A method framework of semi-automatic knee bone segmentation and reconstruction from computed tomography (CT) images

Abstract

Background
Accurate delineation of knee bone boundaries is crucial for computer-aided diagnosis (CAD) and effective treatment planning in knee diseases. Current methods often struggle with precise segmentation due to the knee joint’s complexity, which includes intricate bone structures and overlapping soft tissues. These challenges are further complicated by variations in patient anatomy and image quality, highlighting the need for improved techniques. This paper presents a novel semi-automatic segmentation method for extracting knee bones from sequential computed tomography (CT) images.

Methods
Our approach integrates the fuzzy C-means (FCM) algorithm with an adaptive region-based active contour model (ACM). Initially, the FCM algorithm assigns membership degrees to each voxel, distinguishing bone regions from surrounding soft tissues based on their likelihood of belonging to specific bone regions. Subsequently, the adaptive region-based ACM utilizes these membership degrees to guide the contour evolution and refine segmentation boundaries. To ensure clinical applicability, we further enhance our method using the marching cubes algorithm to reconstruct a three-dimensional (3D) model. We evaluated the method on six randomly selected knee joints.

Results
We evaluated the method using quantitative metrics such as the Dice coefficient, sensitivity, specificity, and geometrical assessment. Our method achieved high Dice scores for the femur (98.95%), tibia (98.10%), and patella (97.14%), demonstrating superior accuracy. Remarkably low root mean square distance (RSD) values were obtained for the tibia and femur (0.5±0.14 mm) and patella (0.6±0.13 mm), indicating precise segmentation.

Conclusions
The proposed method offers significant advancements in CAD systems for knee pathologies. Our approach demonstrates superior performance in achieving precise and accurate segmentation of knee bones, providing valuable insights for anatomical analysis, surgical planning, and patient-specific prostheses.

Full text

© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Original Article
A method framework of semi-automatic knee bone segmentation
and reconstruction from computed tomography (CT) images
Ahsan Humayun1,2,3, Mustafain Rehman1,2,3, Bin Liu1,2,3
1International School of Information Science & Engineering (DUT-RUISE), Dalian University of Technology, Dalian, China; 2Key Lab of
Ubiquitous Network and Service Software of Liaoning Province, Dalian University of Technology, Dalian, China; 3DUT-RU Co-Research Center
of Advanced ICT for Active Life, Dalian University of Technology, Dalian, China
Contributions: (I) Conception and design: A Humayun, B Liu; (II) Administrative support: B Liu; (III) Provision of study materials or patients: B
Liu; (IV) Collection and assembly of data: A Humayun, M Rehman; (V) Data analysis and interpretation: All authors; (VI) Manuscript writing: All
authors; (VII) Final approval of manuscript: All authors.
Correspondence to: Ahsan Humayun, MSCS; Bin Liu, PhD. International School of Information Science & Engineering (DUT-RUISE), Dalian
University of Technology, 2 Linggong Road, Ganjingzi District, Dalian 116042, China; Key Lab of Ubiquitous Network and Service Software
of Liaoning Province, Dalian University of Technology, Dalian, China; DUT-RU Co-Research Center of Advanced ICT for Active Life, Dalian
University of Technology, Dalian, China. Email: ahsanhumayun.ah@gmail.com; liubin@dlut.edu.cn.
Background: Accurate delineation of knee bone boundaries is crucial for computer-aided diagnosis (CAD)
and effective treatment planning in knee diseases. Current methods often struggle with precise segmentation
due to the knee joint’s complexity, which includes intricate bone structures and overlapping soft tissues.
These challenges are further complicated by variations in patient anatomy and image quality, highlighting
the need for improved techniques. This paper presents a novel semi-automatic segmentation method for
extracting knee bones from sequential computed tomography (CT) images.
Methods: Our approach integrates the fuzzy C-means (FCM) algorithm with an adaptive region-based
active contour model (ACM). Initially, the FCM algorithm assigns membership degrees to each voxel,
distinguishing bone regions from surrounding soft tissues based on their likelihood of belonging to specic
bone regions. Subsequently, the adaptive region-based ACM utilizes these membership degrees to guide the
contour evolution and rene segmentation boundaries. To ensure clinical applicability, we further enhance
our method using the marching cubes algorithm to reconstruct a three-dimensional (3D) model. We
evaluated the method on six randomly selected knee joints.
Results: We evaluated the method using quantitative metrics such as the Dice coefficient, sensitivity,
specicity, and geometrical assessment. Our method achieved high Dice scores for the femur (98.95%), tibia
(98.10%), and patella (97.14%), demonstrating superior accuracy. Remarkably low root mean square distance
(RSD) values were obtained for the tibia and femur (0.5±0.14 mm) and patella (0.6±0.13 mm), indicating
precise segmentation.
Conclusions: The proposed method offers signicant advancements in CAD systems for knee pathologies.
Our approach demonstrates superior performance in achieving precise and accurate segmentation of knee
bones, providing valuable insights for anatomical analysis, surgical planning, and patient-specic prostheses.
Keywords: Knee bone segmentation; fuzzy-C means (FCM); adaptive region based active contour model (adaptive
region based ACM); three-dimensional reconstruction (3D reconstruction); marching cubes algorithm
Submitted Apr 22, 2024. Accepted for publication Aug 12, 2024. Published online Sep 26, 2024.
doi: 10.21037/qims-24-821
View this article at: https://dx.doi.org/10.21037/qims-24-821
7175

Humayun et al. Knee bone segmentation and reconstruction from CT images
7152
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Introduction
Musculoskeletal disorders are a significant concern in
healthcare, driving the need for advanced computer-
aided diagnosis (CAD) systems to efficiently detect knee
disorders (1). These systems not only reduce the workload
for medical professionals but also minimize the inherent
variability in manual assessments. Accurate and precise
bone segmentation from Computed tomography (CT)
images is pivotal for thorough evaluation, staging, and
treatment planning. Traditionally, experts have relied
on manual segmentation methods, which involve labor-
intensive annotation or region of interest (ROI) marking on
knee scans. However, these manual approaches are time-
consuming, laborious, and subject to human variability (2).
Automating the knee image segmentation process
presents a promising solution to the challenges of manual
segmentation. In recent years, there has been a remarkable
advancement in automated segmentation methods from
classical image processing techniques to sophisticated deep
learning-based approaches. Despite these advancements,
automating knee image segmentation remains challenging
due to issues like low image contrast, complex knee
structures, and intensity variations within the ROI (3).
Knee arthroplasty has significantly evolved since
its inception in the 1960s, when early efforts laid the
groundwork for modern joint replacement procedures (4).
Initially, techniques focused primarily on alleviating pain
and restoring basic joint function but were limited by the
materials and surgical methods available at the time. Over
the decades, advancements in biomaterials, prosthetic
design, and surgical techniques have signicantly improved
knee arthroplasty outcomes (5).
In the contemporary clinical landscape, the primary
indications for knee arthroplasty include end-stage
osteoarthritis, rheumatoid arthritis, and post-traumatic
arthritis. These conditions lead to severe joint pain,
deformity, and functional impairment, profoundly impacting
patients’ quality of life. Osteoarthritis, in particular, is the
most common reason for knee replacement, characterized
by the degeneration of cartilage and underlying bone,
resulting in pain and stiffness (6).
Modern knee arthroplasty procedures involve the precise
removal of damaged cartilage and bone, followed by the
placement of highly durable artificial implants (7). These
implants are designed to replicate the natural movement and
function of the knee joint, thereby restoring mobility and
reducing pain. The procedure typically includes steps such
as preoperative planning using imaging, bone resection,
implant fitting, and postoperative rehabilitation (8).
Recent advancements have focused on developing patient-
specific instrumentation (PSI) and computer-assisted
surgery (CAS), which enhance the precision of implant
placement and alignment (9). Accurate alignment is crucial
for the longevity of the implant and overall success of the
procedure, as misalignment can lead to increased wear,
implant failure, and the need for revision surgery (10).
Knee replacement surgery has significantly advanced,
with personalized procedures tailored to each patient’s
unique anatomy. This process begins with a CT scan of the
patient’s knee joint, from which a precise three-dimensional
(3D) model of the knee anatomy is generated. This model
serves as the foundation for subsequent surgical planning.
The accurate and automated segmentation of knee bones
from CT images is crucial in clinical settings, offering
streamlined workflows and cost-effective solutions (11).
The demand for effective knee joint treatments, including
total knee arthroplasty (TKA), has signicantly increased. In
2019, 374,833 TKA surgeries were performed in China (12).
Furthermore, projections indicate that TKA surgeries will
escalate to 1.26 million by 2030 in the United States (13).
CT imaging provides high-definition images with an
exceptional signal-to-noise ratio, making it a powerful non-
invasive modality (14). CT imaging offers superior tissue
differentiation capabilities, providing enhanced contrast
for visualizing bone structures. Compared to magnetic
resonance imaging (MRI), CT images deliver higher spatial
resolution, ensuring finer detail and greater accuracy in
bone imaging (15).
Previous studies on automatic knee bone segmentation
have primarily focused on magnetic resonance (MR) data,
utilizing voxel-based (16) or block-wise classification
techniques (17) that incorporate texture features and
intensity distribution. However, these methods have
struggled to effectively address the significant intensity
and texture variations present in both CT and MR images.
To enhance segmentation robustness, many studies have
used statistical shape models (SSM) (18-20) as prior
knowledge to guide the segmentation process. Despite their
potential, these methods face challenges in achieving fast
and accurate model initialization and adaptation. Graph-
based algorithms (21) have been extensively utilized for
various vision tasks, including bone segmentation (22-24).
However, the accuracy of such algorithms usually depends
on seed points often manually provided. Moreover, bones
are often segmented individually rather than jointly, leading

