Bi-objective analytics of 3D visual-physical nature exposures in high-rise high-density cities for
landscape and urban planning
Maosu Li 1, Fan Xue 2*, and Anthony G. O. Yeh 3
This is the peer-reviewed post-print version of the paper:
Li, M., Xue, F., & Yeh, A.G.O. (2023). Bi-objective analytics of 3D visual-physical
nature exposures in high-rise high-density cities for landscape and urban planning.
Landscape and Urban Planning, 233, 104714. Doi: 10.1016/
j.landurbplan.2023.104714
The final version of this paper is available at: https://doi.org/10.1016/j.landurbplan.2023.104714.
The use of this file must follow the Creative Commons Attribution Non-Commercial No
Derivatives License, as required by Elsevier’s policy.
Abstract
Urban dwellers enjoy nature exposure in the neighborhood built environment through visual
and physical ways, such as window views and outdoor activities. However, existing studies
and analytics examine these pathways separately, leading to underinformed urban planning
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practices such as difficult prioritizing urban areas with both low-level nature exposures. The
underinformation problem is particularly severe for high-rise, high-density cities that
embrace high-level vertical diversity. This study aims to propose bi-objective analytics of 3D
visual-physical nature exposures, for holistic – rather than separated – assessments. First, a
floor-level Nature Exposure Index (NEI) is defined with visual and physical components. The

10

visual component NEIv is assessed by window view imagery and deep transfer learning,
while the physical component NEIp reflects the mean time from the floor to the nearest
natural sites (e.g., nature parks and seaside) through the 3D pedestrian network. Then, biobjective optimization-based analytics is designed for (i) identifying buildings and blocks
with holistically low-level visual-physical nature exposures using NEI and (ii) examining

1 Maosu LI, PhD Candidate.

Department of Urban Planning and Design, The University of Hong Kong, Pokfulam, Hong Kong SAR,
China; Email: maosulee@connect.hku.hk, : https://orcid.org/0000-0002-9970-4053
2 Fan XUE, Assistant Professor.

Department of Real Estate and Construction, The University of Hong Kong, Pokfulam, Hong Kong SAR,
China; Email: xuef@hku.hk, : http://orcid.org/0000-0003-2217-3693
*: Corresponding author, Tel: +852 3917 4174, Fax: +852 2559 9457; Email: xuef@hku.hk
3 Anthony G. O. YEH, Chair Professor.

Department of Urban Planning and Design, The University of Hong Kong, Pokfulam, Hong Kong SAR,
China; Email: hdxugoy@hku.hk, : http://orcid.org/0000-0002-0587-0588

1

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probabilistic outputs and robustness of linear weighting schemes. A case study of 519
buildings showed that the NEI-enabled bi-objective analytics is automatic, effective, and
inexpensive. Interviews with field experts confirmed that the analytics provides
comprehensive evidence for a holistic identification of high-rise, high-density areas in need
of nature exposure for landscape management and urban planning.

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Keywords
Nature exposure; Window view; Walkability; Pareto optimality; 3D GIS; High-rise, highdensity cities
Highlights


Nature Exposure Index (NEI) defined on window views and walkability of natural
sites



Holistically assessed physical-visual nature exposures for the built environment



Pareto optimality-based identification of areas with low-level nature exposures



NEI-enabled analytics for probabilistic outputs and robustness of linear weightings



A case study of a high-rise, high-density area with 519 buildings for validation

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1 Introduction
Exposure to nature, such as greenery, sky, and waterbody, is preferred by urban
dwellers because of well-recognized benefits for human physical and mental health,
satisfaction, restoration, and productivity (Ulrich 1984; Kaplan 2001; Jiang et al. 2021). In
35

contrast, less nature access in the urban context may exacerbate stress, depression, and other
mood disorders (Ulrich 1984; Coppel & Wüstemann 2017). Given that almost all urban
dwellers spend considerable time indoors, such as at home or working places (Andersen
2015), a convenient nature exposure from the neighborhood built environment is treasured.

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Natural settings in the urban context are multi-faceted accessible resources for the
built environment, particularly in high-rise, high-density cities with limited and fragmentally
shared natural elements (Wolch et al. 2014). Visual and physical interactions are identified as
two main ways of nature exposure (Keniger et al. 2013; Cox et al. 2017). Visually, natural
elements from the urban landscape, e.g., greenery, water, and sky can be viewed through

45

windows or balconies by urban dwellers. Physically accessible natural elements, embodied in
green and blue spaces (e.g., parks and promenades), often scatter within the walkable range
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for daily outdoor activities. Nature exposures through the visual and physical pathways
indicate inconsistent mediators for urban dwellers’ embracement of nature.
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Identification of the urban areas with both poor visual and physical exposures to
nature, which is a multi-criteria decision analysis (MCDA) problem, can effectively facilitate
smarter landscape management and urban planning (Choguill 2008; Xia et al. 2022).
Nevertheless, traditional planning and design from individual perspectives often hinder a
holistic analysis and allocation of the multi-faceted natural resources. For example, built

55

environment and architectural design fields emphasize more on visual exposure to nature for
buildings (CIBSE 2014; CEN/TC 169 2018), whereas urban planners underline the equal
physical nature accessibility (Wolch et al. 2014; Tang et al. 2021). Researchers have
developed many methods and urban indices to assess visual and physical nature exposures
separately (Park & Guldmann 2020; Yang et al. 2021; Chen et al. 2022), but multi-faceted

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combinations were seldom considered. As a result, urban planners are often underinformed to
balance multi-faceted natural resources. For instance, the buildings and blocks without any
pathway of nature exposure, which should be preferential in urban renewal and revitalization,
used to be unnoticed in traditional practices.

