Estimating construction waste truck payload volume using monocular vision
Junjie Chen, Weisheng Lu∗, Liang Yuan, Yijie Wu, and Fan Xue
Department of Real Estate and Construction, University of Hong Kong, Pokfulam
Hong Kong, China
This is the peer-reviewed post-print version of the paper:
Chen, J., Lu, W., Yuan, L., Wu, Y., & Xue, F. (2022). Estimating construction waste
truck payload volume using monocular vision. Resources, Conservation & Recycling,
177, 106013. Doi: 10.1016/j.resconrec.2021.106013
The final version of this paper is available at http://doi.org/10.1016/j.resconrec.2021.106013.
The use of this file must follow the Creative Commons Attribution Non-Commercial No
Derivatives License, as required by Elsevier’s policy

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Abstract
Quantifying the amount of truck-loaded materials is a universal problem encountered in
numerous industrial operation scenarios. Likewise, in construction waste management,
inspectors at disposal facilities are often required to measure the amount of construction and
demolition waste (CDW) loaded by incoming trucks to determine their admissibility. Due to
the bulky and clutter nature of construction materials, accurate waste quantification without
sacrificing the operability in field has always been a challenge. This study proposes a CDW
volume estimation algorithm based on monocular vision, which can automatically quantify
the amount of specific material components, e.g., rock, gravel, and wood, in waste mixtures
from a single image. The algorithm achieved a relative error of 0.065 in estimating tuck
bucket dimensions, and consumed 3.3 s in average to process per image. The results
demonstrate the efficacy of the proposed algorithm in achieving material-level CDW volume
estimation. The algorithm was applied to analyze 2,914 waste truckloads received by an offsite sorting facility in Hong Kong. It was observed that the facility entrance received around
800.0 m3 CDW per day, of which about 10.8 m3 were rejected. The non-inert wood/cardboard
accounts for the highest proportion among all material types, implying many waste dumps
accepted by the facility might have violated the admissibility criteria. The study contributes
to the knowledge body by providing a novel, non-destructive approach to quantify CDW via
monocular vision. It can also be extended to address the general problem of truck payload
quantification in other scenarios such as road construction, warehouse inventory
management, and logistics and supply chain management.
Keywords: Construction and demolition waste; Amount quantification; Volume estimation;
Computer vision; Semantic segmentation; Photogrammetry.

*

Corresponding author.
E-mail address: wilsonlu@hku.hk.
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1. Introduction
In many industrial activities, it is a conventional need to measure the amount or properties of
truck payloads. A typical example is the operation of expressway, which measures the weight
of incoming vehicles to prevent overloaded trucks from causing road damages (Visco India,
2020). In infrastructure development, load volume of outgoing dump trucks needs to be
tracked and monitored to estimate earthwork volumes and construction intensity (Loadscan
Ltd., 2021). For special materials, it is also required to ensure their physical properties, e.g.,
temperature for asphalt concrete and moisture for earth-fill materials (Liu et al., 2013), have
met relevant construction standards. In cross-region logistics, truck cargo needs to be
inspected with cameras, radio frequency identification devices (RFID), and other sensing
approaches to ensure quality and completeness of the payload before delivery (Zhong et al.,
2017).
Similar scenarios are also observed in construction and demolition waste (CDW)
management. A huge amount of CDW is generated globally every day (Kaza et al., 2018).
The generated waste materials are transported by truck trailers to designated disposal
facilities, and different levies are charged according to their compositions. In Australia, for
example, the state authority of New South Wales has released clear guidelines (NSWEPA,
2020) and criteria (NSWEPA., 2018) to levy different disposal fees for waste loads with
different composition. In Hong Kong, CDW, according to their non-inert and inert properties,
should be directed to landfills and public fills, respectively, while waste mixture with more
than 50% inert content should be transported to off-site sorting facilities (HKEPD, 2019).
Therefore, the truck payloads need to be estimated to ensure waste materials have reached the
designated destinations. Despite the clarity and explicitness of the control criteria, how to
operatize them in field is a challenge. Physical separation by digging into each waste dump
can surely provide precise amount of specific waste types, but is difficult to implement due to
efficiency issues.
In reality, the criteria have always been, more or less, simplified in engineering practice to
ensure operability. For example, the Hong Kong Environmental Protection Department
(HKEPD) materialized the “50% inert content requirements” into two easy-to-measure
indices based on the weight and depth of the waste dumps. A bunch of sensors (e.g.,
weighbridge, range finders, and cameras) have been set up at the entrance of the waste
disposal facilities to collect relevant data. However, the simplification might have led to
significant deviations as the simplified indices do not directly reflect the amount of different
material type in the waste mixture. This is confirmed by a report from the Hong Kong Audit
Commission (Audit Commission, 2016), which revealed that the waste dumps of many truck
loads accepted have not met the inert content requirement. The deficiency of existing
approach calls for a new quantification approach for truck-loaded CDW, which should not
only be efficient enough to implement in field, but also have sufficient granularity to
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precisely sense the volume of the diverse materials in waste mixtures.
The recent development in computer vision (CV) and artificial intelligence (AI) provides
opportunities to tackle the conundrum of CDW quantification. This is especially true as the
stereo vision technology greatly expands the capability of CV, from the original 2D images to
the understanding and perception of 3D information (Liu and Aggarwal, 2005). The
technological advancement has fostered the development of research fields such as robotics,
and is becoming a catalyst for new industries such as autonomous driving (Singh, 2020a) and
augmented reality (Pollefeys, 2017). The technology has also entered people’s daily life with
functionalities unimaginable in the past. For example, people can easily measure objects’
dimension with the cameras of their smart phones (Singh, 2020b); the generation Z is
enjoying videogames with an unprecedented immersive experience by using stereo cameras
such as Kinect and RealSense.
It would be promising if stereo vision can be used to quantify CDW amount without direct
contact or sorting of the waste materials. However, exiting stereo vision solutions either rely
on binocular cameras or utilize the rational of structure-from-motion (SfM) to obtain a sense
of depth from images. These requirements are difficult to meet in CDW disposal facilities, as
the most common setting is monocular cameras installed in fixed places. Quantifying CDW
from monocular vision is notably more challenging for the following reasons. First, there is a
lack of semantic information on waste composition from the raw images, making it difficult
to directly obtain detailed quantities of specific material components. Second, because only
one single image can be captured, the depth dimension is lost, leading to the difficulty of
recovering waste dumps’ 3D geometry.
This research attempts to take the challenges of CDW quantification based on monocular
vision, and proposes an automated volume estimation algorithm for truck-loaded waste
dumps. It does so by leveraging deep learning-enabled semantic segmentation to recognize
waste materials from mixed CDW, and compensating the loss of depth information with prior
knowledge on truck dimension profiles. Our study reaffirms the power of computer
algorithms. With a single camera and a bunch of sensors, 3D geometry of diverse materials in
the truck-loaded CDW dumps can be reconstructed in a matter of seconds. The required
sensors (i.e., camera, range finders, and weight-bridge) are all common configurations at
existing waste disposal facilities. Without any additional hardware, the proposed algorithm
can be easily deployed to existing facilities, benefiting policy makers, waste processing
contractors and other stakeholders with a valuable information on CDW volume to help
determine admissibility of waste truckloads.
The remaining of this paper is organized as follows. Subsequent to this introductory section,
Section 2 describes the current state of construction waste quantification and vision-based
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object dimension measurement. Section 3 illustrates the proposed monocular vision algorithm
for CDW volume estimation, Section 4 delivers its experimental results, and Section 5
presents preliminary applications of the algorithm in a case study. Section 6 discussed general
implications of the research findings and conclusions are drawn in Section 7.

