic structure, transportation, community design, and urban design, and sorted them by research scales from regional, metropolitan, sub-metropolitan, neighborhood to the smallest building block. At the city scale, the measures include the urban built-up size, density, and diversity, the urban structure, and the polycentricity. Dempsey et al. (2008) Dempsey et al. (2008) classified urban forms of different scales into five broad and interrelated elements that constitute a specific city and are encompassed by density, transport, housing, land use, and layout. The indicators of urban form at the city scale reflect the ratio of population, households, or housing units to the area of the entire city, including the city’s population density, the household density, the dwellings density, and the city area. Echenique et al. (2012) Echenique et al. (2012) proposed that urban forms (compaction, dispersed, and planned expansion) in English city regions do not have obvious advantages for sustainable development. Conversely, population growth and changes in residents’ lifestyles dominate the impacts on natural environment and resources. In comparative studies of global cities, openness and proximity are often used to represent the fragmentation or compactness of urban form (Dong et al., 2019; Schneider & Woodcock, 2008; Xu et al., 2020).

The frequently used urban form indicators for extra-large cities should be capable of indicating the outcomes that have great significance at the city or metropolitan scale and can be controlled and describe the different effects caused by the rearranged patterns at this scale (Lynch & Rodwin, 1958). In this study, we applied this criterion and utilized indicators to reflect the five dimensions of urban form, including compactness, centrality, polycentricity, dissimilarity, and density.

Compactness (Fig. 2a). Compactness does not only measure the shape of an individual developed block but also the fragmentation of the overall urban landscape (Li and Yeh, 2004; Angel et al., 2017, 2020). The estimation is based on the average comparison between the perimeters of each developed block and a circumscribed circle of the same area. The CI is calculated as follows:

$$Compactness = \frac{{\sum P_{i} /p_{i} }}{{N^{2} }} = \frac{{\sum 2\pi \sqrt {S_{i} /\pi } /p_{i} }}{{N^{2} }}$$

where \({S}_{i}\) and \({p}_{i}\) are the respective area and perimeter of developed block \(i\), \({P}_{i}\) is the perimeter of the circumscribed circle with area \({S}_{i}\), and \(N\) is the total number of blocks. Given two cities with the same amount of development, when city A is more compacted than city B, then the development of B is more evenly distributed than that of A. With a low degree of compactness, the sprawl-like development model is spreading in this city.

Fig. 2
figure 2

Schematic of assessing spatial urban form

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Centrality (Fig. 2b). Centrality is the degree of proximity of a city’s developed areas to its urban central business district (CBD) (Galster et al., 2001). Centrality is a measurement of the areal size of a city. One of the most common forms of urban development is the loss of centrality, which results in increased travel distance and time as land development is far from the CBD. The centrality index increases with the decrease of the radius between the developed areas and the CBD. Conversely, the centrality index is low when a city has a great spread. The calculation formula of centrality is as follows:

$$Centrality = \frac{{\sum D_{i} /N - 1}}{R} = \frac{{\sum D_{i} /N - 1}}{{\sqrt {S/\pi } }}$$

where \({D}_{i}\) is the distance of the centroid of developed block \(i\) to the centroid of the city center, \(N\) is the total number of developed blocks, \(R\) is the radius of a circle with area \(S\), and \(S\) is the total built-up area of the city. Therefore, centrality is also sensitive to the shape of the city, that is, whether it is elongated or circular. The narrower the shape of the city is, the greater the centrality index, and vice versa.

Polycentricity (Fig. 2c). Polycentricity reflects the degree to which urban areas are characterized by a polycentric (rather than monocentric) development model. If a city’s CBD is the only dense development zone, then this city has a monocentric structure and its polycentricity index equals one. If land development is scattered in several highly developed areas and each area contains an activity cluster, which accounts for a large part of the total number of such activities in the city, then this area is defined as the sub-center of the city. A polycentric city has a high polycentricity index, which equals to the number of sub-centers of the city.

Dissimilarity of housing development (Fig. 2d). The dissimilarity index refers to the unevenness of housing development. The housing development with a high dissimilarity index indicates the houses gathered at some developed places. While a low dissimilarity index represents houses evenly developed in a city (Schwarz, 2010; Tsai, 2005).

$$Dissimilarity = \frac{{\mathop \sum \nolimits_{i = 1}^{N} \left| {X_{i} - Y_{i} } \right|}}{2}$$

where \({X}_{i}\) is the proportion of land area, \({Y}_{i}\) is the proportion of housing development indicator of block \(i\), and \(N\) is the total number of blocks in a city. A dissimilarity near 1 indicates large spatial differences of housing development between blocks in a city, while a value near 0 indicates the even distribution of housing development. In this study, we utilized residential population as the housing development indicator.