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7153
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
to suboptimal segmentation results, particularly in regions
where bones are in close proximity or touching, potentially
causing overlapping segmentations.
Deep learning approaches have gained significant
recognition due to their outstanding results in image
segmentation (25). However, these approaches often
require large annotated datasets for training (26), which can
be problematic in applications where only limited images
are available. Recent advancements, including transfer
learning (27), unsupervised domain adaptation (28) and
zero-shot learning (29), have been introduced to mitigate
the challenge of limited training data. Traditional methods
based on unsupervised learning offer distinct advantages,
including providing interpretable and explainable results
and requiring less computational power compared to deep
learning methods. Multiple methods have been presented in
recent studies For instance, Almajalid et al. (30) presented
a fully automatic detection and segmentation method for
knee bone based on modified U-Net models, achieving
Dice indices of 97% for the femur, 96% for the tibia, and
92% for the patella. Ambellan et al. (18) introduced a robust
segmentation technique using a 3D SSM combined with
convolutional neural networks (CNNs) to segment bone
and cartilage. Hohlmann et al. (31) proposed a method
using SSM for 3D reconstruction from ultrasound (US)
images, enhancing accuracy and reliability in generating
detailed 3D models. Liu et al. (32) introduced a knee joint
segmentation method using adversarial networks. du Toit
et al. (33) presented a deep learning architecture using a
modified 2D U-Net network for segmenting the femoral
articular cartilage in 3D US knee images. Hall et al. (34)
proposed a watershed algorithm to segment tibial cartilage
in CT images. Additionally Liu et al. (35) performed
segmentation of femur, tibia, and cartilages using deep
CNNs and a 3D deformable approach. Their segmentation
pipeline was based on a 10-layers SegNet using 2D knee
images.
Liu et al. (36) introduced a novel 3D U-Net neural
network approach, leveraging prior knowledge, for
segmenting knee cartilage in MRI images. Li et al. (37)
proposed a deep learning algorithm based on plain
radiographs for detecting and classifying knee osteoarthritis,
achieving an accuracy of 96%. Mahum et al. (38) developed
a CNN-based method for classifying knee osteoarthritis,
achieving a classification accuracy of up to 97%. Norman
et al. (39) applied an end-to-end automatic segmentation
technique without any extensive pipeline for image
registration. Chadoulos et al. (40) utilized a multi-atlas-
based model to segment cartilage, attaining Dice similarity
coefficient (DSC) values of 88% and 85% for femur and
tibial cartilage, respectively. Gandhamal et al. (41) presented
a hierarchical level-set-based method for segmenting knee
bones, yielding good results but struggling with small
or separated bone regions. Cheng et al. (42) developed a
simplified CNN-based architecture, termed a holistically
nested network (HNN), for segmenting the femur and
tibial bone. Chen et al. (43) presented a YOLOV2-based
detection mechanism for knee joints, utilizing various
transfer learning-based pre-trained models. Peng et al. (44)
introduced a sparse annotation-based framework for
accurate knee cartilage and bone segmentation in 3D
MR images. Chadoulos et al. (45) proposed a multi-view
knee cartilage segmentation method from MR images,
achieving an accuracy of up to 92%. Deschamps et al. (46)
presented an innovative approach based on hierarchal
clustering to detect joint coupling patterns in lower limbs.
Rahman et al. (47) introduced a novel approach for bone
surface segmentation using a graph convolutional network
(GCN), focusing on enhancing network connectivity by
incorporating graph convolutions.
Despite significant advancements in automated
segmentation methods, precise segmentation of knee
bones remains challenging due to the complex anatomy of
the knee joint, which features intricate bone formations
and overlapping soft tissues. Many existing methods are
either computationally intensive or require extensive
annotated datasets for training, which may not be feasible
in all clinical settings. Our study aims to address these
challenges by developing a robust segmentation method
that enhances anatomical delity, minimizes segmentation
errors, and adapts to variations in CT image quality and
patient anatomy. This approach ensures high accuracy and
reliability in segmenting knee bones from CT images while
maintaining efciency.
This paper introduces a novel medical image
segmentation pipeline designed to accurately segment knee
bones from CT images. The methodology involves a two-
step process: an initial pre-segmentation step followed by a
segmentation renement step. Initially, the ROI is extracted
using the contour extraction method based on Canny edge
detection. Subsequently, a refinement step is applied to
the pre-segmented data using the fuzzy C-means (FCM)
clustering method, which incorporates spatial constraints
to improve segmentation outcomes. The segmentation
is further refined using an adaptive region-based active
contour model (ACM), which utilizes specialized region

Humayun et al. Knee bone segmentation and reconstruction from CT images
7154
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
descriptors to guide the contour’s movement and ensure
precise identication of the ROI boundaries. The detailed
owchart of the manuscript is illustrated in Figure 1.
The manuscript is organized into the following sections:
section “Methods” provides a detailed description and
working of our proposed methodology. Section “Results”
presents the segmentation results and discussion,
highlighting the performance of our method. Lastly, section
“Discussion and Conclusions” presents the conclusion.
Methods
The study was conducted in accordance with the
Declaration of Helsinki (as revised in 2013) and informed
consent was obtained from all volunteers who participated
in the study. Ethical approval for this study was waived
by the ethics committee of Second Affiliated Hospital of
Dalian Medical University.
Dataset preparation
In our study, we utilized CT images from twenty patients,
comprising fifteen males and five females. The CT scans
were acquired using a standardized protocol with a slice
thickness and interval of 0.5 mm, a window width of
2,000 Hounseld units (HU), and a window level of 500 HU.
These images were in DICOM format, with a resolution
of 512×512 pixel and a spatial resolution of 0.5 mm per
pixel. Each dataset consisted of 100 to 300 slices taken in
the axial plane. The CT datasets were collected from the
Second Afliated Hospital of Dalian Medical University. In
compliance with ethical considerations, all patient-specific
information was anonymized to maintain privacy.
Dataset preprocessing
The objective of pre-processing is to enhance the image
quality, as CT scanner-acquired data frequently contains
a variety of artifacts, including noise and distortion, which
can adversely affect segmentation accuracy (48). These
complexities in CT images are illustrated in Figure 2. To
improve the quality of knee bone CT scans and reduce
noise artifacts, we applied a thresholding technique, setting
pixel intensities outside the bone intensity range of 100 to
1,500 HU to zero. This step ensures that only bone
tissues are retained, eliminating other structures and
artifacts. Initially, we performed image cropping to remove
extraneous background and soft tissue pixels, simplifying
the dataset and reducing computational complexity. This
step involved defining the boundaries based on consistent
anatomical landmarks, specically the distal femur, proximal
tibia, and patella, to cover the entire knee joint area.
The cropping ensured the inclusion of all relevant bone
CT image data
Preprocessing
(Noise removal, intensity normalization)
FCM algorithm
(Membership degree calculation from each voxel)
Region based active contour model
(Contour evolution using membership degree)
Marching cubes algorithm
(3D reconstruction of the segmented knee bone)
Results evaluation & analysis
(Quantitative measures, geometrical & visual analysis)
Figure 1 Flowchart of the proposed methodology. CT, computed
tomography; FCM, fuzzy C-means.