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Recent geo-informatics technologies opened new avenues, such as 3D City
Information Model (CIM) view imagery and walkability analyses, for a multi-faceted nature
exposure extraction (Xue et al. 2021b). Deep learning models, e.g., Deeplab V3+ pretrained
on Cityscapes, can be transferred to compute the nature view proportion in window view
photos captured on 3D photorealistic CIMs (Li et al. 2022). The recent 3D pedestrian

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network has yielded opportunities for accurately assessing the walkability of nearby natural
sites from residential buildings (Zhao et al. 2020; Tang et al. 2021). Bi-objective optimization
of visual-physical nature exposures thus becomes technologically enabled especially in a
multi-level 3D urban environment.

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The research question of this study is thus:
“How to assess and analyze the visual and physical facets of nature exposure
holistically for identifying buildings and city blocks with both low values for a
prioritized landscape management and urban planning?”
To answer the question, we propose two objectives: i) to automatically assess floor3

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level visual and physical nature exposures for buildings, and city blocks in the 3D high-rise,
high-density cities, and ii) to bridge the assessment results with decision-support analytics in
landscape management and urban planning. This study first defines a two-dimension Nature
Exposure Index (NEI) for multiple scales of the high-rise, high-density context by inclusively
assessing both visual and physical exposures to nature. Thereafter, the NEI-based

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identification and prioritization of buildings and city blocks are formulated as a bi-objective
optimization problem. An automatic Pareto optimality-based analytical method is adopted to
identify buildings and blocks with low-level exposures to nature; and NEI-enabled analysis of
linear weighting schemes can quantitatively examine the robustness of weightings and their
probabilistic outputs for prioritization of the built environment improvement.

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The main contribution of this study is three-fold.
i.

From a theoretical perspective, this study defines a multi-dimensional NEI for
representing urban dwellers’ multi-faceted nature exposure. The multi-dimensional
NEI enables holistic urban planning and analytics regarding visual and physical nature
exposures. The multi-dimensional definition of NEI complements the existing studies,

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in particular in the 3D high-rise, high-density areas.
ii.

From a methodological perspective, the automatic 3D assessment of NEI using the
latest photorealistic window view imagery and 3D pedestrian network extends the
conventional 2D modeling of nature exposure. NEI-based bi-objective analytics
bridges the assessment results with decision-making in landscape management and

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urban planning.
iii.

For practitioners, the bi-objective analytics of NEI offers a comprehensive and
effective method for identifying buildings and blocks with unsatisfactory nature
exposure. For conventional practices using linear weightings, the analytics can

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support planners’ weight settings with outputs, probabilities, and robustness.
The remainder of this study is organized as follows. Section 2 reviews related work in
the literature. Section 3 presents the definition of NEI, the automatic assessment of NEI using
3D GIS, and a set of NEI enabled bi-objective analytics. Section 4 describes a case study and

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the results. Sections 5 and 6 present the discussion and conclusion, respectively.

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2 Literature review
2.1 Benefits and planning practices regarding exposure to nature
Numerous studies have been conducted to analyze the impact of exposure to nature on
urban inhabitants, e.g., impacts on mental and physical well-being (Jiang et al. 2014; He et al.
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2022). Visual exposure to nature is beneficial for physical and mental health. Window view
as the main way to visually accessing nature is treasured by urban dwellers owing to their
long-term indoor occupations (Cox et al. 2017). The benefits of the window views of nature
include stress relief, attention restoration, and productivity promotion for urban dwellers
(Ulrich 1984; Lottrup et al. 2015), which have been validated in multiple scenarios, such as

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residence, office, and hospital (Ulrich 1984; Kaplan 2001; Lottrup et al. 2015). By contrast,
lacking views of nature may engender mental fatigue, stress, and more potential for violence
(Kuo & Sullivan 2001).
Physical exposure through travels to nearby natural sites, such as natural parks,

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similarly, brings benefits to human health in terms of stress reduction (Hartig et al. 2014).
High walkability of natural sites becomes increasingly important for residential buildings
because it effectively encourages occupants to actively access nature, e.g., daily outdoor
activities (Fan et al. 2017; Tang et al. 2021). More extensively, easy physical exposure to
nature can also facilitate social cohesion, decrease crime rate, and revitalize the community

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(Lwin & Murayama 2011). By contrast, inconvenient physical nature exposure has shown a
negative impact on urban dwellers’ physical and mental health (Coppel & Wüstemann 2017;
He et al. 2022).
Landscape management and urban planning have recently embraced narratives on the

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links between urban health and the benefits of exposure to nature (Wolch et al. 2014).
Balancing the visual and physical nature exposures for buildings and city blocks becomes the
main way for urban planners and designers to optimize natural resource allocation (FisherGewirtzman 2018; Tang et al. 2021). For example, high-quality views of natural landscapes
are considered in space planning of buildings and flats (USGBC 2019, p. 134;