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2. Literature review
2.1 Estimating construction and demolition waste amount
Quantifying CDW has been investigated since around three decades ago (Gavilan and
Bernold, 1994). CDW quantification can be roughly classified into two directions according
to the difference of measuring unit, namely, quantification by weight (ton, kg, or lb) and by
volume (m3). While the former can provide accurate information on the amount of waste
dumps as a whole, it is difficult to weigh each specific material component in the mixture
without onerous physical separation. By comparison, quantification by volume might be a
more operable approach as waste volume is directly related to its visual appearance, floor
space, geometric profiles. This is especially the case in certain scenarios. For example,
volume-based quantification was demonstrated to be more suitable when planning
construction waste hauling trucks (Lu et al., 2021b).

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Scholars have proposed various approaches for volume-based CDW quantification. Most
previous studies focus on predicting project-level waste generation by utilizing historical
statistics, because of the extensive project waste management demand. For example, Gavilan
and Bernold (1994) developed a waste‐management system to estimate the quantity of CDW
in residential projects, based on the data collected through field observation. Llatas (2011)
presented a model which allows technicians to estimate construction waste amount (by
volume) according to building design documents. The basis of this model is the European
Waste List. A similar study can also be found in (Lam et al., 2019). The mentioned studies
aim to forecast future construction waste generation at the design stage. Based on the context
of residential building construction in Spain, Villoria Sáez et al. (2011) developed a
quantification tool to predict the volume of CDW generated during different project stages.
Historical statistics and related indices such as GDP have also been used to predict the CDW
generation volumes at a country level, such as the United States (Prairie Village, 1998),
Greece (Fatta et al., 2003), and so forth.
To serve on-site waste processing, disposal and transport dispatching, research efforts have
been made to estimate CDW volume in field. They did so by harnessing learned waste
accumulation regularities (Katz and Baum, 2011), or by simplifying profiles of waste dumps
as either pyramidal or rectangular shapes (Arumugam et al., 2020). In (Hoang et al., 2020;
Lau et al., 2008), the authors assumed the waste materials are stored in the layout of either
stockpiled, gathered, scattered or stacked. Based on the types of layouts, material volumes
can be estimated accordingly. Despite the easiness of implementation of such methods, they
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tend to oversimplify the cluttered and heterogeneous characteristics of CDW mixture, and fail
to provide accurate material composition information with sufficient granularity. Thus, a
better CDW volume estimation approach is in need, which should not only be precise enough
to sense fine-grained compositions of waste mixtures, but also be efficient and operable
enough to implement in field.