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7155
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
structures while accommodating anatomical differences and
variations in patient positioning. Figure 3 provides a visual
representation of the cropped region.
The segmentation technique presented in this work
was implemented using Python programming language,
specifically on the PyCharm platform. Key libraries for
image processing and visualization included Open-Source
Computer Vision Library (OpenCV) and Visualization
Toolkit (VTK).
Contour detection
A contour extraction method based on Canny edge
detection is employed to extract the knee joint region
from DICOM images. This method effectively locates
and extracts the pixels corresponding to the knee joint’s
ROI. The Canny edge detection algorithm is optimal for
detecting edges in images, adhering to well-dened criteria:
maximizing edge detection while minimizing the error
rate, accurately localizing edges close to the true edges, and
ensuring single-edge detection for minimal responses. This
is achieved through the application of a Gaussian lter, as
shown in Eq. [1]:
( )
22
2
x +y
-2σ
2
1
g x, y = e
2πσ
×
[1]
Here, σ represents the Gaussian standard deviation, set
at 1.4, to smooth the image and enhance edge detection.
The low and high thresholds for edge detection were set
at 0.1 and 0.4 times the maximum gradient, respectively.
Additionally, adaptive thresholding techniques were
implemented to dynamically adjust threshold values
based on local image characteristics. The selection of the
optimal filter is based on two key factors: the σ value,
which controls the degree of smoothing, and the filter
size, which determines the sensitivity to noise. Empirical
experimentation and literature review guided the selection
of these parameters, conclusively determining that a
Gaussian standard deviation (σ) of 1.4 and a filter size of
(3×3) produced optimal results. As the lter size increases,
sensitivity to noise decreases, leading to the preservation of
more accurate edge information. The canny algorithm is
then applied to detect edges, as shown in Eq. [2] and Eq. [3].
The results are shown in Figure 4.
22
1
i
m xi yi
G GG
N
= +
∑
[2]
()( )
( )
,
,
max ,
H xy
H xy
H xy
=
[3]
Here
x
G
and
y
G
represents the mean magnitudes of the
horizontal and vertical gradient, respectively, while
( )
,
H xy
denoting the count of connected pixels associated with each
pixel position.
Figure 2 CT images showing complexities such as regions of soft tissues, noises, and intensity inhomogeneity across different slices.
The green marked boxes identify areas corresponding to soft tissues and noises, while the blue boxes highlight regions of intensity
inhomogeneity. CT, computed tomography.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7156
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 3 Cropping of knee CT image to eliminate extraneous background details and extract relevant bone structures. CT, computed
tomography.
Figure 4 Outer contour extraction of the knee CT image. (A) Knee CT image showing the original data. (B) Outer contour extraction using
Canny edge detection with a σ value of 1.4). CT, computed tomography.
AB

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7157
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
FCM segmentation
FCM clustering is renowned for its efciency and versatility,
making it a widely adopted technique in diverse elds (49).
FCM, an unsupervised clustering method, classies image
voxels into distinct clusters based on their similarity within a
multidimensional feature space (50). In our implementation,
FCM clustering is integrated with pre-extracted knee joint
contours to incorporate additional spatial context into
the segmentation process. Each voxel is represented as
a feature vector with intensity values, and FCM clusters
these voxels based on their inherent similarities within the
knee joint region. This integration not only simplies the
segmentation process but also ensures smoother results,
particularly in regions with intricate anatomical features.
To address the sensitivity of FCM to noise and image
artifacts, we introduced a spatial penalty term into the
objective function. This penalty discourages the assignment
of spatially distant voxels to the same cluster unless their
intensity values are similar. By incorporating this spatial
penalty, our method maintains spatial coherence and
reduces the algorithm’s sensitivity to noise and artifacts.
Specifically, the spatial penalty mitigates the effects of
Gaussian noise by favoring spatially adjacent voxels.
Experimental results demonstrate that our method remains
robust across various levels of Gaussian noise, maintaining
accurate segmentation performance even with a standard
deviation of up to 20. The enhanced optimization objective
function, denoted as E, is dened as:
( )
2
11
spatial
11
||
,
nc
m
ij i j
ij
nc
m
ij
ij
E uxv
uD ij
λ
= =
= =
= −
+
∑∑
∑∑
[4]
Here, n represents the voxel count, c represents the total
number of clusters, m denotes the fuzziness parameter,
ij
u
represents the membership degree of the
th
i
voxel in the
th
j
cluster,
i
x
corresponds to the feature vector of the
th
i
voxel,
and
j
v
represents the centroid of the
th
j
cluster. The term
||
ij
xv−
quantifies the dissimilarity between the feature
vector
i
x
of the
th
i
voxel and the centroid
j
v
of the
th
j
cluster. The term
( )
spatial ,D ij
represents the spatial distance
penalty between voxel i and cluster centroid ϳ, and λ is a
weight parameter balancing the intensity and spatial terms.
The membership degrees
ij
u
are updated using the Eq. [5]:
( )
( )
1
2
21
spatial
2
1
spatial
|| ,
|| ,
m
cik
ij k
ij
x v D ik
ux v D ij
λ
λ
−
−
=


−+

=


−+



∑
[5]
where
||,
ik
xv
denotes the Euclidean distance between the
feature vector
i
x
of the
th
i
voxel and the centroid
k
v
of the
th
k
cluster. This updated equation calculates the membership
degree
ij
u
based on the relative distances between the
voxel and the cluster centroids. The fuzziness parameter m
controls the degree of fuzziness of the clusters, with higher
values resulting in softer clusters. The centroids were
recalculated based on the updated membership degrees
using Eq. [6]:
1
1
nm
ij i
i
jnm
ij
i
ux
v
u
=
=
=
∑
∑
[6]
Here,
i
x
represents the feature vector of the
th
i
voxel,
and
j
v
represents the centroid of the
th
j
cluster. The
convergence criterion for this recalculation was dened as
a change in centroid positions less than 0.001. The final
membership degrees (Figure 5) were then used to assign
voxels to the most suitable cluster.
The FCM algorithm uses a set of input parameters,
including the number of clusters, fuzziness parameter, and
termination criterion, to iteratively assign each voxel to a
specific cluster subject to its membership degree. For our
study, the algorithm was configured with three clusters
and a fuzziness parameter (m) of 2. These parameters were
selected to achieve a balance between segmentation accuracy
and computational efciency. We evaluated the algorithm’s
performance across various iteration limits: 50, 100, 150,
and 200 iterations. Our analysis revealed that clustering
results generally converged within 100 iterations for most
datasets. Increasing the iteration limit beyond 100 did
not substantially improve clustering performance, but did
lead to increased computational time. Conversely, setting
the iteration limit below 100 sometimes led to premature
convergence and suboptimal clustering. Hence, a maximum
of 100 iterations was determined to be optimal, offering a
practical balance between accuracy and computational cost.
Additionally, a convergence criterion of 0.001 was used to
ensure the algorithm’s convergence.
Further evaluation of stability and convergence involved
plotting the objective function’s trajectory across varying
iteration limits (Figure 6). This plot highlights that
the algorithm typically stabilizes within 100 iterations,
reinforcing the necessity of allowing the full iteration
process to achieve consistent performance. Additionally, we
visualized the clustering results using a 3D scatter plot for
100 iterations (Figure 7). This visualization illustrates the
distribution of data points across clusters and the positions

Humayun et al. Knee bone segmentation and reconstruction from CT images
7158
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
of the centroids, demonstrating the FCM algorithm’s
prociency in producing well-dened and accurate clusters.
The following steps summarized the algorithm:
(I) Start by initializing the number of clusters (c) and
the fuzziness parameter (m);
(II) Randomly select (c) centroids (this involves
choosing initial cluster centers randomly from the
data points, which serves as the starting point for
the clustering process);
(III) Calculate the membership degrees of each voxel
using the above equation;
(IV) Update the centroids of each cluster using the
membership degrees;
(V) Repeat steps 3–4 until convergence is achieved, i.e.,
until the algorithm has found stable centroids and
membership degrees.
Once the FCM algorithm is applied, the region-based
active contour approach will use the resulting membership
degrees as an input to enhance the segmentation results
and obtain a more accurate delineation of the knee bone
Figure 5 Image processing using FCM. (A) Original DICOM image. (B) Membership degree values produced by FCM, highlighting
distinct regions of interest. FCM, fuzzy C-means; DICOM, Digital Imaging and Communications in Medicine.
1200
1000
800
600
400
200
0
Objective function value
50 100 150 200
Iteration
Max iterations =50
Max iterations =100
Max iterations =150
Max iterations =200
Figure 6 Convergence of the FCM objective function for different iteration limits. FCM, fuzzy C-means.
A B

