International Journal of E-Health and Medical Communications
Volume 12 • Issue 6 • November-December 2021
Validation of Performance Homogeneity of 
Chan-Vese Model on Selected Tumour Cells
Justice Kwame Appati, University of Ghana, Ghana
 https://orcid.org/0000-0003-2798-4524
Franklin Iron Badzi, University of Ghana, Ghana
 https://orcid.org/0000-0003-4975-6469
Michael Agbo Tettey Soli, University of Ghana, Ghana
 https://orcid.org/0000-0002-9985-000X
Stephane Jnr Nwolley, Npontu Technology, Ghana
 https://orcid.org/0000-0003-1205-0526
Ismail Wafaa Denwar, University of Ghana, Ghana
 https://orcid.org/0000-0002-5777-6163
ABSTRACT
This study aims to analyze the Chan-Vese model’s performance using a variety of tumor images. The 
processes involve the tumors’ segmentation, detecting the tumors, identifying the segmented tumor 
region, and extracting the features before classification occurs. In the findings, the Chan-Vese model 
performed well with brain and breast tumor segmentation. The model on the skin performed poorly. 
The brain recorded DSC 0.6949903, Jaccard 0.532558; the time elapsed 7.389940 with an iteration 
of 100. The breast recorded a DSC of 0.554107, Jaccard 0.383228; the time elapsed 9.577161 with an 
iteration of 100. According to this study, a higher DSC does not signify a well-segmented image, as 
the breast had a lower DSC than the skin. The skin recorded a DSC of 0.620420, Jaccard 0.449717; 
the time elapsed 17.566681 with an iteration of 200.
KEywoRdS
Chan-Vese, Deformable Models, Dice Similarity Coefficient, Level Set, Tumor
INTRodUCTIoN
According to Rajendran & Dhanasekaran (2012), deformable models are among the most widely 
employed techniques for segmentation especially in the field of medical image analysis. This technique 
is mainly used to identify tumor boundaries in Magnetic Resonance Imaging (MRI) images. Though 
various medical image modalities currently exist with great improvement in the analysis and diagnosis 
of patient’s condition, MRI techniques are usually preferred as they are sufficient enough in capturing 
a number of soft tissues in the human body (Kumar & Mankame, 2020). In instances where these 
images contain tumor, it volume becomes a good indicator to track and prepare suitable treatments for 
recovery. The quantification of this volume require segmentation which in practice is done manually 
DOI: 10.4018/IJEHMC.20211101.oa7 *Corresponding Author
This article published as an Open Access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and production in any medium,
provided the author of the original work and original publication source are properly credited.
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Volume 12 • Issue 6 • November-December 2021
by field expects. Although the manual segmentation can be accurate, it is time consuming and also 
require qualified professionals which in effect significantly limit the number of segmentation that can 
be accomplished in practice (Vorontsov, Tang, Roy, Pal, & Kadoury, 2017). In the segmentation of the 
tumor, it can be classified as malignant or benign. The benign tumors are homogeneous in structure 
with the absence of cancerous cells, whereas the malignant tumors are cancerous cells (Sharif et al., 
2020). These cancerous cells can rapture and rapidly spread to other parts of the human body making 
them life-threatening and the need to remove them as soon as detected (Sehgal, Goel, Mangipudi, 
Mehra, & Tyagi, 2016). To detect these cells, methods like active contours become useful. Active 
contour models are subsets of deformable models which have been experimented broadly in image 
processing and are recognized as one of the most widely used and successful approaches for image 
segmentation. The class of region-based active contour models works primarily by incorporating 
special functions called the level set. These functions are deformed under well defined energy 
functions which traces the evolving curve towards a targeted boundary. Although these integrated 
functions are incredibly robust for sophisticated medical images, they suffer in accuracy against the 
contour curve’s initialization.. The Chan-Vese model as a variant of the region-based active contour 
models has gained considerable interest in various image segmentation techniques (Zawish, Siyal, 
Ahmed, Khalil, & Memon, 2019) despite the generally known problem. Extensive investigations 
has been made in recent years with their integration to Computer-Aided Detection (CAD) systems 
for tumor segmentation making it an interesting tool to further investigate their performance across 
selected tumour cells in this study. Since the manual delineation of tumors is an arduous process with 
variations in results; it is therefore critical to develop an automated model for segmentation (Kharote, 
Sankhe, & Patkar, 2019; Chahal, Pandey, & Goel, 2020)).
In this study we seek to analyze the perfornance of the famous Chan-Vese model in an attempt 
to answer the question “Is Chan-Vese Model generally scalable across different tumor types?” To 
address this question, appropriate research data is required and study has shown that the predominate 
datasets sufficient for the current study are MIAS, Navoneel, Diaretdb0, and ISIC. In evaluating the 
performance of the model, the following metrics are used: Dice Similarity Coefficient (DSC) and 
Jaccard Index (JI).