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2.2 Measuring object dimension by computer vision
Measuring dimensions of objects in photographs is not a new problem; rather, it has been
researched for over a century, and was first addressed with the term “Photogrammetry” in
1870s. The basic rationale of photogrammetry is the geometrical-mathematical model of how
light travels from the objects, distorted when passing through camera lens, and finally casts
onto the sensor (Aber et al., 2010). In its early days, the technique of photogrammetry was
implemented manually and relied on delicately designed instruments for the purpose of
topographic mapping and architectural survey (The Center for Photogrammetric Training,
2008). The invention of computers made it possible to process photographs in batch, which
significantly improved the efficiency and push the discipline to a new phase called analytical
photogrammetry (The Center for Photogrammetric Training, 2008). In addition, the
subsequent advancements of computer vision further expand the capability of
photogrammetry by augmenting it with the intelligence to recognize objects in images.
In computer vision, an active research field is computer stereo vision, which aims to obtain
3D information from digital images based on the basic principles of photogrammetry. In the
most common setting, two cameras installed at different known locations are used to capture
photographs of the same scene; thus, depth perception can be achieved by triangulating
features correspondences between the two photographs. Torr and Zisserman (2000) proposed
a robust method to estimate multiple view relations from point correspondences. Hamdan et
al. (2021) demonstrated the viability to extract 3D geometry of structural damages from
multiple overlapped photographs in the lab environments. Other than infrastructure
monitoring, stereo vision has been used in environmental engineering as well for the
monitoring of deep-sea ecosystems (Aguzzi et al., 2019). Where the “two (or multiple)
cameras” setting is not available, multiple photographs taken from different locations and
with different postures are required to extract the 3D information of a stationary object. This
is widely known as the “structure-from-motion (SfM)” technique. Ost et al. (2021) presented
such a SfM system that used overlapping secondary electron images to reconstruct threedimensional topography models of soil microaggregates. Isailović et al. (2020) applied
sequential aerial images to reconstruct point cloud models of bridges, from which geometry
of spalling damages recognized by deep neural networks can be extracted.
Compared with the common settings in stereo vision, object measurement based on monocular
vision is notably more challenging as it lacks diverse views of the scene to generate a sense of
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depth. To compensate that, prior knowledge or certain assumptions of the scene are required by
existing studies (Li et al., 2018; Xue et al., 2018; Zaheer et al., 2018). In (Zaheer et al., 2018),
the regularities of man-made structures (e.g., orthogonal and parallel lines) were leveraged to
reconstruct 3D profiles of multi-planar scenes from a single view. Xue et al. (2018) considered
parametric models of common building elements as a priori, and developed a derivative-free
optimization approach to generate building information models from 2D images. Lim et al.
(2014) assumed cracks are on the same plane with inspection robots, and proposed an
algorithm to extract defect geometry on bridge deck by the camera line-of-sight with the deck
surface. Similar approaches can be used for waste amount estimation as well. As truck
manufacturers all follow designated assembly standards and regulations, it would not be too
difficult to make certain assumptions on the distribution of truck dimensions. Based on such
assumptions, the problem of monocular vision can be simplified, making it solvable to recover
3D geometry of truck-loaded wastes from single images.
3. Methods
3.1. Construction waste semantic segmentation
The rapidly developing deep learning (DL) makes it possible to train computer algorithms to
detect objects from images with a pixel-level granularity. This pixel-level image recognition
task is known as semantic segmentation in the computer science community. Semantic
segmentation based on DL can be used to recognize specific waste components from images
of mixed CDW dumps as well. There are many off-the-shelf semantic segmentation
techniques that have achieved solid performance on public datasets, e.g., Mask R-CNN (He
et al., 2017), U-Net (Ronneberger et al., 2015), and the DeepLab series (Li, 2020). In our
previous work (Lu et al., 2021a), a DeepLabv3+ model was trained to segment 9 types of
CDW materials and relevant objects. Fig. 1 shows some examples of CDW semantic
segmentation, where the meanings of encoded colors in the semantic maps have been
explained in the table at the right side. Note that the area of trucks is also recognized by the
model, which lays the foundation to detect boundary of the dump bucket and further calculate
its dimension in Section 3.3.

Fig. 1. CDW semantic segmentation.
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3.2. Creation of truck dimension profiles
A major challenge for 3D reconstruction from monocular vision is the loss of depth information.
Previous researches have more or less utilized some sort of prior knowledge or assumptions on
the objects of interests to compensate the loss of the depth dimension, e.g., the principle of
perspective (Asadi et al., 2019), and the Manhattan world assumption for built environment scene
reconstruction (Li et al., 2018).
In 3D geometry reconstruction of truck-loaded wastes, similar priori on truck dimensions might
also be leveraged to confine the solution space, making the problem solvable. We notice that
there is a certain level of flexibility in bucket dimensions, as waste haulers can customize their
dump buckets. Nevertheless, the front cabins of trucks are relatively stable, and the bucket size
shall generally be in line with the cabin to abide relevant transportation rules and regulations.
According to Code of Practice for Loading of Vehicles (CPLV) released by the HONG KONG
Transport Department (HONG KONGTD, 2019) , the truck side mirrors should extend beyond
the its payload so that driver can the traffic condition behind. This means the truck bucket has
roughly the same width as front cabin. Meanwhile, to load as much cargo as possible in a single
trip, waste haulers tend to extend their buckets to as high as the cabin.

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Fig. 2. (a) Schematic diagram showing how truck dimensions are defined; (b) Relationship
between CH and PGVW; (c) Relationship between CW and PGVW; (d) Relationship between
CL and PGVW.
Here we develop a mathematical model called truck profiles to describe the variations of truck
dimensions for different types of trucks. The basic rationale is based on the concept of user
profiles, which are frequently used in social media, online shopping, and other Internet sectors to
retrieve useful patterns from users’ behaviors and features. To create the truck profile model, we
have investigated more than 90 truck models from 3 main manufacturers in the CDW
management industry of HONG KONG, i.e., Isuzu, Hino, and Fuso. The investigated factors
include cabin height (CH), cabin width (CW), cabin length (CL), and permitted gross vehicle
weight (PGVW) of the respective truck model, which were collected from the official HONG
KONG websites of the three manufacturers.
Fig. 2 (a) shows how the truck CH, CW, and CL are defined by a schematic diagram, while Fig. 2
(b)~(d) present the scatter plots between the cabin dimensions with the PGVW of all investigated
trucks. It was observed that CH and CW demonstrate significant correlation with the PGVW,
both with their coefficients of determination larger than 0.9. The findings implicate the viability
to estimate the height and width of the cabin (and thus the bucket) according to the truck’s
PGVW, which is a major truck manufacturing parameter that can be easily obtained.

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3.3. Construction waste volume estimation
3.3.1. Camera calibration
The purpose of camera calibration is to obtain both its intrinsic and extrinsic parameters. The
intrinsic parameters are those that describe the internal characteristics of a camera, e.g., focal
length, resolution, and distortion coefficients. The extrinsic parameters, on the other hand,
describe the camera’s posture relative to a global coordinate system. The acquisition of the two
aspects of parameters is a basic prerequisite in many photogrammetric applications, including
CDW volume estimation in our case.

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Fig. 3. (a) Example photos of checkboard pattern used for camera calibration Point cloud; (b) The
created global coordinate system and some of the selected reference points for camera extrinsic
parameter calculation; (c) Layout of ranger finders on top of the toll gate entrance.
(1) Intrinsic parameters
The camera to be calibrated is a DS-2CD2025FWD-IHONG KONG 4mm from the
Hikvision Digital Technology. The camera is installed around 6 m above the ground at the
tollgate of an off-site sorting facility in HONG KONG, as shown in Fig. 3 (b). We used the
Zhang’s method (Zhang, 2000) to calibrate the camera. As the camera is relatively distant from
the ground, the checkboard pattern was printed on an A2 paper to ensure its clear presence on the
corresponding photos. Fig. 3 (a) presents part of the collected photos, which were then input to
the MatLab toolbox for calibration. The second column of Table 1 lists the output intrinsic
parameters.