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7159
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
boundaries.
Adaptive region-based ACM with customized energy
function
To further enhance the knee bone boundary segmentation
accuracy, we used an adaptive region-based ACM. By
leveraging the specialized region descriptor provided
by FCM, our model guides the contour’s movement to
precisely identify the ROI. The integration of the adaptive
region-based ACM with FCM clustering not only improves
segmentation accuracy but also enhances computational
efficiency. Our approach builds upon the methodology
proposed by Chan-Vese (51) and is implemented through
the following steps:
(I) Dene tting energy function: the energy function
quantifies the alignment between the evolving
contour and the adjacent image intensities. The
energy function is expressed as:
( ) ( ) ( )
( )
( )
Area_inside Area_outside
Length
Ev
G I I dxdy
σ
φµ φ φ
λ φα
= ⋅ +⋅

+ ⋅ + ⋅ ∇ ⋅∇

∫
[7]
Here, ϕ represents the level-set function,
with µ, ν, and λ being weighting parameters that
balance internal and external energy terms. A
Gaussian kernel
G
σ
with a standard deviation σ is
used to preserve image smoothness and gradient
information. The parameter α controls the level of
edge attraction.
(II) Integrate the regularization term: the energy
function is integrated with a regularization term to
ensure precise and stable contour evolution. The
variational level-set formulation is given by:
( ) ( )
( )
H
t
φδ φ ακ β φ
∂= −
∂
[8]
where, κ is the curvature of the level-set function,
and H is the Heaviside function.
(III) Formulate the evolving curve equation: the
Euler-Lagrange equation is utilized for energy
minimization, resulting in the evolving curve
equation:
( )
0H
ακ β φ
−=
[9]
(IV) Iteratively apply the gradient descent algorithm:
the gradient descent algorithm is iteratively applied
to optimize the energy function and obtain the
optimal contour, ensuring efficient and accurate
scientic image analysis.
In our study, the parameters µ, ν, λ, α were set to 0.1,
0.9, 0.2, and 0.5, respectively, to balance internal and
external energy terms. The regularization parameter δ
was set to 1.0 to ensure stability and convergence of the
contour evolution. A maximum of 50 iterations were
allowed to optimize the energy function and obtain precise
segmentation results. Figure 8 illustrates the convergence
behavior of our algorithm across various iteration limits
(10, 50, 100, and 150). The results demonstrate that
50 iterations yield the minimum objective function value,
indicating optimal performance in terms of convergence
efciency and precision. Figure 9 presents the segmentation
accuracy (Dice scores) for the femur, tibia, and patella across
different iteration counts. The Dice scores notably increase
from 10 to 50 iterations and then stabilize, suggesting that
additional iterations beyond 50 do not signicantly improve
accuracy but may increase computational overhead. These
results validate our parameter settings and iteration limits,
highlighting their effectiveness in precise and efficient
knee bone boundaries segmentation. Additionally, we
tested various parameter values to assess the robustness of
our method. We found that increasing µ and ν improved
contour smoothness and stability, particularly in noisy
regions, but sometimes led to a loss of ne details. While,
higher λ and α alues enhanced the contour’s adherence to
object boundaries, which was advantageous for images with
Cluster 1
Cluster 2
Cluster 3
Centroids
Patella
Tibia
Femur
7.5
5.0
2.5
0.0
−2.5
−5.0
−7.5
−10.0
−12−10
−10
−8 −6 −4
−5
Clustering results with FCM (100 iterations)
−2 0
0
5
10
24
Figure 7 3D scatter plot illustrating clustering results obtained
using FCM with 100 iterations. 3D, three-dimensional; FCM,
fuzzy C-means.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7160
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 8 Convergence of the region-based active contour model energy function over different iteration limits.
Figure 9 Segmentation accuracy as measured by the Dice score for femur, tibia, and patella over different iteration counts.
1200
1000
800
600
400
200
0
Objective function value
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Iteration
Max iterations =10
Max iterations =50
Max iterations =100
Max iterations =150
98
97
96
95
94
93
Dice score, %
Iteration
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Segmentation accuracy vs. Iterations
Femur
Tibia
Patella
clear edges but could cause instability in highly textured
regions. The final segmentation results, as shown in
Figure 10, demonstrate the model’s ability to achieve precise
and accurate delineation of knee bone boundaries.
3D reconstruction of the knee bone
The knee joint segmentation results were utilized to
generate a 3D volumetric rendering using the marching
cubes algorithm (52). This process involved converting
the contour data into a 3D matrix, creating a spatial model
of the knee bone. Each voxel in this matrix represents a
distinct element in the spatial domain. The iso-surface
for each voxel was computed based on the threshold value
or contour level, effectively delineating the boundary of
the knee bone. The marching cubes algorithm efficiently
generated the surface of the knee bone using triangular
facets, enabling enhanced visualization of its spatial
structure. Figure 11 presents the resulting 3D volumetric
rendering, with the x- and y-axes correspond to the x- and
y-pixels of the image, while the z-axis represents the pixel
height of the knee bone.

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7161
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 10 Segmentation results using an adaptive region-based active contour model. The femur, tibia, and patella are color-coded in red,
blue, and green, respectively. The results are displayed across different views: (A) sagittal, (B) coronal, and (C) axial.
Figure 11 3D reconstruction of knee joint model. 3D, three-dimensional.
ABC
Results
Segmentation results
We evaluated the accuracy and reliability of our proposed
method by comparing its segmentation results with those
obtained from manual segmentation performed by two
expert annotators using the 3D Slicer software. This
comparison served as a reliable benchmark to assess the
effectiveness and reliability of our approach, which can be
seen in Figures 12-14.
Morphological quantitative assessment
We performed a quantitative validation to evaluate the
performance of our segmentation method. For this
purpose, we randomly selected six CT image stacks, each
representing a distinct knee joint. Manual segmentation
of the bone regions was performed on each image, serving
as the ground-truth reference for comparison. We utilized
established metrics, including the DSC, sensitivity, and
specificity, to assess the reliability of our segmented
models (53). The choice of metrics was deliberate and
directly aligned with the objectives of our study. The DSC
quantifies the degree of overlap between the segmented
knee bone region and the ground-truth reference, serving as
a key measure of segmentation accuracy. Sensitivity, assesses
the method’s ability to correctly identify knee bone regions,
reducing the likelihood of missing true positive (TP)
regions. Specicity, evaluates the method’s capacity to avoid
false positives (FP), ensuring that non-knee bone regions
are correctly identied. The mathematical formulations of
these evaluation metrics are as follows:
2 TP
DSC =
2 TP + FP + FN
×
×
[10]
TP
Sensitivity =
TP + FN
[11]
TN
Specificity =
TN + FP
[12]

Humayun et al. Knee bone segmentation and reconstruction from CT images
7162
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 12 Comparative analysis of femur bone segmentation. (A) Automated segmentation using FCM and region-based ACM; (B) manual
segmentation. FCM, fuzzy C-means; ACM, active contour model.
Figure 13 Comparative analysis of tibia bone segmentation. (A) Automated segmentation using FCM and region-based ACM; (B) manual
segmentation. FCM, fuzzy C-means; ACM, active contour model.
AB
AB
In the above equations, TP denotes the accurately
identified bone tissue region, false negative (FN) signifies
the incorrectly identified non-bone tissue region, FP
represents the erroneously identied bone tissue region and
true negative (TN) corresponds to the correctly identied
non-bone tissue region.
Table 1 provides the Dice statistics for the segmented
knee bone across the selected dataset. The Dice scores
ranged from 95.99% to 98.95%, demonstrating a high
level of concordance and precision in segmenting the