RELATEd woRKS
This section gives in chronological form activities in this field of study for the past few years to 
establish gaps and possibly improve term. In the study of Gosse, Jehan-Besson, Lecellier, & Ruan 
(2017), authors quest to appraise the effectiveness of 2D and 3D region-based models. The dataset 
used is positron emission tomography (PET) images by the MICCAI PETSEG Challenge and the 
methods employed are region-based deformable models such as: Chan-Vese, Locally Adaptive Random 
Walk (LARW), Poisson 3D, and Random Walker. The metric for the evaluation of these models was 
the Dice Coefficients. In their findings, the Chan-Vese 3D model recorded a Dice Coefficients of 
0.8158, Poisson 3D recorded 0.7251, Random Walker (RW) recoded 0.7766, and finally, LARW 
recorded 0.8014. This illustrate a significant improvement of the segmentation from 2D to 3D and a 
validate Poisson law’s implication in PET images. Nevertheless, the Chan-Vese model is the highest 
performing technique and delivers comparable outputs to the LARW technique. In the same year, 
Sultana, Blatt, Gilles, Rashid, & Audette (2017) attempts to recognize the boundary of cranial nerves 
and the medial axis by segmenting the ten pairs of brainstem cranial nerves from CNIII (the oculomotor 
nerve) to CNXII (the Hypoglossal nerve). The dataset for training the model was MRI data but the 
methods employed were a medial axis identification algorithm and a 3D deformable 1-simplex discrete 
contour model. The metrics for evaluating the models were the Dice’s coefficient, average distance, 
Hausdorff Distance, and the Mean Square Distance (MSD). The surface segmentation technique 
indicated a positive outcome of 82% Dice Coefficient between semi-automatic and manual outputs 
in their findings. Shil et al. (2017) also designed an automated scheme to address the intricacies of 
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Volume 12 • Issue 6 • November-December 2021
detecting brain tumors. The dataset used was MRI images of Brats13. The methods used were Otsu 
binarization, and K means clustering for segmentation. For feature extraction, the Discrete Wavelet 
Transform (DWT) coupled with Principle Component Analysis (PCA) was used while Support Vector 
Machine (SVM) was used for classification. The metrics for evaluation were sensitivity, specificity, 
and accuracy. Their findings demonstrated that the proposed scheme achieved a classification 
accuracy of 99.33%, sensitivity 99.17%, and specificity 100%. The study of Abbasi & Tajeripour 
(2017) also seek to detect brain tumors accurately to aid patient’s recovery. In the study, BRATS 2013 
(glioma images) was used. The histogram orientation gradient and the local binary patterns were 
the methods employed. The metrics for evaluation were the Dice and Jaccard. In their findings, the 
proposed framework is more effective in detecting brain tumors than other methods. Finally, with 
the study of Fiçici, Eroğul, & Telatar (2017) brain tumor segmentation were perform automatically, 
as the manual approach is time-wasting and less accurate. The dataset employed were FLAIR, T1 
Post Gadolinium (T1C), and T1 Pre Gadolinium, and MRI. The thresholding, skull stripping, and 
fuzzy C mean clustering techniques were used and evaluated using sensitivity, specificity, precision, 
accuracy, overlap (Jaccard Coefficient), and dice similarity. In their findings, the proposed algorithm, 
together with symmetry analysis, performed well experimentally.
In the year 2018, Bal, Banerjee, Sharma, & Maitra (2018) seeks to detect brain tumors as high 
varieties of tumor tissues impede a precise diagnosis. The dataset was MR images of the BRATS: 
Multimodal Brain Tumor Segmentation Challenge, Whole Brain Atlas (WBA), and eHealth laboratory. 
The method employed was fuzzy-possibilistic C-means (FPCM), and K-means. The metrics for 
evaluation were the Similarity index, Jaccard index, False-negative volume function (FNVF), False 
positive volume function (FPVF), Solidity, and Roundness. In their findings, the proposed model 
Patched based K-means and fuzzy possibilistic C-means recoded a high similarity index of 0.91. The 
Cellular automata on the other hand recorded 0.72 while the SVM recorded 0.86. The Concatenated 
RFs, which was trained using asymmetry and first-order statistical features recorded 0.87, and the 
Generative model that performs joint segmentation registration recorded 0.88. Shivhare, Sharma 
& Singh (2018) built an automated model for the diagnosis of brain tumors to resolve challenges 
associated with manual diagnosis. The dataset employed was the BRATS 2015. The methods 
employed were hole-filling operations and parameter-free clustering algorithm and morphological 
dilation. The metric for the evaluation was the Dice Similarity Coefficient (DSC). In their findings, 
the outcome of the segmentation yielded 75% of the DSC for a tumor region after comparing it with 
the ground truth. Finally, the study of Kozegar, Soryani, Behnam, Salamati, & Tan (2018) seeks to 
solve issues of automatically segmenting the breast’s masses due to the large variety in shape, size, 
and texture of 3-D objects. They aim to automate 3-D breast ultrasound—the dataset of 50 masses, 
consisting of 12 benign and 38 malignant lesions. Two kinds of ABUS systems datasets were used: 
the ACUSON S2000 automated breast volume system scan and the SomoVu automated 3-D breast 
ultrasound system. The method employed is a Gaussian mixture model which resulted in a mean 
Dice of 0.74±0.19, which outmatched the adaptive region growing with a mean Dice of 0.65±0.2 
(p-value<0.02). Furthermore, the resulting mean Dice significantly (p-value<0.001) outperformed 
the distance regularized level set evolution method (0.52±0.27).