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Laovisutthichai et al. 2021) and strategically shared in high-density urban environments
(Fisher-Gewirtzman 2018), such as Hong Kong (HKTPB 2010). In addition, physical access
to nature becomes important in urban regeneration and new town planning (Wolch et al.
2014). There is increasing policy interest in planning more neighborhood natural sites, such
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as parks, gardens, and ponds, to sustain urban health and livability (Raymond et al. 2016).
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Nevertheless, existing land constraints and relentless development pressures can hinder
planners from simultaneously providing natural elements (e.g., greenery, water, and sky) for
all buildings and blocks in need (Tang et al. 2021). Thus, identifying buildings and city
blocks with both low-level visual and physical exposures to nature is a prerequisite of
comprehensive orderly planning of natural resource settings for healthy high-rise, high-

150

density urban development.
2.2 Quantified nature exposure measurement
Domain-isolated assessments of exposure to nature were studied from various
perspectives for landscape management and urban planning. The quantification of visual

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exposure to nature utilizes visibility analysis (Fisher-Gewirtzman 2018) and view imagery
(Helbich et al. 2019; Chen et al. 2022; Xue et al. 2021a) on the ground, floor, and overhead
levels (Li et al. 2022). View collection has recently been transferred to the window level
(Laovisutthichai et al. 2021; Li et al. 2021). Natural elements (e.g., greenery, water, and sky)
of window view photos collected from 3D photorealistic CIMs can be automatically

160

identified using a deep transfer learning model, e.g., Deeplab V3+ pre-trained on the
Cityscapes, thereby providing opportunities to represent visual nature exposure of buildings
and blocks in a multi-level urban environment (Li et al. 2022).
Physical accessibility has been measured using buffer zone, model-based, and

165

distance-based assessment methods (Oh & Jeong 2007; Park & Guldmann 2020). For
neighborhood services to function properly, walkability is often used to examine the
connectivity between living and working places and nearby services, such as natural parks
(Lwin & Murayama 2011; Tang et al. 2021). The recent reconstruction of a 3D pedestrian
network with regard to topography and travel speed has enabled high accuracy of walkability

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measurement for physical nature exposure of buildings, particularly in high-rise, high-density
cities (Sun et al. 2021; Tang et al. 2021).
Some emerging studies combined different forms of greenery exposure to understand
the exposure disparity of urban areas comprehensively. For example, availability, physical

175

accessibility, and eye-level visibility have been harmonized for greenspace exposure
examination (Ye et al. 2019; Labib et al. 2021). However, existing nature exposure
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assessment methods encounter challenges in high-rise high-density urban environments.
First, accessible nature by urban dwellers in high-rise, high-density cities cannot be
represented by ground-level visibility (Li et al. 2022) and 2D accessibility (Zhao et al. 2020;
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Sun et al. 2021) of greenery. Furthermore, current integrated visual and physical assessments
fail to bridge the multi-criteria decision-making process for prioritized improvement of the
built environment. Thus, next-generation decision-support analytics for landscape
management and urban planning should be able to examine multi-dimensional exposures to
nature and identify buildings and city blocks with low-level visual-physical nature exposures

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for 3D high-rise, high-density cities, with up-to-date multi-criteria decision methods.
2.3 Multi-criteria decision analysis for urban planning
MCDA attempts to solve complex geospatial problems with multiple constraints,
particularly for decision support applications (Malczewski 2006). In general, MCDA

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comprises two categories: multi-attribute decision analysis and multi-objective optimization.
Compared to the multi-attribute decision analysis returning a single result, multi-objective
optimization outputs multiple results for a set of specific objectives (Malczewski & Rinner
2015), enabling a comparison for planners’ final decisions. Pareto optimality is one of the
cornerstone concepts of multi-objective optimization that attempts to identify all non-

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dominated results as Pareto-optimal solutions (Huang et al. 2008; Malczewski & Rinner
2015). This concept has been used in typical multiple objective scenarios, such as land use
allocation and urban infrastructure site planning (Huang et al. 2008; Rahman & Szabó 2021).
Thus, Pareto optimality-based optimization can be used to identify a set of solutions for biobjective analytics of 3D visual-physical exposures to nature in high-rise, high-density cities.

200

In summary, the targeted bi-objective optimization analytics of 3D visual-physical
nature exposures in this paper is a research gap to close in landscape management and urban
planning studies. Among the reasons are the previous immature 3D visual-physical
representations (e.g., window views and walkability) of nature exposures in high-rise, high205

density cities, and the minimal consideration in their integrated assessment and analytics for
comprehensive decision-making in landscape management and urban planning. Meanwhile,
automatic deep transfer learning-based window view assessment, 3D pedestrian network
analysis, and Pareto optimality-based optimization may provide opportunities to advance the
automatic multi-dimensional nature exposure analytics for significantly improving the visual7

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physical nature exposures of the built environment in high-rise, high-density cities.
3 Research methods
Figure 1 shows the conceptual framework of the proposed NEI and related analytics.
In general, 3D data inputs comprise photorealistic CIM and building footprints for window
view measurement, as well as pedestrian network, floor sites, and natural site entries for the

215

physical accessibility. The proposed automatic integrated nature exposure assessment and
analytical methods for prioritized built environment improvement consists of two parts: (i)
NEI definition together with the automatic floor-level visual-physical nature exposure
assessment and (ii) Bi-objective optimization-based analytics of NEI. The final output
includes three parts: buildings or blocks with both low-level nature exposures, probabilistic

220

outputs of linear weightings, and robustness of target weighting for an invariant output.

Figure 1. Conceptual framework of the proposed NEI and bi-objective analytics.

