Active contours

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 @(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)) = xx2 yà ´Ã‚€Â€Â€2xyxy+yy2 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) à ´Ã‚€Â€Â€ I1 j2 + R Cout j I(x; y) à ´Ã‚€Â€Â€ 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 [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