Subsequent to 2018, Shivhare, Kumar, & Singh (2019) attempts to automate brain tumors’ 
detection with a hybrid approach as the prediction is challenging manually with the shape of the 
tumor being unstructured. The dataset used is BRATS2015 MRI images. The methods used were 
active contour model and convex hull. In their findings, the proposed method is validated in terms 
of the Sensitivity, Positive Predictive Value (PPV), and Dice Similarity Coefficient. An average 
DSC score of 92% for a complete brain tumor, 81% for brain tumor core, and 83% for an enhanced 
brain tumor was recorded which yielded more than the conventional approach adopted. The study 
of Kharote, Sankhe, & Patkar (2019) also segmented the prostate from Multiparametric Magnetic 
Resonance Imaging as segmentation of the prostate is a complicated process due to the extensive 
variations of unclear prostate boundaries in prostate shape. The database used T2-weighted prostate 
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Volume 12 • Issue 6 • November-December 2021
MR images of 184 subjects. The methods employed were Hidden Features and Deformable Model, 
which involves stacked sparse AE. The metrics used were mean absolute surface distance (MASD) and 
the dice similarity coefficient. In their findings, the model’s DSC is 87.4% ±4.6%, and MASD of 1.80 
mm. The outcome indicates that the features learned are more capable of MR prostate segmentation. 
The study of Zawish, Siyal, Ahmed, Khalil, & Memon (2019) also seek to detect brain tumors by 
segmentation which is considered a challenging task due to the overlapping of tissues. The dataset 
used was MRI images from Brain Atlas research. The method employed was the Chan-Vese active 
contour and evaluated using the computational time. In their findings, the proposed model indicated 
promising segmentation results. The proposed model (Chan-Vese without contours) recorded the lowest 
time with 3.7s for segmentation with respect to existing models like FCM, Region growing, K-mean, 
and Hist-Thr with running time 7.2s, 5.5s, 4.8s, 3.4s, and 3.7s respectively. Furthermore, the study of 
Mohamed Sathik & Synthiya Judith Gnanaselvi (2019) attempts to automate the detection of brain 
tumors as the diagnosis can be complicated. The dataset employed were MRI scans while employing 
the Radial Basis Function and Random Forest as the computational methods. The evaluation metrics 
were accuracy, MSE (Mean Square Error), and PSNR (Peak Signal-to-Noise-Ratio). In their findings, 
the Radial Basis Function and Random Forest recorded an accuracy of 68.61 and 77.58 respectively 
for Glioma. The Radial Basis Function and Random Forest also recorded an accuracy of 67.08 and 
81.41 respectively for Meningioma a 67.5 and 86.38 respectively for Normal. Finally, Agarwal & 
Bhardwaj (2019) focused on detecting brain tumors, specifically Gliomas, as considerable structural 
and spatial variation between tumors poses an automation challenge. The dataset used was BRATS 
challenge datasets with extreme learning machine (ELM) as the method. The metrics used for the 
evaluation were DSC, PPV and sensitivity. In their findings, the ELM recorded a Dice of 0.98, and 
the Regression Extreme Learning Machine(RELM-L00) recorded 0.96 on a BRATS 2012 and 0.99 
for both methods when evaluated on the BRATS 2013 dataset.
Finally in 2020, the study of Badshah, Rabbani, & Atta (2020) worked to reduce brain and breast 
tumors’ manual workload by quantifying the deformed tissues. The database used was the MRI/
mammogram images (T1-w, T2-w, and FLAIR sequences) and the method employed was the Laplacian 
of Gaussian. The metrics for the evaluation were specificity, dice coefficient, Jaccard similarity, 
Accuracy, and sensitivity. In their findings, the proposed model obtains average values of 99.96% 
for Jaccard similarity, 99.88% for dice coefficient, 99.91% for Accuracy, 99.91% for sensitivity, and 
99.95% for specificity, which outperformed the existing techniques. Again, the study of Shrivastava 
& Bharti (2020) attempted to detect breast cancer early, as tumor segmentation and classification 
accuracy can make diagnosis efficient. The dataset used were; RIDER breast MR Images and Digital 
Database for Screening Mammography (DDSM), and Mammographic Image Analysis Society 
(MIAS). The method used was Seeded Region Growing (SRG) and the metric used for evaluation 
was sensitivity known as the True Positive Fraction (TPF), specificity known as the False Negative 
Fraction (FNF), Dice Similarity Coefficient (DSC), Relative Overlap (RO), Sum of True Volume 
Fraction (SVTF), Misclassification Rate (MCR), Accuracy, False Positive Fraction(FPF), True 
Negative Fraction (TNF), Precision (P), and F-measure. In their findings, classification accuracy is 
better than previous techniques, which is 91.4%. The hybrid technique detects the tumor’s size and 
shape from both mammograms and MR Images and efficiently distinguishes the tumor as malignant 
or benign. Finally, the study of Khalil, Darwish, Ibrahim, & Hassan (2020) detects brain tumors from 
3D Magnetic Resonance Imaging (3D-MRI) as the brain tumor’s size, structure, and form can be 
challenging. The dataset employed were the (BRATS) 2017 dataset and the method employed was 
the two-step dragonfly algorithm (DA) clustering technique. The metrics employed were Accuracy, 
Recall, and Precision. In their findings, the hybrid approach on 3D-MRI images from the multimodal 
brain tumor segmentation challenge BRATS2017 dataset indicates that the proposed technique for 
brain tumor segmentation shows potential just like the existing methods.