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3.1 Automatic assessment of NEI
3.1.1 General definition of NEI
Given a floor of a building in the built environment, NEI is a two-dimension vector:
NEI = (NEIv, NEIp),

(1)

NEIv = (FNVI − FNVImin) ⁄ (FNVImax − FNVImin) ∈ [0, 1],

(2)

NEIp = (tmax – t) ⁄ (tmax – tmin) ∈ [0, 1],

(3)

where NEIv denotes a relative floor-level visible nature proportion in an area, FNVI represents
an absolute nature view proportion of a floor, and FNVImin and FNVImax are the maximum and
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minimum values of FNVI in the context area. In addition, NEIp is the physical component
representing the relative walkability from the floor to the nearest natural site (e.g., nature
parks and seaside) in the area. Considering the set of walking time t for all floors in the
context area, NEIp is denoted as a normalized value computed by t, tmax, and tmin. Thus, both
NEIv and NEIp are scalars bounded between 0 and 1, and the closer to 1 they are, the higher

235

levels of visual and physical nature exposures the floor owns.
Given a two-dimension vector of weighting w = (wv, wp), where wv + wp = 1, the
weighted sum of an NEI is a scalar:
wNEI = NEI × wT ∈ [0, 1],

(4)

where wv and wp represent the weighting values for NEIv and NEIp, respectively. Moreover, w
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used to be set by experts or statistics from surveys. For example, an equal weighting pair w =
(0.5, 0.5) indicates the equal significance of visual and physical exposures to nature. A small
wNEI value indicates the inconvenience of daily access to nature, thereby deserving a high
priority for the renewal and revitalization in the context area.

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3.1.2 The visual component of NEI
This study defines NEIv using the average visible nature proportions of window view
photos captured at the floor level. Given a virtual view photo captured on a window of the 3D
photorealistic CIM, WVIα defined in (Li et al. 2022) presents the ratio of visible greenery,
waterbody, and sky:
WVIα = Number of pixels in α ⁄ Total pixels of the view photo, α ∈
{greenery, waterbody, sky}.

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(5)

Regarding greenery, water, and sky as visible natural elements, we first summarize the FNVI
from WVIα of floor-level window view photos. More specifically, assuming m view photos
captured on the different facades of a floor, FNVI is calculated from WVIαi (i = 1, 2, 3, …, m)
with the sampling interval Ii as weights as shown in Eq. 6. Last, NEIv is computed as an
output using FNVI, FNVImin, and FNVImax.
FNVI = ∑i = 1, …, m (WVIαi × Ii) ⁄ ∑i = 1, …, m Ii.

(6)

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Figure 2 shows the workflow consisting of view site sampling, view generation, and
deep transfer learning-based computing of WVIα. We compute the modeled NEIv on 3D
photorealistic CIMs instead of physical sites, as shown in Figure 2a. Li’s (2022) method is
9

utilized to automate the photorealistic window view quantification as shown in Figure 2b. We
260

first apply an even sampling method to ensure at least two view sites for individual facades of
a floor (max Ii = 20 m). Then, a virtual camera with a 60-degree field of view (Tara et al.
2021; Li et al. 2022) is set on the designated sites of CIMs to capture the window view
outside. A deep transfer learning model, DeepLab V3+ trained on the Cityscapes with a
machine-learning classifier helps segment the window view photo for nature view

265

quantification. In the end, sample window view photos on the same floor of the building are
aggregated to summarize WVIαi for NEIv, as shown in Figure 2c. 3D locations and their floor
and building IDs are geo-tagged to the NEIv datasets.

Figure 2. Deep transfer learning-based estimation workflow for NEIv.
270

3.1.3 The physical component of NEI
NEIp is modeled using walking time from the occupant’s building floor to the entry of
the nearby natural site through the shortest path S. Natural sites in this study include parks,
gardens, and promenades, which are dominantly covered or surrounded by natural elements,
275

such as vegetation and waterbody to serve outdoor activities and recreation. Within the highrise, high-density context, we connect the staircase and lift of buildings with exterior
pedestrian urban fabrics, thereby updating a more comprehensive and computable 3D urban
system. Meanwhile, pedestrian walking speed is different on walkway types, such as the path
of different slopes, transport systems, and interference like crossing and traffic islands. Thus,

280

S is divided into n segments s1, s2, …, sn, where the corresponding walking speeds are v1,
v2, …, vn. The walking time t is computed as the sum of the n quotients as follows:
t = ∑i = 1, …, n d (si) ⁄ vi,

(7)

where d is a function to calculate the distance of si. Last, NEIp is computed by t, tmin, and tmax.
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We compute the NEIp from the simulated walking through a 3D pedestrian network,
285

consisting of interconnected path segments, such as lifts, staircases, sidewalks, and footpaths.
We measure the closest natural site to compute NEIp. 3D building floor sites and natural site
entries are set as origins and destinations, respectively, as shown in Figure 3. Within the
interior buildings, lifts and staircases are used to simulate the walking situation. Travel
distance by lift is considered the vertical distance between the floor and ground levels, while

290

staircase length is assumed as the vertical distance divided by sin 35° (HKLWB 2006).
Walking speed vi of different walkway types is added to the 3D pedestrian network
following the field tests of normal adults, previous studies, and regulations (Oh & Jeong
2007; Tang et al. 2021; HKBA 2011). Urban planners and researchers can finetune the control