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Table 1. Details information of the calibrated camera.
Model
DS2CD2025FW
D-IHONG
KONG 4mm

Intrinsic parameters
•

•

Distortion coefficients:
[-0.523, 0.278, 0, 0]
Intrinsic matrix:
1530.2
0
0
� 0
1550.5 0�
843.3 635.1 1

Extrinsic parameters
•

•

Position (mm):
[3151, 575, 6455]
Orientation matrix:
0.185 0.924 0.336
�0.9654 -0.107 -0.238�
-0.184 0.369 -0.911

(2) Extrinsic parameters

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To calculate the camera pose, i.e., extrinsic parameters, a global coordinate system needs to
be set up first. As shown in Fig. 3 (b), we use the upper-left corner of the weighbridge as origin.
The system follows the basic rules of Cartesian coordinates, and its X and Y axes are respectively
along the short and long side of the weighbridge. On the weighbridge, we measured the actual
coordinates of around 8 points in the coordinate system. With these reference points, the extrinsic
parameters of the camera can be obtained by solving the classic Perspective-n-Points (PnP)
problem in photogrammetry. The third column in Table 1 lists the derived position and orientation
matrix of the camera.
3.3.2. Truck bucket boundary detection
Different from irregular heterogeneous CDW dumps, a truck bucket is a hollow cubic box with
explicit regularity. Thus, it is sensible to first detect and measure the boundaries of truck buckets,
and then estimate volumes of CDW contained inside. Based on the semantic maps provided by
CDW semantic segmentation in Section 3.1, the procedure of bucket boundary detection includes
four steps, i.e., distortion rectification, candidate point detection, line fitting and line refinement.
(1) Distortion rectification
As the camera has a wide-angle lens, the radial distortion is too significant to neglect. The
camera intrinsic parameters can be used to rectify the distortion. Fig. 4 shows photos of an identical
scene before and after distortion rectification, from which it can be observed that the bended bucket
boundaries have been successfully undistorted to straight lines. The same rectification is also
applied to the semantic maps as they will be used for line detection in later steps.

Fig. 4. Comparison between photos before and after distortion rectification.
(2) Candidate point detection
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The bucket boundaries comprise four lines extending along its edges. Facing the direction of
truck front cabin, they can be defined as front line lfront, left line lleft, rear line lrear, and right line lright,
respectively, as shown by Fig. 5 (a). To obtain mathematical expression of lfront, lleft, lrear, and lright,
we first find collections of candidate points, i.e., {𝑃𝑃𝑖𝑖

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

}, {𝑃𝑃𝑖𝑖

𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑡𝑡

}, {𝑃𝑃𝑖𝑖𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 }, and {𝑃𝑃𝑖𝑖

},

scattered along the four lines. As the camera is in the rear-right direction of the trucks, the rear and
right end of the bucket can be detected by detected and reflected in the semantic maps in most cases.

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𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑡𝑡

Thus, the acquisition of {𝑃𝑃𝑖𝑖𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 } and {𝑃𝑃𝑖𝑖

} is straightforward: subsample the leftmost pixels

(corresponding to the bucket rear end) and bottommost pixels (corresponding to the bucket right
end) of areas recognized as truck in the semantic map. As illustrated by the first diagram in Fig. 5
(a), the subsampling is conducted according to a predetermined distance interval (e.g., every 20
pixels), and should avoid starting regions of the leftmost pixels as those pixels are corresponding
to the vertical lines of the bucket rear end.
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

The detection of {𝑃𝑃𝑖𝑖

} is comparatively more complicated as the payload in the bucket

could occlude the bucket left boundary, as illustrated by the second diagram in Fig. 5 (a). The
algorithm described in Fig. 6 is adopted to address the issue. First, a similar procedure of iterative
subsample is performed to the uppermost pixels, and if the corresponding semantic labels of the
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

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subsampled pixel is “Truck”, the pixel coordinates [u,v] will be added to the {𝑃𝑃𝑖𝑖
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

the number of points in {𝑃𝑃𝑖𝑖

}. After iteration,

} will be compared with a preset threshold th (e.g., th = 5). If it is

greater than th, either there is no occlusion or the occlusion is not severe enough to hide most of
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

the boundary points. In such case, the {𝑃𝑃𝑖𝑖

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compromise solution will be used. The solution assumes that even though the CDW can occlude
most area of the left boundary, it will not normally cover the upper-left corner of the bucket and the
upper-right area of the truck. Therefore, the “truck” pixels on the upper-left corner and upper-right
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

area can be detected and added to {𝑃𝑃𝑖𝑖
The detection of {𝑃𝑃𝑖𝑖

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} will be preserved for later line fitting. Otherwise, a

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

} as candidate fit points.

} is different from the others because the bucket front boundary does

not explicitly show in the “Truck” labels of semantic maps, as illustrated by the third diagram in
Fig. 5 (a). Bucket boundaries after rectification are straight lines. This empirical observation can be
used to detect the front boundary candidate points. First, Hough transform is performed to detect
lines in the truck region. Among the detected results, we only consider the vertical (or nearly
vertical) ones in the front half of the truck region. The lines closest to the upper-left corner of the
image are most likely to the bucket front boundary. Thus, their starting and end points are selected
to be included in {𝑃𝑃𝑖𝑖

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

}.

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Fig. 5. (a) Schematic diagram for boundary candidate points detection; (b) Line fitting based on
least square method; (c) Bucket vertices calculation; (d) Rationale of estimating world coordinates
from 2D pixel coordinates.

