Active contours

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

k5k ) (23)

The deformation of the contour is reprsented in a numerical

form as a partial differential equation


@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)) =






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 =



j I(x; y) 􀀀 I1 j2 +



j I(x; y) 􀀀 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.


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 [35]. 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. [8] and blue

ratio image based detection done by Irshad et al. [21]. The

segmentation performance is compared with local threshold

method done by Cheng Lu et al. [22].

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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