# Essay: Active contours

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• Subject area(s): Information technology essays
• Published on: March 8, 2016
• File format: Text
• Number of pages: 2
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Active contours are one category of variational methods
that have been used widely within image segmentation applications.
An energy functional is defined with arguments
as the image parameters and a closed curve that partitions
the objects in the image. There are two main methods of
representing the curves such as (a) extrinsic and (b) intrinsic.
Extrinsic representation keeps function values at boundary
points. Intrinsic lets use of functions that are defined on
all the point of the image and are more desirable. Intrinsic
representation of a planar curve C using an auxiliary function
is denoted as
C = f(x; y) j (x; y) = 0g (22)
where (x; y) is called level set function of curve C and the
zero level of (x; y) is taken as the contour. Curvature  of
the closed curve C with level set function  is given by
 = div( 5
k5k ) (23)
The deformation of the contour is reprsented in a numerical
form as a partial differential equation
@(x;y)
@t =j 5(x; y) j ( + ((x; y))) (24)
where  is a constant speed term to push or pull the
contour. Mean curvature of the level set function is defined as:
((x; y)) =
xx2
yô2xyxy+yy2
x
(2
x+2
y)3=2 (25)
where x is the first derivative with respect to x and xx
is the second derivative with respect to x. The role of the
curvature term is to control the regularity of the contour and 
controls the balance between the regularity and robustness of
the contour.
Chan & Vese formulated the energy function F in terms of
an internal force Eint and an external force Eext
F(C) =
R 1
0 [Eint(C(S)) + Eext(C(S))]ds (26)
Eint = length(C) + Area(Cin) (27)
Eext =
R
Cin
j I(x; y) ô I1 j2 +
R
Cout
j I(x; y) ô I2 j2 (28)
where  and  are positive fixed parameters which help to
smoothen the growing contour. I(x; y) is intensity value of
image region and I1 and I2 are average intensity value inside
and outside the object region, respectively.
IV. IMPLEMENTATION AND ANALYSIS
All qualitative and quantitative outcome of the algorithm
were recorded by running the Matlab programs with Intel(R)
Core (TM) i7 CPU, 3.4 GHz, 4 GB RAM with Matlab 14 (a)
on Windows 8.
A. Description of Test Data
The dataset used in the proposed algorithm consists of
scanned images of stained breast biopsy slides from MITOS
dataset . Each set is composed of 96 high power field
(HPF) images of breast tissue scanned at 40X magnification
using two different scanners, Aperio (AP) and Hamamatsu
(HM), with a resolution of 0.23-0.24 m:. All the images are
1376  1539  3 size.
B. Experimental Strategies
This paper qualitatively and quantitatively compares the
KHO based optimal nuclei detection performance with the
watershed based detection done by S. Ali et al.  and blue
ratio image based detection done by Irshad et al. . The
segmentation performance is compared with local threshold
method done by Cheng Lu et al. .
1) Experiment 1: Evaluating the optimal threshold value:
Goal of this experiment was to prove the power of KHO
based optimal thresholding to detect the exact nuclei regions in
histology images. It also compares the optimum value of the
threshold obtained by KHO in breast histopathology images
with GA, HSA and BFA.
2) Experiment 2: Comparison of Detection Accuracy: Aim
of this work is to validate the detection performance of
the proposed technique against the watershed and blue ratio
techniques in terms of detection sensitivity and precision.
3) Experiment 3: Comparison of Segmentation Accuracy:
This evaluates the performance of the detection algorithm
in ACM segmentation and compare the results against two
state-of-the-art techniques in terms of boundary based distance
measures. This experiment also measure the strength of the
algorithm to resolve the touching nuclei in terms of touching
nuclei resolution.1) Evaluation of Detection Performance: This paper qualitatively
and quantitatively evaluates the application of optimal
thresholding in nuclei detection performance. The mean objective
value and standard deviation express the consistency and
stability of the algorithms. The results obtained by KHO are
compared with GA, HSA and BFA. The parameters used in
these algorithms are given in Table II.The quantitative evaluation of detection performance is
carried out by locating the centroid of detected nuclear regions.
The measures used to assess the nuclei detection comprise
of: 1) Sensitivity (SD); 2) Positive Predictive value or
Precision (PD); and 3) F-measure (FD) as given in eq. (26),
(27), and (28), respectively. The results obtained are compared
with manual detection results by an expert pathologist. The
SD and PD values are computed from the number of truepositives
(number of correctly detected nuclei, Ntp) , falsepositives
(number of wrongly identified nuclei, Nfp) and false
negatives(number of nuclei not detected by the algorithm,
Nfn). The detected object is considered as true positive if
its centroid is within 10 pixels range of manually determined
centroid location. If no centroid was manually located within

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