Fig. 6. Pseudo code for detecting bucket left boundary candidate points.
(3) Line fitting
Mathematical expressions of bucket boundaries lfront, lleft, lrear, and lright can be obtained by fitting

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𝑓𝑓

them to candidate points {𝑃𝑃𝑖𝑖 }, {𝑃𝑃𝑖𝑖𝑙𝑙 }, {𝑃𝑃𝑖𝑖𝑟𝑟𝑟𝑟 }, and {𝑃𝑃𝑖𝑖𝑟𝑟𝑟𝑟 }, respectively. The fitting process is

essentially an optimization problem aiming to minimize the square error between the predictive
and observation values, as shown by Fig. 5 (b). Suppose kf and df are the slope and intercept of lfront
respectively, the fitting of lfront(kf, df) is mathematically formulated as:
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𝑣𝑣 = 𝑓𝑓front (𝑢𝑢) = 𝑘𝑘f 𝑢𝑢 + 𝑑𝑑f
�s. t. min ∑𝑁𝑁 [𝑣𝑣 − 𝑓𝑓
2
front (𝑢𝑢𝑖𝑖 )]
𝑖𝑖=1 𝑖𝑖
(𝑘𝑘f ,𝑑𝑑f )

(1)
𝑓𝑓

Where, (ui, vi) is an observed value in the collection of candidate point {𝑃𝑃𝑖𝑖 }(i = 1,2,…, N).

Similarly, mathematical expressions of the other boundaries can be obtained and denoted as
lleft(kl, dl), lrear(kre, dre), and lright(kri, dri).
(4) Line refinement

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The fitted lines need to be further refined to obtain bucket boundaries as precise as possible.
The refinement includes two aspects. First, as the camera is at the rear-right direction of the trucks,
the original lrear(kre, dre) and lright(kri, dri) only reflects the bottom boundaries of the bucket. They thus
should be translated from the bottom to the upper edge. The refinement can be implemented by
iteratively changing the values of intercepts (i.e., dre and dri) until certain termination conditions are
met. Second, empirical rules are used to rectify lfront(kf, df) and lleft(kl, dl) that contradict with
common sense. For example, as an effect of perspective projection, lfront and lrear, and lleft and lright
should intersect somewhere in the negative V axis and positive U axis direction respectively. If the
pattern is not followed, slope k of violating lines will be adjusted accordingly to ensure intersection
at the correct direction. In addition, the bucket front line lfront should neither be too close nor too far
away from the camera viewpoint, and if it happens, its intercept df would be adjusted to put lfront in
a proper place (e.g., 1/6 of total truck length to the tuck front end). Fig. 7 shows some examples of
detected bucket boundaries after refinement.

Fig. 7. Examples of detected boundary lines before and after refinement.
375

3.3.3. Bucket dimension calculation

380

The pixel coordinates of bucket vertices on respective images are calculated first. As shown by Fig.
5 (c), suppose P1, P2, P3, and P4 are vertices of four corner of the bucket, their pixel coordinates in
the image coordinate system can be obtained by calculating intersections between the boundary
lines:

13

𝑘𝑘l 𝑢𝑢1 − 𝑣𝑣1 + 𝑑𝑑l = 0
⎧ 𝑘𝑘 𝑢𝑢 − 𝑣𝑣 + 𝑑𝑑 = 0
1
f
⎪ f 1
𝑘𝑘f 𝑢𝑢2 − 𝑣𝑣2 + 𝑑𝑑f = 0
⎪
𝑘𝑘ri 𝑢𝑢2 − 𝑣𝑣2 + 𝑑𝑑ri = 0
⎨ 𝑘𝑘ri 𝑢𝑢3 − 𝑣𝑣3 + 𝑑𝑑ri = 0
⎪𝑘𝑘re 𝑢𝑢3 − 𝑣𝑣3 + 𝑑𝑑re = 0
⎪𝑘𝑘re 𝑢𝑢4 − 𝑣𝑣4 + 𝑑𝑑re = 0
⎩ 𝑘𝑘l 𝑢𝑢4 − 𝑣𝑣4 + 𝑑𝑑l = 0

(2)

Where, (u1, v1), (u2, v2), (u3, v3), and (u4, v4) are pixel coordinates of P1, P2, P3, and P4 respectively.

385

Let Pj, (uj, vj), and (xj, yj, zj) (j = 1,2,3,4) denote any one of the bucket vertices and its corresponding
pixel coordinates and world coordinates in the global coordinate system. According to the
coordinate transformation model of pin-hole cameras (see Fig. 5 (d)), we have:
𝑇𝑇

𝑧𝑧𝑐𝑐 �𝑢𝑢𝑗𝑗 𝑣𝑣𝑗𝑗 1� = 𝐾𝐾[𝑅𝑅|𝑇𝑇][𝑥𝑥𝑗𝑗 𝑦𝑦𝑗𝑗 𝑧𝑧𝑗𝑗 1]𝑇𝑇

390

395

400

Where K and [R|T] are the camera intrinsic and extrinsic matrix respectively; zc is the scale factor.
Let CaMAT denote the overall camera matrix after the multiplication of K and [R|T], and assume
𝑚𝑚11 𝑚𝑚12 𝑚𝑚13 𝑚𝑚14
𝑚𝑚
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = � 21 𝑚𝑚22 𝑚𝑚23 𝑚𝑚24 �. Then Eq. (3) can be transformed to the following:
𝑚𝑚31 𝑚𝑚32 𝑚𝑚33 𝑚𝑚34
𝑥𝑥𝑗𝑗
𝑧𝑧𝑐𝑐 𝑢𝑢𝑗𝑗
𝑚𝑚11 𝑚𝑚12 𝑚𝑚13
𝑦𝑦𝑗𝑗
𝑧𝑧𝑐𝑐 𝑣𝑣𝑗𝑗
𝑚𝑚
𝑚𝑚
𝑚𝑚
� 𝑧𝑧 � = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 � 𝑧𝑧 � = �𝑚𝑚21 𝑚𝑚22 𝑚𝑚23
𝑗𝑗
31
32
33
𝑐𝑐
0
0
0
1
1
Multiply both ends with the inverse of CaMAT, and we can obtain:
𝑥𝑥𝑗𝑗
𝑧𝑧𝑐𝑐 𝑢𝑢𝑗𝑗
𝑛𝑛11 𝑛𝑛12 𝑛𝑛13
𝑦𝑦𝑗𝑗
𝑧𝑧
𝑣𝑣
𝑛𝑛
𝑛𝑛
𝑛𝑛
� 𝑧𝑧 � = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 −1 � 𝑐𝑐 𝑗𝑗 � = �𝑛𝑛21 𝑛𝑛22 𝑛𝑛23
𝑧𝑧
𝑗𝑗
31
32
33
𝑐𝑐
0
0
0
1
1