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MATERIALS ANd METHodS
This section investigates the current approach employed in deformable models for tumor detection 
and discusses the various techniques used in detail. It also explains the data used for the study as well.
datasets
In this study, the MIAS, Navoneel, and ISIC datasets were used to validate the Chan-Vese model. 
These datasets were specifically choosen as they were publicly available and widely used in this study 
area noted from the review done. Broadly, tumors cells can be associated with the brain, eye, skin, 
liver, and breast making it quite vasetile to study. However, as a proof of concept of the scalability 
of the famous Chan-Vese model the breast from MIAS, brain from Navoneel and skin from ISIS 
was considered.
Image Preprocessing
To carry out with the segementation process, data preprocessing is required. At that level, the images 
are converted to grayscale while the identified noise is filtered out with the anisotropic filters using 
Eqn. 1.
∂x
= div(c (m,n,t)∇I ) = ∇c ⋅∇x +c (m,n,t)∇x (1)  
∂t
where ∇c  denotes the image gradient and c (m,n,t)  denotes the coefficient.
deformable Models
Chan-Vese Technique
According to Lakshmi Priya, Saraswathi, & Punitha Lakshmi (2019), Chan-Vese (CV) model as a 
segmentation tool is one of the state-of-the-art segmentation approach derived from gradient-based 
and thresholding segmenting technique. The approach employs an energy reduction function that can 
be formulated using a level set. As part of its formulation, it makes use of the Shah algorithm which 
is derived from edges and colors for the segmentation phase. The algorithm holistically, consists of 
some stages such as: feature extraction at different parameters and the optimization of its values. 
In optimizing the values, the position of the features are detected more accurately. These properties 
make them more advantageous over gradient-based approach as they resolve their inherent challenges. 
Figure 1 gives a detailed workflow of the current Chan-Vese segmentation algorithm. At the heart 
of Chan-Vese algorithm is the “fitting energy” function with an associated attribute derived from 
features such the image length and the color intensity. In the study of Z. Wang, Wang, Yang, Pan, & 
Han (2018), the CV approach is generally implemented to images that require the segmentation of its 
regions into two: background and target. For a given image I(x, y) on the domain Ω the CV algorithm 
seeks to decrease the energy function as mathematically expressed in Eqn. 2.
Ε(c ,c ,C )= uiLength(C )+λ ∫ Ω | I(x,y)−c |
2 dxdy
1 2 1 1 1
2  (2)+λ ∫ Ω | I(x,y)−c | dxdyI(x,y)+ vArea(inside(c))2 2 2
where C denotes the curve, coefficients v, λ , andλ are fixed parameters, and constants 
1 2
c andc represents the average intensities in and out of the curve respectively. The length of C and 
1 2
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the area in C are employed to check the boundary smoothness. Using the level set to denote C as the 
Lipschitz function’s ϕ(x,y) zero-level set, Eqn. 2 can be rewritten as Eqn. 3.
Ε(c ,c ,φ)= λ ∫ Ω | I(x,y)−C |
2 H (φ(x,y))dxdy +λ ∫1 2 1 1 2 Ω | I(x,y)  (3)
−c |2 (1−H (φ(x,y)))dxdy + µ ∫ Ω δ (φ(x,y)) |∇φ(x,y) |dxdy + v ∫ Ω H(φ(x,y))dxdy2
where δ(ϕ) and H(ϕ) are the Dirac and Heaviside functions, respectively. Mainly, the regularized 
variant is expressed as shown in Eqn 4
1  2 φ 1 ε
H (φ) = 1+ arctan   , δ (φ = ⋅  (4)2  π 
)
ε  π ε
2 +φ2
Maintaining c andc fixed, E (c ,c ,C )  is minimized with regards to ϕ(x, y), as we derive 1 2 1 2
the Euler-Lagrange equation for ϕ(x,y). Parameterizing the descent position arbitrarily by time t, the 
formulation of the corresponding variation level set can be obtained as Eqn 5.