295

parameters for specific application scenarios.
100e-3.5|tanθ+0.05| , type(si ) ∈ Footpath
⎧
120,
type(si ) = Travellator
⎪
⎪
105,
type(si ) = Lift
vi =
,
type(si ) = Escalator
⎨48,
⎪
type(si ) = Staircase
⎪39,
⎩6,
type(si ) ∈ Interference

(8)

where vi is measured in meters per minute, Footpath = {Footway, footbridge, service lane,
ramp, generalized walkway, underpass} is the set of paths with different slopes, and
Interference = {Crossing, traffic island} is the set of places where pedestrians need to wait to
cross the street. Tobler’s hiking function (Tobler 1993) is used to simulate slope impact on
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walking speed. The slope θ is positive for walking uphill and negative for walking downhill.
Last, the value of t is computed by combining all the time consumed on the segments of the
shortest path and NEIp is computed using t, tmax, and tmin (see Figure 3). Values of NEIp are
saved with the corresponding 3D locations and floor and building IDs.

305

Figure 3. NEIp computing based on the pedestrian network analysis

11

3.1.4 Scaling up for buildings and city blocks
Modern landscape management and urban planning aim to improve nature exposure
to the built environment through active intervention, such as planning more parks, roof
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gardens, and vertical greenery. Moreover, buildings and blocks are the main analytical units
in measuring nature exposure to help priority identification. For fulfilling urban planners’
needs, floor-level datasets can be adaptively aggregated into corresponding buildings and
blocks based on building IDs and topological relationships. For example, at the building
level, NEIv sets with the same building IDs are considered as a group and the NEIv_bldg is

315

computed as a floor-area-based linear weighted sum.
3.2 Bi-objective optimization-based analytics of NEI
3.2.1 Pareto optimality for identifying least-nature-exposure areas
An NEI-based MCDA is a bi-objective optimization problem. Pareto optimality is

320

used to identify all potential areas with both low-level exposures to nature. For example, the
search of buildings with low-level visual-physical nature exposures can be formulated as:
P = arg minx ∈ X NEIbldg (x),

(9)

where X is the set of buildings x in the planning area, as shown in Figure 4a. Figure 4b shows
that Pareto optimal building set P ∈ X is the set of non-dominated buildings x* in terms of
least NEIbldg. Any rest building, i.e., in X \ P, have both NEIv_bldg and NEIp_bldg greater than at
325

least one Pareto optimal building x* in P:
P = {x* | ¬ ∃x ∈ X, NEIv_bldg(x) ≤ NEIv_bldg(x*) and NEIp_bldg(x) ≤ NEIp_bldg(x*)}.

(10)

Thus, by excluding dominated buildings (X \ P), the Pareto optimal buildings x* of P become
the least-nature-exposure candidates for the prioritized improvement. In practice, a buffer
zone of Pareto front constructed by P, as shown in Figure 4b, can also be set to involve more
buildings with near-low-level visual-physical nature exposures (e.g., building #1) for more
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inclusive consideration.

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Figure 4. Identification of the Pareto optimal buildings. (a) Example buildings X, and (b)
Pareto optimal building set P visualized in the plot of NEIv_bldg and NEIp_bldg.
335

3.2.2 Linear weighting analysis for probabilistic outputs and robustness
We present a linear weighting analysis to decipher the relationship between
weightings and the final output from P. In traditional practices, urban planners employ linear
weightings from various scientific assumptions (e.g., expert knowledge and statistics) to
340

integrate multiple indices for a final output, where planners are often puzzled by various
weightings due to varied strengths and weaknesses. The presented analysis involves all the
recommended weightings at one time and returns the probabilistic outputs and robustness of
linear weightings.

345

Figure 5 shows that a fixed linear weighting represents a set of straight parallel lines
with a determined slope. For example, weighting pair w = (0.5, 0.5) represents parallel lines
with the slope k = − wv / wp = −1 passing Pareto optimal building points. The closer the line
to the origin, the lower the level of wNEI the building access. When the weighting ratio k
changes, the convex point with the lowest wNEI may change, i.e., C1, C2, and C3, as shown in

350

Figure 5b. Isoline with the lowest wNEI reaches the same convex point(s) on the Pareto front
when k changes within the ranges of A1, A2, or A3 in blue. The relationship between the output
and the weighting ratio k = − wv / wp is shown in Eq. 11.
C1 , k∈A1 =(−∞, k1 ]
C = �Ci , k∈Ai =[ki , ki+1 ], 1 ≤ i ≤ N − 1.
CN , k∈AN =[kN , 0]
13

(11)

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Figure 5. Analysis of linear weighting schemes. (a) Parallel lines indicating equal weightings,
(b) relationship between weightings and outputs, and (c) least NEI building identification by
overlapping the target range to the weighting ratio range of C.
When the recommended weightings are in a range and not finally determined, urban

360

planners can directly use the range Atarget as the input in Figure 5c. Then, the probability of
any candidate Ci is measured using the overlap between Ai and Atarget:
Probability (Ci) = rad (Ai ∩ Atarget) ⁄ rad (Atarget),

(12)

where rad is a function to compute the radian of A. For example, Figure 5c indicates that the
Atarget is a subset of A2. Thus, considering all the weightings, the candidate building C2 is
always the final output, with probability = 100%. In addition, the robustness of target
365

weighting for an invariant final output can also be assessed. Eq. 13 shows the robustness of
target weighting ratio k is computed based on the corresponding radian of Ai. For example,
the target weighting pair, w = (wv, wp), k = − wv ⁄ wp = −1 within A2, as shown in Figure 5b,
owns a robustness, rad(A2) ⁄ 0.5π, to ensure the invariance of the final output C2.
Robustness (w) = rad(Ai) ⁄ 0.5π, k = − wv ⁄ wp ∈Ai.