𝑚𝑚14 𝑥𝑥𝑗𝑗
𝑚𝑚24 𝑦𝑦𝑗𝑗
𝑚𝑚34 � � 𝑧𝑧𝑗𝑗 �
1
1

𝑛𝑛14 𝑧𝑧𝑐𝑐 𝑢𝑢𝑗𝑗
𝑛𝑛24 𝑧𝑧𝑐𝑐 𝑣𝑣𝑗𝑗
𝑛𝑛34 � � 𝑧𝑧𝑐𝑐 �
1
1

(4)

(5)

In Eq. (5), the scale factor zc represents how far the object point corresponding to pixel (uj, vj) is
away from the camera along the principal optic axis, or the so-called depth. Not knowing zc, Eq.
(5) is unsolvable because numerous points in the real world can be projected onto an identical
image pixel, as the P4’ and P4’’ in Fig. 5 (d).
The analysis of trunk dimension profile in Section 3.2 indicates the viability to estimate bucket
height based on PGVW of the truck. Leveraging this priori, zc can be calculated as follows:
𝑧𝑧𝑗𝑗 = 𝑓𝑓truckDim (𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃)
(6)
(𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃)−𝑛𝑛

34
𝑧𝑧𝑐𝑐 = 𝑓𝑓truckDim
𝑛𝑛31 𝑢𝑢 + 𝑛𝑛32 𝑣𝑣 + 𝑛𝑛33
𝑗𝑗

405

(3)

𝑗𝑗

(7)

Where ftruckDim(x) is the regression model in Fig. 2 (b) that estimates bucket height from PGVW;
n31, n32, n33 and n34 are values in the third row of CaMAT-1.
With the calculated zc, the world coordinates of P1, P2, P3, and P4 can be easily obtained by via Eq.
(5) Finally the calculation of bucket dimensions (i.e., bucket length (BL) and bucket width (BW))
14

410

415

is straightforward, which is simply the Euclidean distance between the bucket vertices:
𝐵𝐵𝐵𝐵 = [𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑃𝑃1 , 𝑃𝑃4 ) + 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑃𝑃2 , 𝑃𝑃3 )]/2
𝐵𝐵𝐵𝐵 = [𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑃𝑃1 , 𝑃𝑃2 ) + 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑃𝑃3 , 𝑃𝑃4 )]/2
Where dist(A, B) gives the Euclidean distance between world coordinates of point A and B.

(8)
(9)

Fig. 8. Orthogonal rectification and subsequent world coordinate calculation for arbitrary points in
truck bucket.
3.3.4. Orthogonal rectification

420

With the pixel coordinates of bucket vertices, the original image and its semantic map can be
rectified to an orthogonal view by applying homography transformation (Kim et al., 2019), as
shown by Fig. 8. The rectification mitigates the effect of perspective projection, and thus allow
dimension measurement of the waste materials in the bucket. Based on the bucket dimensions
obtained in previous step, it is viable to derive world coordinates corresponding to arbitrary pixels
inside the bucket area, or vice versa:
𝐵𝐵𝐵𝐵

𝑥𝑥𝑘𝑘 − 𝑥𝑥4 = 𝑣𝑣′ −𝑣𝑣′ (𝑣𝑣𝑘𝑘′ − 𝑣𝑣4′ )

425

3

4

1

4

𝐵𝐵𝐵𝐵

𝑦𝑦𝑘𝑘 − 𝑦𝑦4 = 𝑢𝑢′ −𝑢𝑢′ (𝑢𝑢𝑘𝑘′ − 𝑢𝑢4′ )

(10)
(11)

Where (𝑢𝑢4′ , 𝑣𝑣4′ ) and (𝑢𝑢𝑘𝑘′ , 𝑣𝑣𝑘𝑘′ ) are pixel coordinates after rectification of P4 and arbitrary point inside
the bucket respectively; and (x4, y4) and (xk, yk) are their corresponding X and Y components of
world coordinates.
430

3.3.5. Waste volume estimation

435

The range finders installed at the entrance of the sorting facility provide further information to
precisely estimate waste volumes. As shown by Fig. 3 (c), there are totally 8 range finders, denoted
by RF#1~#8 respectively. Table 2 lists installation position of the sensors in relative to the global
coordinate system. The range finders have been calibrated in prior so that the data given by the
sensors directly represents the distance of targets from the weighbridge.

15

Table 2. Range finder installation position.
ID

RF#1

RF#2

RF#3

RF#4

RF#5

RF#6

RF#7

RF#8

X (m)
Y (m)
Z (m)