∂φ 
= δ(φ)
  ∇φ  2 2µidiv 
−v −λ I(x,y)−c  +λ I(x,y)−c 
   1  1  2  2  

∂t  |∇φ | 
∫ ΩI(x,y)H(φ)dxdy
c =
1 ∫ ΩH(φ)dxdy  (5)
∫ ΩI(x,y) 1−H(φ)
dxdy
c =
2 ∫ Ω 1−H(φ) dxdy
φ(x,y, 0)= φ (x,y)
0
In Eqn. 4, the CV uses the local gradient details to check the curve’s deformation movement 
and the contour curve evolution. Two issues arise with this approach which require attention when 
extracting the target leaf from a given MR/CT image. The first is the initialization, and the second is 
the failure for the curve to evolve. Resolution of this problem requires the initialization to be done at 
the center of the image for the evolving curve to halt when its curvature is stable for a particular period.
Level Sets
Level-Set methods have been widely employed to capture interface development, especially when the 
interface experiences extreme topological changes. It adopts Hamilton Jacob and Partial Differential 
Equations method to fix the segmentation issue. In the formulation of the level set, a closed contour 
C ⸦ Ω is usually denoted by zero level set implicitly as a Lipschitz function ϕ: Ω→R. The signed 
distance function (SDF, ∇ = ϕ 1) denoting the surface is usually the appropriate choice of the active 
contour models and is expressed as Eqn. 6.
 dist (x,C ) ifφs (x) > 0
φ(x,t) =  0 ifφ(x) = 0  (6)−dist (x,C ) ifφ(x r ) < 0
where the evolving curve Ct at time t is the shortest; dist(x, Ct) is Euclidean distance from the 
pixel position x. Generally, it enables the curve to go through topological changes by resolving the 
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energy functional solution spontaneously. The level set function ϕ take negative and positive values 
inside and outside the contour C, and further deduce the model’s energy function as shown in Eqn. 7.
2
F (φ,c ,c ) = ∑ (λ ∫ (∫ K (x −y)(f (y)−c )2dy)Mcσ φ xp 2 j i i ( ( ))dx )+ µ∫ ∇H (φ(x)) dx  Ω Ω
i=1 2
(7)
where Mc (i)  is defined in Eqn. 8i
Mc (φ(x)) = H (φ) = 1/ 2×(1+ 2 / π×arctan(φ(x)/ ε)) and Mc (φ) = 1−H (φ)  (8)1 c 2 c
The level set function’s regularity ϕ(x) is critical for stable evolution, and precise computation 
particularly close to the zero levels set position is expected. The effective fix is to apply re-initialization 
that is evolving to a steady-state defined by the partial differential equation in Eqn. 9
∂φ
+ sgn(φ )(∇φ −1) = 0,φ(x,τ = 0) = φ x  (9)
∂t 0 0
( )
where ϕ0 represents the level set function to be re-initialized. Nevertheless, ϕ0 does not remain 
steeper or smoother after multiple iterations. To skip high time-consumption during the re-initialization 
process, a level set regularization is formulated as in Eqn. 10.
P (φ) = ∫ 1 / 2 ⋅(∇φ(x) −1)2dx  (10)Ω
Typically, during curve evolution, the penalty term induces the level set function ϕ near a signed 
distance function. Hence, the complete energy function is expressed as in Eqn. 11.
F (φ,c ,c ) = λ ∫ (∫ K (x −y)(f (y)−c )2dy1 2 1 1 )H (φ(x))dx +Ω s
λ ∫ (∫ K (x −y)(f (y)−c )2dy)(1−H (φ x2 2 s ( )))dx  (11)Ω
+µ ⋅ ∫ δε (φ(x)) ∇φ(x) dx + v∫ 1 / 2 ⋅(∇φ(x) −1)2dxΩ Ω
where v is Lagrange multiplier coefficient and the positive constants are as shown in Eqn 12
∫ f (x)H (φ(x))dx ∫ f (x)(1−H (φ(x)))dx
c (φ) = 0 c c,c (φ) = Ω  (12)1
∫ Hs (φ(x)) 2dx ∫ (1−H (φ(x)))dxΩ Ω s
δε is the derivative of Hε and is written as Eqn 13
1  2 z ( ) 1 εH ε z = ×  1+ ×arctan 

2 

 π ε

,δ = ,ε > 0  (13)
s π x 2 + ε2
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On the Heaviside function’s profile’s smoothness, the parameter ε generates an effect. Using a 
considerable value ε allows the Heaviside function (regularized) to less steep close to the zero position, 
while expanding the range of capture and triggering less sensitive to blur boundary.
Active Contours
Given U as a class of domains (regular bounded sets, open, C2) of Rn (n = 2 or 3), and Ωi an element 
of U with boundary ¶Ωi, a segmentation problem (region-based) seeks at identifying a partition of 
ΩI in two regions {Ωin, Ωout} that minimizes the criterion in Eqn 14.