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7163
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 14 Comparative analysis of tibia bone segmentation. (A) Automated segmentation using FCM and region-based ACM; (B) manual
segmentation. FCM, fuzzy C-means; ACM, active contour model.
A B
bone regions. These values, notably high within the field
of medical imaging, afrm the effectiveness and reliability
of our method. The high Dice scores for the femur and
tibia are indicative of their relatively simpler geometry and
larger size, which the algorithm can segment with greater
consistency. However, the patella, due to its smaller and
more complex structure, exhibited slightly lower Dice
scores. This suggests that finer anatomical details present
additional challenges, leading to minor deviations in
segmentation performance.
Table 2 provides the sensitivity scores for the segmented
knee bone regions. These scores illustrate the method’s
effectiveness in identifying TP regions within the dataset.
Sensitivity scores for the femur ranged from 97.96%
to 99.21%, demonstrating high accuracy in identifying
femur regions. This high sensitivity is attributed to the
distinct shape and clear boundary contrast of the femur in
CT images. The tibia achieved sensitivity scores between
96.92% and 98.36%, reflecting reliable detection, with
slight variation due to its elongated structure. Sensitivity
scores for the patella ranged from 94.68% to 98.15%,
indicating successful identification despite challenges
such as partial volume effects and its articulating position
with the femur. Figure 15 illustrates the distribution and
variability of sensitivity scores across different bone regions
using box-whisker plots.
Table 3 provides the specicity scores for the segmented
knee bone regions. Our method achieved average specicity
scores of 99.67%, 99.50%, and 99.33% for the femur,
tibia, and patella, respectively. These high specificity
scores reflect the method’s effectiveness in accurately
distinguishing non-bone tissue from the targeted regions.
The specicity scores, consistently above 99%, reect the
algorithm’s robustness in avoiding FP and ensuring that
non-bone structures are correctly identified and excluded
from the segmented regions. The slightly lower specicity
for the patella compared to the femur and tibia suggests
that the patella’s complex interface with surrounding tissues
can occasionally be misinterpreted, leading to a marginal
increase in FP rates. However, these differences are
minimal, underscoring the overall high performance and
reliability of our segmentation method. Figure 16 presents
box-whisker plots of the specicity scores, conrming the
method’s robust performance.
Overall, our method’s performance, as reflected in
Table 1 Dice score values for femur, tibia and patella
Dataset Femur (%) Tibia (%) Patella (%)
1 98.61 97.67 97.14
2 98.31 97.14 96.67
3 97.56 96.84 96.41
4 98.95 98.10 96.92
5 97.33 96.75 95.99
6 97.48 97.60 96.89

Humayun et al. Knee bone segmentation and reconstruction from CT images
7164
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
the Dice coefficients, sensitivity, and specificity scores,
demonstrates its robustness and precision in knee bone
segmentation. The slight variations in performance across
different bone structures are consistent with the inherent
anatomical and imaging challenges. Our results highlight
the effectiveness and clinical applicability of our method in
providing accurate delineations of knee bone structures in
CT imaging.
Geometrical accuracy assessment
Despite achieving an impressive Dice score of 98%, a
more comprehensive evaluation of segmentation accuracy
was imperative through geometric validation. To validate
geometric precision of our segmentation approach,
we implemented the Iterative Closest Point (ICP)
algorithm (54) to register and align the segmented bone
surfaces with a reference model. The geometric accuracy
was quantitatively evaluated using the root mean square
distance (RSD), as dened in Eq. [13] (55).
( ) ()
12
0
RSD , 1
n
ii
i
ab
AB n
−
=
−
=−
∑
[13]
The comparison involved evaluating segmented models
against manually segmented ground-truth models. Differences
in mesh geometry between the two models were visualized
using a color-coded scale, which highlighted variations in
shape and structure. Geometric validation was performed
on all six randomly selected datasets. The RSD values were
computed for the femur, tibia, and patella across all datasets.
Table 4 summarizes the RSD values for each bone model.
Table 2 Sensitivity score values for femur, tibia and patella
Dataset Femur (%) Tibia (%) Patella (%)
1 99.16 98.23 98.15
2 99.10 98.11 96.97
3 98.04 96.92 95.74
4 99.21 98.36 96.67
5 98.31 97.41 94.68
6 97.96 98.33 95.45
99
98
97
96
95
Sensitivity score, %
Box-Whisker plot for sensitivity scores with data points
Dataset
Dataset 1
Dataset 2
Dataset 3
Dataset 4
Dataset 5
Dataset 6
Femur Tibia
Bone structure
Patella
Figure 15 Box-whisker plot illustrating sensitivity scores for segmented knee bone regions. The plot visualizes the distribution of sensitivity
scores for femur, tibia, and patella.
Table 3 Specicity score values for femur, tibia and patella
Dataset Femur (%) Tibia (%) Patella (%)
1 99.83 99.67 99.60
2 99.67 99.55 99.50
3 99.50 99.33 99.17
4 99.73 99.65 99.57
5 99.17 99.10 98.83
6 99.33 99.50 99.10

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7165
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
The RSD values indicate the geometric differences for
the femur, tibia, and patella models across the datasets. The
average RSD values were 0.5±0.0183 mm for the femur,
0.5±0.0213 mm for the tibia, and, 0.6±0.0163 mm for the
patella. These results demonstrate the high geometric
accuracy of our method, with minimal deviations from the
manually segmented ground-truth models. The spatial
resolution of the CT images was 0.5 mm per pixel, which is
sufciently ne to capture detailed anatomical features. The
observed RSD values are close to the pixel size, conrming
that the segmentation accuracy aligns closely with the
inherent resolution of the imaging data.
Additionally, visual inspection of the segmented models
(Figures 17-22) further validated our method. The color-
coded error maps did not reveal significant over- or
underestimation in any specific regions, demonstrating
consistent performance across the entire bone structures.
Computational time efciency
Computational efficiency is crucial for the practical
implementation of medical image analysis algorithms.
To evaluate the performance of our knee bone
segmentation method, we conducted a detailed evaluation
on a dedicated system equipped with an Intel® Core
(TM) i5-1115G4 CPU, 16GB of RAM, and a 64-bit
Windows 10 environment. We measured the execution
time for each step of our algorithm to determine its
overall computational efficiency. In Step 1, we applied
preprocessing techniques, including Canny edge detection
and Gaussian ltering, to enhance the image quality and
prepare it for segmentation. Step 2 involved using FCM
to classify pixels and separate knee bone structures from
surrounding tissues. In Step 3, a region-based ACM was
employed to refine the initial segmentation obtained
from Step 2, ensuring accurate delineation of the knee
bone structures. Finally, in Step 4, we used the marching
cubes algorithm to reconstruct the segmented knee bone
structure in three dimensions.
99.8
99.6
99.4
99.2
99.0
98.8
Specificity score, %
Box-Whisker plot for specificity scores with data points
Dataset
Dataset 1
Dataset 2
Dataset 3
Dataset 4
Dataset 5
Dataset 6
Femur Tibia
Bone structure
Patella
Figure 16 Box-whisker plots illustrating the specicity scores for segmented knee bone regions. The plot visualizes the distribution of
specicity scores for femur, tibia, and patella.
Table 4 Geometrical accuracy (RSD) values for femur, tibia and
patella
Dataset Femur RSD (mm) Tibia RSD (mm) Patella RSD (mm)
1 0.51 0.49 0.59
2 0.49 0.53 0.61
3 0.52 0.48 0.58
4 0.50 0.50 0.60
5 0.48 0.52 0.62
6 0.53 0.47 0.57
RSD, root mean square distance; mm, millimeters.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7166
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
−0.100
−0.200
−0.300
−0.400
−0.500
−0.600
Figure 18 Geometric validation of tibia bone 3D mesh using color coded map for Case 1. 3D, three-dimensional.
Considering the inherent complexity of knee bone
segmentation and the variability in the number of slices
per dataset (ranging from 100 to 300), the average total
execution time per dataset ranged from approximately 190
to 230 seconds. Figure 23 illustrates the efficiency of our
methodology, as it achieves accurate segmentation results
within a reasonable timeframe, making it suitable for
clinical settings.
Completeness & accuracy of segmentation
Completeness of the segmented knee bone region
A critical concern in knee bone segmentation is the ability
to accurately encompass the entire knee bone region. Our
methodology addresses this concern comprehensively
through an iterative process. Initially, the FCM clustering
algorithm segments the image into clusters based on voxel
1.250
1.000
0.750
0.500
0.250
0.000
−0.100
−0.200
−0.300
−0.400
−0.500
−0.600
Figure 17 Geometric validation of femur bone 3D mesh using color-coded map for Case 1. 3D, three-dimensional.