1.0
6.0
6.5

2.0
6.0
6.5

1.0
4.5
6.5

2.0
4.5
6.5

1
3
6.5

2
3
6.5

1
1.5
6.5

2
1.5
6.5

440

445

450

Let Ω(𝑃𝑃4 , 𝐵𝐵𝐵𝐵, 𝐵𝐵𝐵𝐵) denote a rectangular region with P4 as its upper-left corner and BL and BW
as length and width of along the Y and X axis respectively. It represents the horizontal space
covered by the truck bucket. Then range finders that fall within this range can be refer to as 𝑀𝑀 =
{RF#𝑘𝑘|RF#𝑘𝑘 ∈ Ω(𝑃𝑃4 , 𝐵𝐵𝐿𝐿, 𝐵𝐵𝐵𝐵)}. Thus, the waste depth corresponding to RF#k is calculated by:
𝐷𝐷RF#𝑘𝑘 = 𝐻𝐻RF#𝑘𝑘 − 𝐻𝐻0
(11)
Where 𝐻𝐻RF#𝑘𝑘 is the height data collected by sensor RF#k, and H0 is the height of the bucket
bottom, which has been pre-stored in the record of the facility system.
With a collection of {𝐷𝐷RF#𝑘𝑘 } , the waste depth of arbitrary points in Ω(𝑃𝑃4 , 𝐵𝐵𝐵𝐵, 𝐵𝐵𝐵𝐵) can be
interpolated, as demonstrated by Fig. 9 (a). The Ω(𝑃𝑃4 , 𝐵𝐵𝐵𝐵, 𝐵𝐵𝐵𝐵) is turn into mesh grid according
to a preset interval (e.g., Δd = 150 mm) to determine positions of interpolation point PIij.
𝐵𝐵𝐵𝐵

𝑥𝑥PI𝑖𝑖𝑖𝑖 = 𝑥𝑥4 + ∆𝑑𝑑 × 𝑖𝑖, (𝑖𝑖 ∈ 𝑁𝑁 ∗ , 𝑖𝑖 ≤ ∆𝑑𝑑 )
�
𝐵𝐵𝐵𝐵
𝑦𝑦PI𝑖𝑖𝑖𝑖 = 𝑦𝑦4 + ∆𝑑𝑑 × 𝑗𝑗, (𝑗𝑗 ∈ 𝑁𝑁 ∗ , 𝑖𝑖 ≤ ∆𝑑𝑑)

(11)

Where (xPIij, yPIij) is the coordinates of PIij, and N* denote a set of positive integers. The predictive

455

�PI𝑖𝑖𝑖𝑖 at after interpolation is:
waste depth 𝐷𝐷

�PI𝑖𝑖𝑖𝑖 = ∑𝑀𝑀 𝜆𝜆𝑘𝑘 𝐷𝐷RF#𝑘𝑘
𝐷𝐷

(12)

Where 𝑀𝑀 = {RF#𝑘𝑘|RF#𝑘𝑘 ∈ Ω(𝑃𝑃4 , 𝐵𝐵𝐵𝐵, 𝐵𝐵𝐵𝐵)} , and 𝜆𝜆𝑘𝑘 is the weight factor of observed waste
depth at RF#𝑘𝑘 on the predictive waste depth. Different interpolation methods calculate 𝜆𝜆𝑘𝑘
differently. With Kriging interpolation, for example, 𝜆𝜆𝑘𝑘 is determined by the relative distance of
predictive points, spatial layout of observation points, and other factors.

16

Fig. 9. Schematic diagrams of (a) interpolation and
(b) waste volume estimation.
460

Via Eq. (10) and (11), the type of waste material corresponding to PIij can also be obtained from
the semantic map, and be denoted by 𝑇𝑇PI𝑖𝑖𝑖𝑖 . Hence, geometry and semantic information for all

465

�PI𝑖𝑖𝑖𝑖 , 𝑇𝑇PI𝑖𝑖𝑖𝑖 }. Assuming that waste materials
interpolation points can be obtained as {𝑥𝑥PI𝑖𝑖𝑖𝑖 , 𝑦𝑦PI𝑖𝑖𝑖𝑖 , 𝐷𝐷

at the bottom are consistent with the surface materials, the volume of any specific type or the entire
dump of CDW can be then estimated. This is done by simple accumulation of column volumes
corresponding to certain waste materials, as shown by Fig. 9 (b). Eq. (13) shows mathematical
formula to calculate the volume of a waste dump.
𝐼𝐼

470

475

480

𝐵𝐵𝐵𝐵

𝐽𝐽

𝑚𝑚𝑚𝑚𝑚𝑚
𝑚𝑚𝑚𝑚𝑚𝑚 �
∑𝑗𝑗=1
𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 = ∑𝑖𝑖=1
𝐷𝐷PI𝑖𝑖𝑖𝑖 ∆𝑑𝑑2

(13)

𝐵𝐵𝐵𝐵

Where 𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 = � ∆𝑑𝑑 � and 𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚= �∆𝑑𝑑�, and ⌊𝑥𝑥⌋ gives the floor integer of x.

4. Results and analysis
This section analyzes the results of the proposed algorithms in an off-site sorting facility in
HONG KONG. The algorithms were implemented with MatLab and Python on an OptiPlex
7080 computer with Intel(R) Core (TM) i7-10700 CPU and NVIDIA GeoForce RTX 2070
SUPER GPU.
4.1. Results of bucket dimension calculation
We first evaluated bucket dimensions calculated by the proposed algorithm. As mentioned in
Section 3.2, the width of dump buckets is supposed to be roughly the same with cabin width so as
to comply relevant regulations. According to truck models and their PGVW, the width data of 78
trucks passing through the facility entrance was collected from official websites of corresponding
17

485

490

495

500

505

manufacturers. Fig. 10 (a) shows a comparison between the estimated bucket width and the
observed ground-truth values, and the relative error for each sample is represented by a gray bar
at the bottom. The general trend of the predictive values is consistent with the observed values.
As summarized by Fig. 10 (b), the average relative error is 0.065, which is satisfactory.

Fig. 9. Evaluation of bucket dimension calculation performance: (a) Comparison between
predictive and observed bucket width of 78 investigated trucks; (b) Histogram distribution of
relative errors.
4.2. Results of waste volume estimation
The satisfactory precision of bucket dimensions calculation lays the foundation for 3D
reconstruction of truck-loaded waste and further volume estimation. Fig. 11 shows some example
results. The first column is the original RGB images, and on top of each image the corresponding
transaction number, truck plate number, and the estimated bucket dimensions are presented. In
the second column are the reconstructed 3D geometric models with real texture applied onto the
waste dump surface. In the last column are the reconstructed 3D semantic models with different
CDW types encoded by different colors. The estimated waste volumes are also listed on the right
hand side.
It can be found that the estimated geometry, semantic types, and volumes of the wastes are
aligned with the observations from RGB photos. Note that there might be waste areas covered by
the grippers mounted to the truck buckets. The semantic properties of these areas are replaced
with the waste types of their nearest voxels when estimating the CDW volumes (An example is
the fourth row of Fig. 11). The average processing time of the proposed algorithm is 3.3 s per
image, including 3.22 s for bucket dimensions calculation and 0.08 s for volume estimation.