E (Ω ,Ω , “ = J Ωin out ) r ( in )+Jr (Ωout )+αJ “reg ( )  (14)
where Jr(Ωi) illustrates the similarity of the region Ωi which can be categorized into sections 
A and B depending on the distribution, the expression Γ between the two regions represents the 
common interface. The energy term Jreg is a regularization expression which is a balanced positive 
real parameter α selected as Jreg = R Γ da, where da denotes an area element. In 2D, the term relates 
to minimizing the curve length while in 3D it minimizes the surface area. This term ensures a smooth 
curve or surface delineating the tumor. The shape gradient descent is performed by computing the 
evolution equation of an active contour by employing shape derivation tools. Computationally, the 
shape derivative deduced from the evolution equation to move the active contour is expressed in 
Eqn. 15.
∂“ (p,τ)
= v (x,Ω)N (x)  (15)
∂τ
where v(x, Ω) is the active contour’s velocity (using 2D or 3D) obtained from the shape derivatives 
with the velocity positioned along the unit inward normal N of ∂Ω. From an initial curve Γ(τ = 0) = 
Γ0, the active contour can evolve.
Metrics
As noted from the the review in Section 2, the most widely used metrics for performance evaluation 
are Dice Similarity Coefficient and the Jaccard Coefficient. In this study the performance of the 
standard Chan-Vese models is re-evaluated to assess is scalability on selected dataset of various 
forms of tumors. The dice similarity coefficient is primarily used as a quantitative measure of an 
algorithm’s ability to automatically determine the segmentation accuracy. The Jaccard Coefficient on 
the other hand is used to measure the similarity of two sets. Their value ranges from 0 to 1, where a 
value closer to one indicates acceptability. Mathematically, we have Eqn. 16 and Eqn. 17 to represent 
DSC and JC respectively.
2 *TP
Dice Similarity Coefficient =  (16)
(TP +FP)+ (TP +FN )
where FP, TP, TN, and FN represent false positive, true positive, true negative, and false negative, 
respectively.
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Figure 1. The Chan-Vese Model (Lakshmi Priya et al., 2019)
A∩B
Jaccard (A,B) =  (17)
A∪B
where A and B indicate the ground truth and segment result, respectively.
The Chan-Vese Architecture
The process flow diagram of the Chan-Vese architecture is shown in Figure 1. The first stage takes 
an initial image and establishes the contour. In the second stage, some variables are declared; the 
number of iterations of the model is set for the model to perform segmentation; the variables are 
initially declared with zero value. In the firth stage, the current iterations are displayed as segmentation 
occurs. In stage six, the iterations run according to the number set starting for one. In stage seven, the 
model records the current segmented results and in the last stage, after training, the model is ready 
to accept the next iteration value.
RESULTS ANd dISCUSSIoN
This section discusses the performance of the Chan-Vese model in the detection of tumor from the 
brain, breast, and skin. The segmentation algorithm is trained and tested on an Intel ® Core (TM) 
i3-3220 CPU @ 3.30 GHz processor of three GigaHertz speed and eight GigaByte RAM (Random 
Access Memory) Dell Machine. Each analysis was performed at iteration 100, 150, 200, 250 and 
300. Images with label “Y” are images with tumor present while “N” indicate images withour tumor.
observations with Brain Tumor Analysis
Figure 2 illustrates the preprocessing phase. After performing segmentation on an image with a 
tumor, a Dice Similarity of 0.694993, and Jaccard of 0.532558 was recorded. The elapsed time was 
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Table 1. Performance Value on Brain Tumor Image
Iteration Dice Similarity Jaccard Elapsed Time Image Name
100 0.694993 0.532558 7.389940 Tumor Image 1
150 0.694980 0.532543 11.043630 Tumor Image 1
200 0.694993 0.532558 12.817540 Tumor Image 1
100 0.598459 0.427001 9.831900 Tumor Image 2
150 0.598485 0.427027 13.925961 Tumor Image 2
200 0.598531 0.427074 16.637554 Tumor Image 2
7.389940 seconds at iteration 100, as shown in Figure 3. Figure 4 shows that of iteration 150 with 
Dice Similarity of 0.694980, and Jaccard of 0.532543 at an elapsed time 11.043630. The iteration 
was stopped at 200 since there is no significant change as shown in Table 1.
After performing segmentation on an image without a tumor a Dice Similarity of 0.616987, 
and a Jaccard of 0.446118 was recorded. The elapsed time was 16.556324 seconds at an iteration of 
200, as shown in Figure 5.
Breast Tumor Analysis
With the breast tumor of the first image, after performing the segmentation, a Dice Similarity of 
0.554107, and Jaccard of 0.383228 was observed at an elapsed time of 9.577161 seconds with an 
iteration of 100, as shown in Figure 6. Repeating the process for iteration 150 and 200 with two test 
images we have Dice Similarity and Jaccard values recorded in Table 2.
After repeating the process again on a breast image without a tumor, a Dice Similarity of 0.518233, 
and Jaccard of 0.349740 was recorded with an elapsed time of 11.232338 seconds at iteration 200 
as shown in Figure 7.