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7167
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
−0.250
−0.500
−0.750
−1.000
−1.250
1.750
1.500
1.250
1.000
0.750
0.500
0.250
0.000
Figure 19 Geometric validation of patella bone 3D mesh using color coded map for Case 1. 3D, three-dimensional.
intensity similarities. This step helps in distinguishing the
knee bone components (femur, tibia, and patella) from
other tissues. Subsequently, the adaptive region-based
ACM renes these initial clusters by incorporating spatial
continuity and boundary regularization. By iteratively
updating membership degrees and centroids based on voxel
similarities, our algorithm adeptly identifies and assigns
voxels to their corresponding clusters. This process ensures
6.000
5.000
4.000
3.000
2.000
1.000
0.000
−0.500
−1.000
Figure 20 Geometric validation of femur bone 3D mesh using color coded map for Case 2. 3D, three-dimensional.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7168
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 22 Geometric validation of patella bone 3D mesh using color coded map for Case 2. 3D, three-dimensional.
3.000
2.500
2.000
1.500
1.000
0.500
0.000
−0.500
−1.000
−1.500
−2.000
−2.500
−3.000
4.500
4.000
3.500
3.000
2.500
2.000
1.500
1.000
0.500
0.000
−0.500
−1.000
−1.500
−2.000
Figure 21 Geometric validation of tibia bone 3D mesh using color coded map for Case 2. 3D, three-dimensional.
that even in the presence of missing regions, the algorithm
can adaptively adjust to capture the entire knee bone region
accurately. The completeness of segmentation is visually
conrmed in Figures 24,25, where our method is compared
against other state-of-the-art segmentation techniques. Our
method demonstrates superior performance in maintaining
completeness of the knee bone region.
Accuracy of the segmentation boundaries
Another key aspect is the fidelity of the segmented
boundaries in aligning with the true anatomical contours
of the knee bone. We scrutinized the potential for
deviations or inconsistencies in the segmentation results.
Our methodology excels in achieving highly accurate
segmentation boundaries that closely adhere to the true
anatomical contours of the knee bone. The FCM algorithm
performs precise clustering by analyzing voxel similarities in
a multidimensional feature space, effectively distinguishing
the knee bone components from surrounding tissues.
Furthermore, the region-based ACM iteratively

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7169
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Figure 23 Execution time (seconds) for each step of our framework, highlighting the method’s computational efciency across different
image series.
200
150
100
50
0
Computation time, seconds
Computation time across steps and total time for different datasets
Dataset 1
30.8
79.5
190.8 191.6
230.5 230.6 230.4
191.5
50.3
30.2
40.2
89.9
60.1
40.3
30.5
80.3
50.7
30.1
40.1
90.2
59.9
40.4
30.9
79.7
50.6
30.3
40.3
89.8
60.2
40.1
Dataset 2 Dataset 3 Dataset 4
Datasets
Dataset 5 Dataset 6
Total time
Step I
Step II
Step III
Step IV
ABC
DEF
Figure 24 Comparison of segmentation results for femur and patella bones in CT images with missing regions. (A) Manually segmented,
(B) proposed method, (C) CPSM, (D) atlas-based, (E) ASM, and (F) deformable model. CT, computed tomography; CPSM, coupled prior
shape model; ASM, active shape model.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7170
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
A B C
DEF
Figure 25 Comparison of segmentation results for tibial bone in CT images with missing regions. (A) Manually segmented, (B) proposed
method, (C) CPSM, (D) atlas-based, (E) ASM, and (F) deformable model. CT, computed tomography; CPSM, coupled prior shape model;
ASM, active shape model.
optimizes the active contour to align closely with the true
anatomical boundaries. This is achieved by minimizing an
energy function that balances internal forces (smoothness
of the contour) and external forces (image gradient and
intensity information). The regularization term ensures that
the contour evolves smoothly while accurately adhering to
the bone boundaries. Minor deviations or inconsistencies,
which may arise due to inherent variations in the image
data or limitations in the segmentation process, have
minimal impact on the overall accuracy and reliability of the
segmentation results. This boundary accuracy is illustrated
in Figures 24,25, where the segmented contours closely
match the manual annotations by expert annotators.
Comparison with other state-of-the-art methods
To validate the accuracy of our bone region segmentation
method, we conducted a benchmarking process against
established image segmentation techniques using the Dice
score metric for quantitative assessment. This comparison
involved adapting MRI-based segmentation techniques
for CT data, requiring specic preprocessing steps such as
intensity normalization, noise reduction through ltering,
and adjustments to algorithm parameters tailored to CT
imaging characteristics. These steps were crucial to optimize
our method’s performance given the higher contrast and
noise levels typically encountered in CT compared to MRI.
For instance, methods by Shan et al. (56) and Fripp
et al. (57) incorporated prior data and pre-defined models,
which may not generalize well to the varied intensity proles
and artifacts present in CT images. This limitation can lead
to under-segmentation or over-segmentation, especially in
regions with ambiguous boundaries or overlapping tissue
structures. Our approach operates independently of prior data,
offering exibility and broader applicability in diverse clinical
settings. Additionally, Zhou et al. (58) focused exclusively
on single MRI sequences, which are computationally
intensive and less adaptable to the high-resolution and
varied intensity characteristics of CT datasets. The
computational complexity and specificity to MRI sequences
limit their practical application to CT images, where our
method demonstrates a significant advantage in both
performance and computational efficiency. Pang et al. (59)
reported average surface distances primarily for specic slice

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7171
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Table 5 Comparison of mean Dice values among proposed method and other benchmark methods
Method Mean Dice(femur) Mean Dice(tibia) Mean Dice(patella)
Pang et al. (59) 94.5 92.7 –
Shan et al. (56) 97.1 96.7 –
Zhou et al. (58) 97 96.2 89.8
Fripp et al. (57) 95.2 95.2 86.2
Proposed method 98.04 97.35 96.67
locations rather than comprehensive measurements across
the entire bone surface, making it challenging to assess their
method’s effectiveness on full volumes.
Table 5 provides a detailed comparison of our results with
recent studies, demonstrating that our method consistently
achieves high average Dice scores across the six randomly
selected cases. However, direct comparisons are nuanced
due to differences in methodologies, imaging modalities,
and dataset characteristics. These results indicate that our
method performs at a comparable or superior level to the
other methods, underscoring both the high anatomical
delity and robustness of our segmentation approach.
Figure 26 visually compares our method’s segmentation
outcomes with those of various approaches. Our method
consistently exhibits sharper and more precise delineation of
bone regions, showcasing robustness in handling challenges
like soft tissue variations, intensity irregularities, and noise
inherent in CT images. This improvement is attributed
to advanced clustering algorithms and contour renement
techniques that effectively preserve bone boundaries and
minimize segmentation errors.
Discussion
In this study, we presented a semi-automatic method for
segmenting multiple knee bones from CT images. Our
approach combines various image preprocessing techniques,
including canny edge detection and gaussian ltering, with
advanced algorithms such as FCM, region-based ACM, and
marching cubes for 3D reconstruction (60).
The methodology begins with the application of Canny
edge detection and Gaussian filtering to enhance image
quality by emphasizing significant edge features. The
FCM algorithm is then used to classify pixels into distinct
tissue classes, considering the uncertainty associated with
tissue intensity variations and overlapping regions. This
classification provided an initial segmentation, which was
then rened using a region-based ACM. The ACM iteratively
ABCDEF
Figure 26 Comparison of segmentation results for two cases using the proposed method and other methods. (A) Manually segmented, (B)
proposed method, (C) CPSM, (D) atlas-based, (E) ASM, and (F) deformable model. CT, computed tomography; CPSM, coupled prior
shape model; ASM, active shape model.