Density (Fig. 2e). Density is generally accepted as a dimension of urban form. Usually, density is calculated by comparing the footprint of buildings to the extracted built-up area. Density indicates the number of residents per square kilometer of developable area in the city. However, building density cannot distinguish between the high-density forms of high- and low-rise buildings. With the enrichment and availability of 3D information, the building area ratio (BAR) has been defined to reflect the dense 3D urban form (Long et al., 2019). The BAR is expressed as follows:

$$BAR = \frac{{\mathop \sum \nolimits_{n} A_{i} }}{S} = \frac{{\mathop \sum \nolimits_{n} P_{i} \times F_{i} }}{S}$$

where \(\sum {A}_{i}\) is the total indoor area of all the buildings within the city. \(S\) is the area of the urban built-up region. \({P}_{i}\) is the footprint of individual building i, and \({F}_{i}\) is the floor number of building i. n is the total number of buildings. A high BAR indicates a dense urban form and vice versa.

2.3 Effects of urban forms and urban functional zones on housing prices

Existing studies have extensively demonstrated the influence of house location and accessibility on the housing prices in a specific city on the basis of hedonic price models. Usually, scholars investigate the positive impact of the distribution of urban functional zones on housing prices with the point-like benefits facilities, such as educational facilities (Wen et al., 2014, 2018), and increasing the compactness contributes to increased land values and may cause increased housing prices, especially in newly developed urban areas that must accommodate migrant populations (Hamidi & Ewing, 2015). However, with the increase in compactness, transportation costs have dropped faster than the housing costs have increased, resulting in a net decrease in household costs. Whereas Wassmer and Baass (2006) argued that no evidence that centralization would raise the housing prices in the urban area has been found. In view that a single indicator, such as compactness, density, or concentration, cannot fully show the comprehensive physical environment of the city (Galster et al., 2001), and the lack of comprehensive urban form indicators in the past comparative studies limited the understanding to the impact of urban form on urban housing prices. This study attempted to comprehensively measure the urban form of 10 large cities through the five dimensions described in Sect. 2.2 to bridge this research gap.

In general, the improved urban functional zones and urban forms indicators of the two sub-market levels, namely, intra- and inter-cities, help answer the research question on whether the layout of the urban physical environment can regulate the housing market. This study can help urban planners and policymakers have a better understanding of the impact of the urban physical environment on housing prices.

3 Comparative cases

3.1 Extra-large cities

This study measured the distribution of urban functional zones from the intra-city scale and the difference in urban form from the inter-city scale. These cross-level indicators were applied to estimate the impacts of urban forms and urban functional zones on housing prices between cities. We selected Shanghai, Bei**g, Shenzhen, Guangzhou, Chengdu, Hangzhou, Wuhan, Nan**g, Changsha, and ** centers, commercial business zones, parks and green spaces, 3A hospitals, and primary and middle schools, are selected as the level 1 indicators (Qiao et al., 2021; Tam et al., 2019; Wang et al., 2017; Wen et al., 2020).

5 Conclusions

Although previous studies have affirmed the contribution of a city’s uniqueness to the housing market in that city, this study supplements the empirical evidence of the influence of urban forms and urban functional zones on the differentiated performance of the housing market on multiple scales (within and between cities). Our findings indicate that the difference in housing prices across cities is not only attributable to the city’s uniqueness in the social and economic environment (Mirkatouli et al., 2018; Waltert & Schläpfer, 2010; Wang et al., 2017; Yi & Huang, 2014) but also to the urban form, which is led by urban growth strategies.

For the different urban forms in the five dimensions, our results show that land use development policies for low compactness, high centrality, high polycentricity, low density, and high dissimilarity in housing development may significantly increase the average housing price of the city’s housing market. This phenomenon indicates that paying attention to the housing unaffordability within the cities due to the influences of house location should also regulate the housing market on the city level through appropriate urban planning and design. For example, when considering develo** a new urban sub-center, constructing high-density communities could provide more houses for migrants and reduce the housing prices (Fesselmeyer & Seah, 2018). Our research proposes to examine the impacts of the compactness, centrality, polycentricity, and dissimilarity in housing development and the density on housing prices in the evaluation of urban development projects.

For the distribution of urban functional zones within the cities, housing prices are affected by the spatial distribution of urban functions is well studied in previous studies (Qiao et al., 2021; Tam et al., 2019; Wang et al., 2017; Wen et al., 2017). But our finding provides a unified perspective for such single-city housing price studies (Shen & Karimi, 2017). After controlling the city as an influencing factor of housing price differences, working centers, high-quality hospitals, and schools can increase the housing prices of neighboring areas.

This research has its limitations. The spatial form of a city is always more or less related to its level of economic development. The world’s most economically developed global cities (e.g., Chicago, Tokyo, Hong Kong, New York, Shanghai) are high-density cities with high housing prices. We cannot rashly infer that if a city is actively designed and built into a certain type of form, it will automatically push up or decrease local housing prices. The focus of this research is to answer whether the design and planning of the city’s physical facilities and urban functional zones’ layouts can certainly affect the housing prices if the social and economic conditions are equivalent to other cities. The findings emphasize that the moderating role of urban design and planning in social inequality caused by the housing unaffordability is feasible and our conclusions highlight a series of urban design indicators as a toolbox for planners and policymakers.