Figure 2. Preprocessed Brain Tumor Image with Anisotropic Filter
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Figure 3. Chan-Vese Segmentation at Iteration 100 on Brain Tumor Image
Skin Tumor Analysis
After performing segmentation on an image with a tumor, the model recorded a Dice Similarity of 
0.618725, and Jaccard of 0.447938. The elapsed was 10.403951 seconds with an iteration of 100, as 
shown in Figure 8. Repeating this process again at iteration 150 and 200, a Dice Similarity of 0.618719 
and 0.618725 and a Jaccard of 0.447931 and 0.447938 were respectively obtained. Their computational 
time were noted to be 14.111079 and 16.480397 respectively at iteration 150 and 200. Figure 9 and 
Figure 10 represent the visual performance of the model as applied to a skinned image containing 
tumor. Applying the model on the second image with skin tumor, a Dice Similarity of 0.620293,and 
Jaccard of 0.449584 was recorded with an elapsed time of 9.597521 seconds at iteration 100 as shown 
Figure 4. Chan-Vese Segmentation at Iteration 150 on Brain Tumor Image
Figure 5. Chan-Vese Segmentation at Iteration 200 on Brain Tumor Image
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Table 2. Performance Value on Breast Tumor Image
Iteration Dice Similarity Jaccard Elapsed Time Image Name
100 0. 554107 0. 383228 9. 577161 Tumor Image 1
150 0. 553814 0. 382948 13. 222634 Tumor Image 1
200 0. 553696 0. 382835 16. 973739 Tumor Image 1
100 0. 367115 0. 537066 11. 327466 Tumor Image 2
150 0. 536902 0. 366962 13. 400257 Tumor Image 2
200 0. 536852 0. 366915 16. 543606 Tumor Image 2
Figure 6. Chan-Vese Segmentation at Iteration 100 on Breast Tumor Image
Figure 7. Chan-Vese Segmentation at Iteration 200 on Breast non-Tumor Image
in Figure 11. At iteration 150 and 200, a Dice Similarity of (0.620350, 0.620420), and Jaccard of 
(0.449643, 0.449717) was recorded respectively at an elapsed time of (13.496094, 17.566681). The 
visual performance of the model at iteration 150 and 200 on the second image of the skin tumor is as 
shown in Figure 12 and Figure 13. Finally, this model recorded a Dice Similarity of 0.620680, and 
Jaccard of 0.449990 when applied on the skin image without a tumor cell. Computationally, it took 
17.921264 seconds at iteration of 200 the generated the needed result.
discussion
From the results reported for the brain, breast, and skin tumor, there is an indication that an increase in 
iterations do not necessarily affect performance, instead it only introduces time complexity at higher 
iterations. Using time as a performance indicator, it is observed that of all the tumors employed for this 
study, the Chan-Vese model performed relatively well on brain tumor segmentation, followed by breast 
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Figure 8. Chan-Vese Segmentation at Iteration 100 on Skin Tumor Image
Figure 9. Chan-Vese Segmentation at Iteration 150 on Skin Tumor Image
Figure 10. Chan-Vese Segmentation at Iteration 200 on Skin Tumor Image
Figure 11. Chan-Vese Segmentation at Iteration 100 on Second Skin Tumor Image
Figure 12. Chan-Vese Segmentation at Iteration 150 on Second Skin Tumor Image
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Figure 13. Chan-Vese Segmentation at Iteration 200 on Second Skin Tumor Image
Table 3. Evaluation of the CV Technique
Dataset Tumor Iteration Time Elapsed Dice Similarity Jaccard
Coefficient
BRAIN WITH 100 7.389940 0.6949903 0.532558
BREAST WITH 100 9.577161 0.554107 0.383228
SKIN WITH 200 17.566681 0.620420 0.449717
tumor segementation and finally with skin tumor segmentation. Table 3 gives a summary evaluation 
of the Chan-Vese model indicating best performance on brain tumor in the light of disc similarity 
coefficient. The brain recorded an of disc similarity coefficient 0.6949903, Jaccard 0.532558, the 
time elapsed 7.389940 with an iteration of 100,. The breast also recorded a DSC of 0.554107, Jaccard 
0.383228, the time elapsed 9.577161 with an iteration of 100. According to this study, a higher disc 
similarity coefficient does not signify a well-segmented image as the breast had a lower score than 
the skin yet performed better by visual inspection. The skin recorded a disc similarity coefficient of 
0.620420, Jaccard 0.449717, the time elapsed 17.566681 at an iteration of 200.
CoNCLUSIoN
In conclusion, the study was able to segment tumor cells from MR/CT images using the MIAS, 
Navoneel, and ISIC dataset to investigate the performance scalability of the well known Chan-
Vese model. The datasets involved images consisting of tumors of the brain, breast, and skin. From 
the analysis of the various datasets, the Chan-Vese could be rated high only when applied to the 
segmentation of brain tumors other than the other forms of tumors like the breast and skin. This 
conclude that though the Chan-Vese model is known to be very good for tumor detection it does not 
scale across all tumor type. Moving forward other models known to work well should be further 
investigated on their scalability. Furthermore, hybrid models can also be considered for investigation 
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an assess their scalability. It is important to obtain models that scales well with some predefined 
parameter to better build a unified diagnostic system.