Humayun et al. Knee bone segmentation and reconstruction from CT images
7172
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
adjusted the contours by minimizing an energy function that
integrated both image-based and geometric priors, ensuring
precise delineation of the knee bone boundaries. Finally, the
marching cubes algorithm was employed to reconstruct the
3D model of the segmented bone regions, enabling enhanced
visualization and providing critical support for accurate
diagnosis and treatment planning (61).
The quantitative evaluation of our method, using
well-established benchmark metrics, including the Dice,
sensitivity, and specificity, demonstrated its exceptional
performance. The obtained high Dice scores for the femur
(98.95%), tibia (98.10%), and patella (97.14%) underscore
the remarkable overlap between the segmented regions and
the corresponding ground truth manual segmentations.
These results strongly afrm the reliability and accuracy of
our methodology (62).
Further validation was conducted through geometrical
validation, focusing on the alignment and geometric
similarity of the segmented bone surfaces. Utilizing the
ICP algorithm, we registered the segmented surfaces and
computed the RSD to quantify geometric differences. The
low RSD values for the tibia and femur (0.5±0.14 mm) and
patella (0.6±0.13 mm) highlight the method’s ability to
accurately capture the intricate geometries of knee bone
structures with high consistency (63).
Conclusions
In conclusion, our study presents an advanced integration
of the FCM algorithm with an adaptive region-based
ACM for the segmentation of knee joints from CT images.
This approach has demonstrated exceptional accuracy and
efciency, making it a valuable tool for precise orthopedic
surgery planning. The results provide distinct and non-
overlapping segmentation of knee bones, highlighting
its clinical relevance and applicability. However, several
challenges and limitations must be considered. A key
limitation is the dependency on image preprocessing
techniques, which, although essential for enhancing image
quality, may inadvertently introduce noise or artifacts that
could compromise segmentation accuracy. Furthermore,
the current study does not fully explore the method’s
performance in pathological cases, where abnormal bone
structures might present significant challenges. While
this study has focused on knee bone segmentation, future
research could explore the segmentation and geometrical
modeling of other anatomical structures within the knee
joint, such as ligaments and cartilage. Moreover, to establish
the clinical utility of our segmentation framework, rigorous
clinical trials involving orthopedic surgeons and radiologists
are essential. These trials would evaluate the method’s
integration into routine clinical practice and its impact
on improving surgical outcomes. By addressing these
limitations, we aim to enhance the robustness and clinical
applicability of our segmentation method.
Acknowledgments
The authors express their gratitude to all the staff at the
Second Afliated Hospital of Dalian Medical University for
their support during this research.
Funding: None.
Footnote
Conicts of Interest: All authors have completed the ICMJE
uniform disclosure form (available at https://qims.
amegroups.com/article/view/10.21037/qims-24-821/coif).
The authors have no conicts of interest to declare.
Ethical Statement: The authors are accountable for all
aspects of the work in ensuring that questions related
to the accuracy or integrity of any part of the work are
appropriately investigated and resolved. The study was
conducted in accordance with the Declaration of Helsinki
(as revised in 2013) and informed consent was obtained
from all volunteers who participated in the study. Ethical
approval for this study was waived by the ethics committee
of Second Afliated Hospital of Dalian Medical University.
Open Access Statement: This is an Open Access article
distributed in accordance with the Creative Commons
Attribution-NonCommercial-NoDerivs 4.0 International
License (CC BY-NC-ND 4.0), which permits the non-
commercial replication and distribution of the article with
the strict proviso that no changes or edits are made and the
original work is properly cited (including links to both the
formal publication through the relevant DOI and the license).
See: https://creativecommons.org/licenses/by-nc-nd/4.0/.
References
1. Kishore VV, Dosapati UB, Deekshith E, Boyapati K,
Pranay S, Kalpana V. CAD Tool for Prediction of Knee
Osteoarthritis (KOA). 2024 10th International Conference
on Communication and Signal Processing (ICCSP),

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7173
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Melmaruvathur, India, 2024:18-23.
2. Starmans MP, van der Voort SR, Tovar JMC, Veenland
JF, Klein S, Niessen WJ. Radiomics: data mining using
quantitative medical image features. Handbook of medical
image computing and computer assisted intervention.
Academic Press, 2020:429-56.
3. Chen H, Sprengers AMJ, Kang Y, Verdonschot N.
Automated segmentation of trabecular and cortical bone
from proton density weighted MRI of the knee. Med Biol
Eng Comput 2019;57:1015-27.
4. Walker PS. The Articial Knee: An Ongoing Evolution.
Springer, 2020.
5. Poliakov A, Pakhaliuk V, Popov VL. Current trends in
improving of articial joints design and technologies for
their arthroplasty. Front Mech Eng 2020;6:4.
6. Coaccioli S, Sarzi-Puttini P, Zis P, Rinonapoli G, Varrassi
G. Osteoarthritis: New Insight on Its Pathophysiology. J
Clin Med 2022;11:6013.
7. Kim CW, Lee CR, Seo YC, Seo SS. Total knee
arthroplasty. A Strategic Approach to Knee Arthritis
Treatment: From Non-Pharmacologic Management to
Surgery 2021:273-364.
8. Mijiritsky E, Ben Zaken H, Shacham M, Cinar IC, Tore
C, Nagy K, Ganz SD. Variety of Surgical Guides and
Protocols for Bone Reduction Prior to Implant Placement:
A Narrative Review. Int J Environ Res Public Health
2021;18:2341.
9. Sood C. Patient-specic Instrumentation in Total Knee
Arthroplasty. In: Sharma M. editors. Knee Arthroplasty.
Springer, Singapore, 2022:459-75.
10. Suneja A, Deshpande SV, Pisulkar G, Taywade S,
Awasthi AA, Salwan A, Goel S. Navigating the Divide: A
Comprehensive Review of the Mechanical and Anatomical
Axis Approaches in Total Knee Replacement. Cureus
2024;16:e57938.
11. Hohlmann B, Broessner P, Phlippen L, Rohde T,
Radermacher K. Knee Bone Models From Ultrasound.
IEEE Trans Ultrason Ferroelectr Freq Control
2023;70:1054-63.
12. Feng B, Zhu W, Bian YY, Chang X, Cheng KY, Weng XS.
China articial joint annual data report. Chin Med J (Engl)
2020;134:752-3.
13. Gao J, Xing D, Dong S, Lin J. The primary total knee
arthroplasty: a global analysis. J Orthop Surg Res
2020;15:190.
14. Peñate Medina T, Kolb JP, Hüttmann G, Huber R, Peñate
Medina O, Ha L, Ulloa P, Larsen N, Ferrari A, Rafecas M,
Ellrichmann M, Pravdivtseva MS, Anikeeva M, Humbert J,
Both M, Hundt JE, Hövener JB. Imaging Inammation -
From Whole Body Imaging to Cellular Resolution. Front
Immunol 2021;12:692222.
15. Demehri S, Baffour FI, Klein JG, Ghotbi E, Ibad HA,
Moradi K, Taguchi K, Fritz J, Carrino JA, Guermazi
A, Fishman EK, Zbijewski WB. Musculoskeletal CT
Imaging: State-of-the-Art Advancements and Future
Directions. Radiology 2023;308:e230344.
16. Martel-Pelletier J, Paiement P, Pelletier JP. Magnetic
resonance imaging assessments for knee segmentation
and their use in combination with machine/
deep learning as predictors of early osteoarthritis
diagnosis and prognosis. Ther Adv Musculoskelet Dis
2023;15:1759720X231165560.
17. Yao Y, Zhong J, Zhang L, Khan S, Chen W. CartiMorph:
A framework for automated knee articular cartilage
morphometrics. Med Image Anal 2024;91:103035.
18. Ambellan F, Tack A, Ehlke M, Zachow S. Automated
segmentation of knee bone and cartilage combining
statistical shape knowledge and convolutional neural
networks: Data from the Osteoarthritis Initiative. Med
Image Anal 2019;52:109-18.
19. Wu J, Mahfouz MR. Reconstruction of knee anatomy
from single-plane uoroscopic x-ray based on a nonlinear
statistical shape model. J Med Imaging (Bellingham)
2021;8:016001.
20. Charon N, Islam A, Zbijewski W. Landmark-free
morphometric analysis of knee osteoarthritis using joint
statistical models of bone shape and articular space
variability. J Med Imaging (Bellingham) 2021;8:044001.
21. Ahmed SM, Mstafa RJ. A Comprehensive Survey on
Bone Segmentation Techniques in Knee Osteoarthritis
Research: From Conventional Methods to Deep Learning.
Diagnostics (Basel) 2022;12:611.
22. Patekar R, Kumar PS, Gan H-S, Ramlee MH. Automated
Knee Bone Segmentation and Visualisation Using Mask
RCNN and Marching Cube: Data from The Osteoarthritis
Initiative. ASM Sci J 2022;17:1-7.
23. Chadoulos C, Tsaopoulos D, Symeonidis A, Moustakidis
S, Theocharis J. Dense Multi-Scale Graph Convolutional
Network for Knee Joint Cartilage Segmentation.
Bioengineering (Basel) 2024;11:278.
24. Pattanaik P, Alsubaie N, Alqahtani MS, Souene BO. A
Novel Detection of Tibiofemoral Joint Kinematical Space
using Graph-based Model of 3D Point Cloud Sequences.
2023. doi: 10.21203/rs.3.rs-3029157/v1.
25. Liu X, Song L, Liu S, Zhang Y. A review of deep-learning-
based medical image segmentation methods. Sustainability