18

Fig. 11. 3D geometric and semantic models reconstructed from monocular vision.
510

515

5. Case study
The proposed algorithm was applied to analyze 2,914 transaction records happed in October
2019 at one lane of the sorting facility. Fig. 12 (a) demonstrates the daily CDW volumes
arriving at the toll gate of the facility. It can be clearly observed that the waste volumes
fluctuate periodically according to a cycle of roughly every seven days. Among the seven
material types, wood/cardboard accounts for the largest proportion, followed by the “Mixed”
waste which is a clutter combination of inert and non-inert materials. The three inert
19

materials, i.e., rock, gravel and earth, have the least proportion, possibly because the waste
haulers elect to primarily send such waste types to the public fills for lower disposal price.
520

525

530

535

540

The facility toll gate received around 800.0 m3 CDW per day, of which about 10.8 m3 were
rejected for not meeting the requirements of inert content proportion (HKEPD, 2019). Fig. 12
(b) and (c) show volume distribution over diverse materials accepted and rejected by the
facility, respectively. Most of the rejected materials are non-inert wastes such as wood and
packaging, implying the rejected waste dumps indeed have not reached the required
proportion of inert materials. Meanwhile, non-inert materials also account for a great
proportion in the accepted wastes. This is in line with the HONG KONG Audit Commission
report (Audit Commission, 2016), which criticized that many truck loads accepted by the
facility not actually meeting the inert-content requirements.

Fig. 12. Statistics of estimated waste volume in October 2019: (a) Amount of daily incoming
waste dumps; (b) Distribution over different materials for the accepted waste dumps; (c)
Distribution over different materials for the rejected waste dumps.
6. Discussion
“A picture is worth a thousand words”. From an information technology perspective, the
widespread adage reflects how immense magnitude of information can be conveyed by a
single image. Indeed, a top-down photo of truck-loaded waste dump not only tells much
about its composited material components, but also implicitly encodes information of its
geometry. However, without effective algorithms and proper use of domain knowledge, such
abundant information will remain undiscovered treasure inaccessible to those in need. This
paper presents a monocular vision algorithm that integrates semantic segmentation and
domain knowledge of truck dimension profiles to reconstruct 3D geometric and semantic
models of CDW dumps from single images. The algorithm can estimate truck bucket
dimensions with a relative error of 0.065, while only consumes 3.3 s to process each image. It
20

545

only requires common hardware configurations (e.g., camera and weight bridge) at existing waste
disposal facilities, and can estimate CDW volumes in sufficient granularity without physical
separation. The effectiveness of the algorithm makes it a promising solution to address the
conundrum of balancing between “accuracy” and “operability” in waste quantification.

550

The algorithm is primarily implemented and validated in the HONG KONG context.
However, it can be easily extended to other places of the world by simple recalibration of its
core modules. For example, different countries/regions generate different types of
construction wastes; thus, the CDW semantic segmentation model needs to be re-train or
finetuned accordingly based on the specific contexts. In addition, the prevalent manufacturers
and truck dimensions in other places might be different from those in HONG KONG, making
it necessary to re-calibrate the “Cabin height-PGVW” regression model.

555

560

The broad concept of the proposed algorithm can also be generalized to other industries
where similar truck payload amount estimation requirements and hardware setup are shared.
An exemplary scenario is infrastructure construction, in which volumetric measurement is an
important task for quality control. Similar systems can be set up at the entrance of such
infrastructure projects. Then the proposed algorithm can be deployed to calculate volumes of
incoming materials such as asphalt concrete and rockfill for compliance check or progress
monitoring.

565

570

575

580

7. Conclusions
How to accurately quantify construction and demolition waste (CDW) with easy and operable
approaches in field is an unsolved dilemma. Physically segregating the waste materials can
certainly provide precise amount information, but is onerous and time-consuming. To tackle
the dilemma, this paper presents a non-destructive and precise algorithm for truck-loaded
CDW volume estimation based on monocular vision. In the proposed algorithm, a deep
learning model is trained to extract semantic information of waste types (e.g., rock, gravel,
and wood); prior knowledge of truck dimension profiles is used to achieve depth perception,
and recover 3D geometry of the waste dumps. The algorithm achieved a relative error of
0.065 in estimating bucket dimensions while consumed 3.3 s to process each image. A case
study was carried out to analyze 2,914 waste dumps received by an off-site sorting facility in
Hong Kong during October 2019. It was found that the facility entrance received around
800.0 m3 CDW per day, of which about 10.8 m3 were rejected. Among the accepted
materials, the non-inert wood/cardboard accounts for the highest proportion, revealing many
CDW dumps accepted by the facility did not actually comply with the inert-content
requirements.
Despite the demonstrated efficacy, future studies are recommended to address the following
limitations. First, the algorithm might fail to work with oversize trucks of which the buckets
21

585

590

595

600

cannot be entirely covered by the camera field of view. Thus, further improvement is required
to infer the location of invisible bucket boundaries from the images. Second, although
materials on waste dump surface provide important clues on the types of underneath waste
materials, they are not necessarily identical. Integration of physical features such as weight
and bulk density of the waste dumps might be useful to further distinguish the waste
materials beneath the surface. Such integration can be realized based on machine learning
techniques such as Bayesian inference.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This research is jointly supported by the Strategic Public Policy Research (SPPR) Funding
Scheme (Project No.: S2018.A8.010.18S) and the Environment and Conservation Fund
(ECF) (Project No.: ECF 2019-111) of the Government of the Hong Kong Special
Administrative Region.
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