(13)

4. Case study
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4.1 Study area and settings
The study area includes a total of 519 buildings in 57 town blocks of Wan Chai, one
of the most high-rise, high-density areas in Hong Kong (HKPlanD 2018), as shown in Figure
6. The average building height is 35.5 m and the maximum plot ratio is 10.0. Major natural
elements, e.g., vegetation and water from mountains and sea, are located in the northern and

375

southern areas, while the minor scatters in parks and gardens. Because of the vertical
development and imbalanced natural settings, the occupants in the case area encounter
considerably different visual and physical nature exposures, the variance of which is
14

confirmed in Sections 4.2.1 and 4.2.2.
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Building footprints with height information were extracted from the iB1000 digital
map of Hong Kong (HKLandsD 2014), as shown in Figure 6c, while a 3D photorealistic CIM
was from the Planning Department (2019). For physical accessibility, the 3D entry points of
case natural sites in blue were collected from the Leisure and Cultural Services Department
of Hong Kong and Google Map in Figure 6e, while the 3D pedestrian network in red was

385

from the Lands Department (HKLandsD 2021). Moreover, the number of stories of buildings
in yellow and lift information were extracted from the Home Affairs Department (HKHAD
2021) and Electrical and Mechanical Services Department (HKEMSD 2021), respectively.

Figure 6. Study area of Wan Chai, Hong Kong. (a) Location, (b) 519 buildings, (c) building
390

footprints and heights, (d) CIM, and (e) 3D pedestrian network with floors and entry points.
The computational process was set up as follows. This study used a workstation with
an Intel i7-10700 CPU (2.90GHz, 16 cores), 128 GB memory, one NVIDIA GeForce RTX
2070 graphic card, and Windows 10 and Ubuntu 20.04 dual system (64-bit). Floor-level

395

window views were generated with the Cesium (ver. 1.75), a software platform for processing
and visualization of 3D geospatial data. We adopt Li’s (2022) deep transfer learning-based
15

window view quantification with the environment of Tensorflow (ver. 2.4), Python (ver. 3.6),
and Orange 3 (ver. 3.26, a Python machine learning platform). The NEIp measurement and
multi-scale spatial pattern visualization were implemented with ArcGIS Pro (ver. 2.7.3). Last,
400

Pareto optimality-based bi-objective optimization analytics was implemented through a
decision support tool developed on the ArcGIS Pro platform.
4.2 Results
Table 1 lists the time cost of all the steps in the case study. The full assessment and

405

analytical process was completed within 21.37 hours. The window view quantification
consumed > 99.9% of the processing time, while all rest steps consumed < 62 s in total. The
accuracy of NEIv was satisfactory (R2 > 0.95) according to Li et al. (2022), while the accuracy
of NEIp was confirmed (RMSE < 0.12) by a normal adult through field tests.

410

Table 1. Computational time of the proposed automatic assessment and analytical method.
Ref. sect.

Variable to produce

Processing

Software library

Total time

3.1.2

NEIv

View quantification (Li et al.

Cesium, Deeplab V3+,

21.35 h

2022)

and Orange 3

Floor-level aggregation

ArcGIS Pro

2.62 s

3.1.3

NEIp

Closest natural site analysis

ArcGIS Pro

58.16 s

3.1.4

NEIbldg

Building-level aggregation

ArcGIS Pro

0.63 s

3.2.1

P

Pareto optimality-based

ArcGIS Pro

0.52 s

ArcGIS Pro

0.01 s

optimization
3.2.2

wNEI

Linear weighting analysis

Total

21.37 h

4.2.1 Floor-level results
NEIv and NEIp were computed and visualized on the 3D building footprints, as shown
in Figure 7. Figure 7a shows upper building floors often enjoyed high-level nature views,
415

while inland lower building floors were with less visual exposure to nature. Although some
floors could have a high-level nature view (FNVI = 0.62), there still existed floors with no
visual nature exposure. Meanwhile, Figure 7b shows buildings surrounded by natural sites
tended to own better convenience for physical access. By contrast, building floors in the
lighter color indicated lower accessibility, in which the maximum t was above 10 min.

16

420

Figure 7. Disparity of exposures to nature. (a) NEIv and (b) NEIp.
The box plots in Figure 8 suggest that the holistic nature view acquisition of the
building floors in this area was not high, where the median value of FNVI was approximately
425

0.16. One-fourth of the building floors were without exposure to nature (FNVI < 0.1) due to
compact surrounding construction elements. Meanwhile, the median t was approximately 4.5
mins, with a distribution from 0.14 to 11.86 mins. Travel time from at least one-fourth of the
building floors to the closest natural site was longer than 5.7 mins. As shown in Figure 8c,
NEIv nearly had an ignorable negative correlation with NEIp (Spearman’s coefficient ρ =

430

−0.149, p ≤ 0.0001). The ignorable correlation also indicated that it is necessary to use an
integrated assessment for a more comprehensive understanding of exposure to nature in the
case area.

435

Figure 8. Statistical results. Box plots for (a) FNVI and (b) t, and (c) Spearman’s correlation
coefficient of NEIv and NEIp (#: two-tailed significance p ≤ 0.0001).