Humayun et al. Knee bone segmentation and reconstruction from CT images
7174
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
2021;13:1224.
26. Wang R, Lei T, Cui R, Zhang B, Meng H, Nandi AK.
Medical image segmentation using deep learning: A survey.
IET Image Process 2022;16:1243-67.
27. Kora P, Ooi CP, Faust O, Raghavendra U, Gudigar A,
Chan WY, Meenakshi K, Swaraja K, Plawiak P, Acharya
UR. Transfer learning techniques for medical image
analysis: A review. Biocybern Biomed Eng 2022;42:79-107.
28. Dong D, Fu G, Li J, Pei Y, Chen Y. An unsupervised
domain adaptation brain CT segmentation method
across image modalities and diseases. Expert Syst Appl
2022;207:118016.
29. Xie W, Willems N, Patil S, Li Y, Kumar M, editors. SAM
Fewshot Finetuning for Anatomical Segmentation in
Medical Images. Proceedings of the IEEE/CVF Winter
Conference on Applications of Computer Vision (WACV),
2024:3253-61.
30. Almajalid R, Zhang M, Shan J. Fully Automatic Knee
Bone Detection and Segmentation on Three-Dimensional
MRI. Diagnostics (Basel) 2022;12:123.
31. Hohlmann B, Radermacher K. Augmented active shape
model search—Towards 3D ultrasound-based bone surface
reconstruction. Proc EPiC Ser Health Sci 2020;4:117-21.
32. Liu F. SUSAN: segment unannotated image structure
using adversarial network. Magn Reson Med
2019;81:3330-45.
33. du Toit C, Orlando N, Papernick S, Dima R, Gyacskov
I, Fenster A. Automatic femoral articular cartilage
segmentation using deep learning in three-dimensional
ultrasound images of the knee. Osteoarthr Cartil Open
2022;4:100290.
34. Hall ME, Black MS, Gold GE, Levenston ME. Validation
of watershed-based segmentation of the cartilage surface
from sequential CT arthrography scans. Quant Imaging
Med Surg 2022;12:1-14.
35. Liu F, Zhou Z, Jang H, Samsonov A, Zhao G, Kijowski R.
Deep convolutional neural network and 3D deformable
approach for tissue segmentation in musculoskeletal magnetic
resonance imaging. Magn Reson Med 2018;79:2379-91.
36. Liu H, Sun Y, Cheng X, Jiang D. Prior-Based 3D U-Net:
A model for knee-cartilage segmentation in MRI images.
Comput Graph 2023;115:167-80.
37. Li W, Xiao Z, Liu J, Feng J, Zhu D, Liao J, Yu W, Qian
B, Chen X, Fang Y, Li S. Deep learning-assisted knee
osteoarthritis automatic grading on plain radiographs: the
value of multiview X-ray images and prior knowledge.
Quant Imaging Med Surg 2023;13:3587-601.
38. Mahum R, Rehman SU, Meraj T, Rauf HT, Irtaza A,
El-Sherbeeny AM, El-Meligy MA. A Novel Hybrid
Approach Based on Deep CNN Features to Detect Knee
Osteoarthritis. Sensors (Basel) 2021;21:6189.
39. Norman B, Pedoia V, Majumdar S. Use of 2D U-Net
Convolutional Neural Networks for Automated Cartilage
and Meniscus Segmentation of Knee MR Imaging Data
to Determine Relaxometry and Morphometry. Radiology
2018;288:177-85.
40. Chadoulos CG, Tsaopoulos DE, Moustakidis S, Tsakiridis
NL, Theocharis JB. A novel multi-atlas segmentation
approach under the semi-supervised learning framework:
Application to knee cartilage segmentation. Comput
Methods Programs Biomed 2022;227:107208.
41. Gandhamal A, Talbar S, Gajre S, Razak R, Hani AFM,
Kumar D. Fully automated subchondral bone segmentation
from knee MR images: Data from the Osteoarthritis
Initiative. Comput Biol Med 2017;88:110-25.
42. Cheng R, Alexandridi NA, Smith RM, Shen A, Gandler W,
McCreedy E, McAuliffe MJ, Sheehan FT. Fully automated
patellofemoral MRI segmentation using holistically nested
networks: Implications for evaluating patellofemoral
osteoarthritis, pain, injury, pathology, and adolescent
development. Magn Reson Med 2020;83:139-53.
43. Chen P, Gao L, Shi X, Allen K, Yang L. Fully automatic
knee osteoarthritis severity grading using deep neural
networks with a novel ordinal loss. Comput Med Imaging
Graph 2019;75:84-92.
44. Peng Y, Zheng H, Liang P, Zhang L, Zaman F, Wu X,
Sonka M, Chen DZ. KCB-Net: A 3D knee cartilage and
bone segmentation network via sparse annotation. Med
Image Anal 2022;82:102574.
45. Chadoulos CG, Tsaopoulos DE, Moustakidis SP,
Theocharis JB. A Multi-View Semi-supervised learning
method for knee joint cartilage segmentation combining
multiple feature descriptors and image modalities.
Comput Methods Biomech Biomed Eng Imaging Vis
2024;12:2332398.
46. Deschamps K, Eerdekens M, Geentjens J, Santermans
L, Steurs L, Dingenen B, Thysen M, Staes F. A novel
approach for the detection and exploration of joint
coupling patterns in the lower limb kinetic chain. Gait
Posture 2018;62:372-7.
47. Rahman A, Bandara WGC, Valanarasu JMJ, Hacihaliloglu
I, Patel VM. Orientation-Guided Graph Convolutional
Network for Bone Surface Segmentation. In: Wang L,
Dou Q, Fletcher PT, Speidel S, Li S. editors. Medical
Image Computing and Computer Assisted Intervention
– MICCAI 2022. Lecture Notes in Computer Science,

Quantitative Imaging in Medicine and Surgery, Vol 14, No 10 October 2024 7175
© AME Publishing Company. Quant Imaging Med Surg 2024;14(10):7151-7175 | https://dx.doi.org/10.21037/qims-24-821
Springer, 2022;13435:412-21.
48. Kanthavel R, Dhaya R, Venusamy K. Detection of
Osteoarthritis Based on EHO Thresholding. Comput
Mater Contin 2022;71:5783-98.
49. Hashemi SE, Gholian-Jouybari F, Hajiaghaei-Keshteli M.
A fuzzy C-means algorithm for optimizing data clustering.
Expert Syst Appl 2023;227:120377.
50. Latif G, Alghazo J, Sibai FN, Iskandar DNFA, Khan
AH. Recent Advancements in Fuzzy C-means Based
Techniques for Brain MRI Segmentation. Curr Med
Imaging 2021;17:917-30.
51. Ruiying H. An Improved Chan-Vese Model. 2021 IEEE
Asia-Pacic Conference on Image Processing, Electronics
and Computers (IPEC), Dalian, China, 2021:765-8.
52. Wang X, Gao S, Wang M, Duan Z. A marching cube
algorithm based on edge growth. Virtual Reality &
Intelligent Hardware 2021;3:336-49.
53. Müller D, Soto-Rey I, Kramer F. Towards a guideline for
evaluation metrics in medical image segmentation. BMC
Res Notes 2022;15:210.
54. Zhang J, Yao Y, Deng B. Fast and Robust Iterative
Closest Point. IEEE Trans Pattern Anal Mach Intell
2022;44:3450-66.
55. Hodson To. Root mean square error (RMSE) or mean
absolute error (MAE): When to use them or not. Geosci
Model Dev 2022;2022:1-10.
56. Shan L, Zach C, Charles C, Niethammer M. Automatic
atlas-based three-label cartilage segmentation from MR
knee images. Med Image Anal 2014;18:1233-46.
57. Fripp J, Crozier S, Wareld SK, Ourselin S. Automatic
segmentation of the bone and extraction of the bone-
cartilage interface from magnetic resonance images of the
knee. Phys Med Biol 2007;52:1617-31.
58. Zhou Z, Zhao G, Kijowski R, Liu F. Deep convolutional
neural network for segmentation of knee joint anatomy.
Magn Reson Med 2018;80:2759-70.
59. Pang J, Driban JB, McAlindon TE, Tamez-Peña JG,
Fripp J, Miller EL. On the use of coupled shape priors for
segmentation of magnetic resonance images of the knee.
IEEE J Biomed Health Inform 2015;19:1153-67.
60. Ebrahimkhani S, Jaward MH, Cicuttini FM,
Dharmaratne A, Wang Y, de Herrera AGS. A review
on segmentation of knee articular cartilage: from
conventional methods towards deep learning. Artif Intell
Med 2020;106:101851.
61. Fan X, Zhu Q, Tu P, Joskowicz L, Chen X. A review of
advances in image-guided orthopedic surgery. Phys Med
Biol 2023. doi: 10.1088/1361-6560/acaae9.
62. Wang Z, Wang E, Zhu Y. Image segmentation evaluation:
a survey of methods. Artif Intell Rev 2020;53:5637-74.
63. Fischer MCM, Grothues SAGA, Habor J, de la Fuente
M, Radermacher K. A robust method for automatic
identication of femoral landmarks, axes, planes and
bone coordinate systems using surface models. Sci Rep
2020;10:20859.
Cite this article as: Humayun A, Rehman M, Liu B. A method
framework of semi-automatic knee bone segmentation and
reconstruction from computed tomography (CT) images.
Quant Imaging Med Surg 2024;14(10):7151-7175. doi: 10.21037/
qims-24-821