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Justice Kwame Appati is a lecturer in the School of Physical and Mathematical Science (SPMS) and the Department 
of Computer Science. He began his teaching career at Kwame Nkrumah University of Science and Technology 
in Kumasi as a graduate assistant and then later moved to the University of Ghana in 2017 as a lecturer. Justice 
earned a PhD, in Applied Mathematics from Kwame Nkrumah University Science and Technology in 2016. He also 
graduated in 2010 and 2013 with a BSc. Mathematics and MPhil Applied Mathematics from the same institution. 
His current research includes data science, mathematical intelligence, image processing and scientific computing, 
He has singly and jointly supervised undergraduate and postgraduate students from Kwame Nkrumah University 
of Science and Technology (KNUST), National Institute of Mathematical Sciences (NIMS), African Institute of 
Mathematical Sciences (AIMS) and the University of Ghana Currently, Justice handles course like Design and 
Analysis of Algorithm, Artificial Intelligence, Formal Methods and Computer Vision. He looks forward to working 
with everyone interested in his field of study more especially, Intelligence and Data Science.
Franklin Iron Badzi is a teacher at the Yilo Krobo Senior High School department of Information and Communication 
Technology. Mr Badzi taught computer related course in Afife Secondary Technical and Mount Mary College of 
Education Somanya. His current research interest include Parallel Computing, Ubiquitous Computing, Neural 
Networks, Data Mining and Artificial intelligence. He received the regional Best Teacher’s award in Science and 
Mathematics Junior Category in the Volta Region of Ghana. Born in Aflao V/R Ghana, Mr. Badzi earned his B.Sc 
in Information Technology from University of Education Winneba Kumasi campus.
Michael Agbo Tettey Soli is a critical thinker and solutions engineer with over a decade of experience in software 
engineering and algorithm design. He is currently a Ph.D. student with the Department of Computer Science of 
the University of Ghana.
Stephane Nwolley Jnr. holds a PhD in ICT Management (Big Data), with high-level expertise in synthesizing 
large amounts of information into insights for strategy, innovation, and business development. He was highly 
instrumental in creating an automated machine learning tool (snwolley) designed to make data analytics easy 
and affordable. He has had training in project management, Master of Business Administration in information 
systems from SMU, and Bachelor of Applied Computer Science from Royal Melbourne Institute of Technology, 
Australia. His key qualities are in Big Data, Data Science, Cloud Computing, Business intelligence and ERP, UNIX/
LINUX Programming, Web Application Design and Development, Project Management and Risk Analysis, Human 
Computer Interaction, DB Management skills and Operating System Administration. Dr. Stephane Nwolley Jnr. 
has more than 14 years of practical experience in the ICT industry and previously worked with MTN and Huawei 
as an OSS engineer. His experience and hands-on knowledge of the industry enables him to proffer solutions 
that are both practical and innovative. Formerly, the CEO of Nalo Solutions Limited, he was the product lead for 
projects with clients including Ecobank, GIPC, UBA, amongst others. He currently serves as an adjunct lecturer 
in the Computer Science department of Ashesi University. With the distinction of being an academic and an 
entrepreneur, he is noted for his skill in breaking down complex conceptual frameworks into simple, practical and 
useful terms. He has contributed to the Big data and AI conversations through publications. Dr. Stephane Nwolley 
Jnr. is Founder and CEO of Npontu Technologies, an IT company with three integrated product offerings, Big Data 
and Machine Learning, Software development and Value-Added Services. His company currently provides service 
for organizations like GCB Bank, Stanbic Bank, Standard Chattered Bank, Cal Bank, Access Bank, Enterprise 
Insurance, Vanguard Assurance, Allianz Insurance, Goil, Total Petroleum, National Identification Authority, Office 
of the President, USAID, PWC just to name a few.
Ismail Wafaa Denwar is an IT Officer at Ghana Electrometer Limited, an electricity manufacturing company 
supplying the Electricity Company of Ghana (ECG) with electricity meters; he has been working there since 2017. 
He obtained a Bachelor of Science in Information Technology degree at Valley View University, Accra, Ghana, 
from 2013 to 2017. Mr. Ismail proceeded to the University of Ghana, which led to an award of a Master of Science 
in Computer Science degree from 2019 to 2020, running concurrently with his job at Electrometer. He is currently 
assisting in the publication of research papers in other journals. His research interest is in areas of Neural Networks 
(Text Generation, Text Classification, Time-series forecast), Machine Learning (Classification problems such as 
intrusion detection based on network traffic among others), Databases, and Image Processing (particularly tumor 
detections). Mr. Ismail has a strong passion for research and is looking forward to doing a Ph.D. in the future; he 
has a passion for finding answers to solving complex problems.
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