17

4.2.2 Building-level results
Figure 9 shows spatial patterns of NEIv_bldg and NEIp_bldg. The distribution of NEIv_bldg
440

was found to be discrete. Through the validation from 3D photorealistic CIM, unobstructed
buildings nearby the hills, artificial greenery, or seaside, as shown in circles #1 and #2,
tended to have a better nature view acquisition. By contrast, the spatial distribution of
NEIp_bldg was more clustered. For example, buildings in red circle #3 had higher NEIp_bldg,
whereas NEIp_bldg of buildings in circle #4 was lower. Observation of CIM showed that

445

buildings in circle #3 owned a close-range park in the surrounding environment, while there
only existed surrounded construction elements for the buildings in circle #4. That is, the
current natural resource setting has led to an evident disparity of visual and physical nature
acquisitions for urban dwellers in the context area.

450

Figure 9. Building-level results with observational validation. (a) NEIv_bldg and (b) NEIp_bldg.
4.2.3 Automatic identification of least-nature-exposure areas for urban planning
The building-level analytics was implemented as a user-friendly add-on on the
455

ArcGIS platform, as shown in Figure 10. A user can input NEIv_bldg and NEIp_bldg in Section
4.2.2, as well as the buffer zone of the Pareto front, acceptable weighting range, and target
weighting pair for robustness analysis, as shown in Figure 10b. Note that representations of a
weighting pair (wv, wp), e.g., “0.25, 0.75” and its ratio “0.33” are both acceptable for the
18

inputs. The analytics outputs comprised three parts: (i) Pareto optimal buildings, namely, the
460

set of buildings with both low-level visual and physical nature exposures; (ii) probabilistic
outputs according to acceptable linear weightings; and (iii) robustness of the target weighting
for an invariant output.

Figure 10. Results of automatic identification. (a) Pareto optimal buildings, (b) NEI-based
465

building query through an ArcGIS addon, (c) two probabilistic output buildings from a range
of linear weightings, (d) results of probabilities in the addon, (e) robustness of a target
19

weighting for an invariant output, and (f) results of robustness in the addon.
The Pareto optimal solutions included six buildings with the least NEIs using
470

exhaustive Pareto optimality-based bi-objective optimization (buffer zone range = 0), as
shown in Figures 10a and 10b. No other buildings could have poorer visual and physical
nature exposures than the six in red in Figure 10a. Figures 10c and 10d show the probabilistic
buildings under a target linear weighting ratio range—from wv : wp = 0.33 to 3 set by users.
Only two buildings were possible to be the final outputs because Atarget covered two weighting

475

ratio ranges (i.e., A2 and A3) as shown in Figure 10c. Figure 10d shows building #110***16
was selected when the weight ratio ranged between 0.46 and 3, while building #110***94
represented the ratio from 0.33 to 0.46. Within the acceptable weighting ratio range, building
#110***16 had a higher possibility (88.12%) to be considered as the final output. By
contrast, concave points on the Pareto front, such as building #110***08, had zero possibility

480

of being selected when using the acceptable weight ratio range, though they also owned lowlevel visual-physical nature exposures. Table 2 details the values of wNEI for two
probabilistic buildings using the acceptable maximum and minimum weighting pairs.
Table 2. List of probabilistic buildings for the acceptable weighting ratio range.
No.

Building ID

Weighting pair (wv, wp)

Least wNEI

1

110***16

(0.75, 0.25)

0.09

2

110***94

(0.25, 0.75)

0.11

485

Figures 10e and 10f show the robustness analysis of a target weighting ratio wv : wq = 0.33.
The robustness of the weighting ratio wv : wq = 0.33 was 27.34% to ensure invariance of the
output (i.e., building #110***94) using Eq. 13. In summary, the in-house developed ArcGIS
add-on can effectively guide a user to examine buildings’ NEIs, list the probabilistic outputs,
490

present robustness of a linear weighting, and support explainable decision-making processes.
4.2.4 Comments from domain experts
Four domain experts were interviewed independently to validate and evaluate the
proposed method. Two experts are professors of landscape management, while the other two

495

are urban planners working at planning and redevelopment authorities. Before asking
questions in the interviews, we introduced and demonstrated NEI and the analytical results
20

through the case study. The two professors emphasized the integrated 3D quantification of the
exposure to nature in the vertical metropolis and compared the fixed weight setting method
with the Pareto optimality-based bi-objective analytics, respectively:
500

Professor A: “It is promising for guiding urban landscape management and planning,
especially in high-rise, high-density cities. The integrated 3D nature exposure assessment
is more comprehensive and effective for understanding the multi-level urban
environment.”
Professor B: “Expert knowledge is often used to determine the weight setting. Pareto

505

optimality-based bi-objective optimization method and the linear weighting analysis can
identify all the building candidates and explain the possible outputs.”
In the end, both professors suggested that the view is “rather complex than a simple
proportional indicator.” Views can be “further quantified from in-depth perspectives such as
view structure in the future.”

510

In comparison, the two planners focused on the potential scenarios and availability for
decision-making:
Planner C: “It allows the user to better understand the data relationship, and thus
minimizes the data size to be studied. The full picture between the linear weightings and
515

probabilistic outputs gives us a much clearer understanding and decision-making space.”
Planner D: “It can effectively provide insights on how to enhance the site selection process
for urban renewal, and to my best knowledge, no bi-objective optimization-based analytics
was utilized to help the identification of buildings and blocks in need of nature exposure.”
Although it is promising and practical to identify the “first-needed” area with comprehensive

520

evidence, both suggested other indicators, such as building condition, to supplement NEI for
more comprehensive decision-making in urban redevelopment and preservation.
In general, both disciplines of experts confirmed that the proposed method was
promising for guiding landscape management and urban planning. First, the integrated 3D

525

nature exposure assessment is markedly comprehensive and effective for understanding the
multi-level urban environment. The proposed analytics can narrow the focus scope, identify
all building candidates with low-level visual-physical exposures to nature, and explain the
probabilistic outputs of linear weightings. As far as they were concerned, no bi-objective
21

optimization-based analytics was available for identifications of buildings and blocks with
530

low-level visual-physical exposures to nature. In terms of applicability, all experts agreed that
the Pareto optimality-based bi-objective decision support tool could effectively help inform
decision-making in both disciplines.
5 Discussion
5.1 Significance

535

From a theoretical perspective, the proposed visual-physical NEI definition extends
the existing studies on isolated nature exposure measurement to an integrated examination
process. The NEI enables and advocates holistic urban planning and analytics for multidimensional nature exposures. Integrated analytics of visual-nature nature exposures for
buildings and city blocks is significant in improving the current urban planning paradigm in

540

the high-rise, high-density cities.
From a methodological perspective, an integrated 3D assessment of visual and
physical exposures to nature effectively examines the disparity of natural resource possession
in the multi-level urban environment. NEI-based bi-objective analytics bridges the

545

assessment results with decision-making in landscape management and urban planning. The
proposed Pareto optimality-based optimization method can ensure all the buildings and
blocks with low-level visual and physical nature exposures are identified at one time, thereby
offering an entire picture of the focus scope.

550

For practitioners, the proposed method is easy to use and low-cost. Assessment
methods can automatically identify buildings and blocks with low-level visual-physical
nature exposures from holistic perspectives. The analytical results of prioritization of
buildings for improvement in visual-physical nature exposures are comprehensive and
explainable with the possible linear weighting schemes. Accordingly, urban planners and

555

other decision-makers are enabled to make a well-informed determination with quantified
evidence. In summary, the proposed method contributes an integrated visual-physical nature
exposure assessment using CIM and pedestrian network, and thus provides a low-cost and
highly explainable analytical tool for landscape management and urban planning.

560

5.2 Limitations and future work
This study has several limitations. First, NEIv and NEIp in this paper involve neither
22

window settings nor personalized travel preferences. Thus, NEIv modeled on the
photorealistic CIM can be extended to represent window settings such as grills and scales
through Building Information Modeling, while NEIp can be personalized by path weighting,
565

such as a 50% “psychological” discount on walking time for a clean, familiar, and safe path
environment. Another future research direction is integrating other representations of
exposure to nature, e.g., incidental nature interactions on the streets and inverse
representation of acoustic nature exposure, such as urban noise. Moreover, urban planners
and landscape architects need to review the exposure suggestions with other indicators, such

570

as availability of lands, maintenance costs, and social concern, to determine the final
objectives for improvement of the built environment. Another future endeavor is to
incorporate related indicators and turn the proposed bi-objective optimization analytics into a
multi-objective decision-making. Besides, despite the acceptable time cost of Pareto
optimality-based bi-objective analytics, the NEIv computing process is still time-consuming

575

owing to the generation and segmentation of view photos. Thus, given that the proposed
definition is compatible with various window view quantification techniques, more efficient
methods will be useful. Last, the aggregation of human-level assessment results of nature
exposure into buildings and blocks can be more accurate than the floor-level one in this study,
which can be another direction to advance fine-scale nature exposure modeling in future

580

landscape management and urban planning.
6 Conclusion
Natural settings in the urban context are multi-faceted resources for urban dwellers. A
holistic visual-physical nature exposure assessment is needed for improving the built
environment. Traditional assessment often focuses on either visual or physical dimension in

585

isolation, and thus fails to identify the buildings and blocks with both low visual and physical
nature exposures.
This study defines a Nature Exposure Index (NEI) that has both visual and physical
components. Thereafter, NEI is measured through floor-level window views and walkability

590

of nearby natural sites. By aggregating the results into building or block levels, a bi-objective
optimization-based analytics is presented to identify areas with the least visual-physical
nature exposures. Last, probabilistic output buildings or blocks and robustness of linear
weightings are gauged through a linear weighting analysis. Our method achieved a
satisfactory result for a pilot study of 519 buildings in the high-rise, high-density area of Wan
23

595

Chai in Hong Kong. Comments from experts and planners indicated that the proposed
method is effective and applicable for better landscape management and urban planning.
The proposed method is automatic, effective, and scalable up to buildings and city
blocks. The assessment results of NEI represent a full picture of visual-physical nature

600

exposures. The analytical results of Pareto optimality and weighting analysis enable a holistic
and in-depth understanding of the buildings and city blocks that need improvement in visualphysical exposures to nature. Future directions include in-depth and comprehensive visualphysical nature exposure examination, more efficient view quantification methods, humanlevel analytics of nature exposure, and incorporating related indicators to the presented addon

605

for a decision-making system.
Acknowledgment
This study was supported in part by the Hong Kong Research Grant Council (RGC)
(Nos. T22-504/21-R, 27200520) and Guangdong-Hong Kong-Macau Joint Laboratory for

610

Smart Cities of the 2020 Guangdong New Innovative Strategic Research Fund, Guangdong
Science and Technology Department (Project No.: 2020B1212030009).

615

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