光电学院外文翻译论文

Segmentation of CT Lung Images Based on 2D Otsu Optimized by Differential EvolutionSushil Kumar，Millie Pant，and A.K. RayIndian Institnte of Technology Roorkee，India{kumarsushiliitr，millidma，akray}@Abstract. Image segmentation played a vital role in medical imaging system. With the help of image segmentation pulmonary parenchyma can be detected from multi sliced CT images. Pulmonary diseases such as lung cancer，tumor，and mass cells can be detected with 2D Otsu algorithm. 2D Otsu algorithm is a well-known image segmentation method. In CT images segmentation 2D Otsu playa vital role. Main drawback of 2D Otsu method is its computation complexity and computational time. In this paper 2D Otsu algorithm has implemented with Differential Evolution (DE) Algorithm. This results in reducing the computational complexity as well as computational time. Further the results are compared with 2D Otsu and 2D Otsu with PSO，which proves the efficiency of using DE with 2D Otsu.Keywords: Segmentation，CT Lung image，Pulmonary，parenchyma，DE，Thresholding，2D Otsu.1 IntroductionCT (Computed Tomography) scan is the standard for pulmonary imaging.It provides high spatial and high temporal resolution，excellent contrast resolution for the pulmonary structures and surrounding anatomy，and the ability to gather a complete three-dimensional (3-D) volume of human thorax in a single breath hold [1]. Pulmonary CT images have been used for applications such as lung parenchyma density analysis[习，airway analysis and lung and diaphragm mechanics analysis.Firstly，lD Otsu method was used for segmenting the lung CT images. But lD Otsu method gives better result only for high contrast images than for low contrast images. So a better 2D Otsu method was proposed for low contrast lung CT images. In this paper a new approach will be suggested for lung CT images segmentation. In this approach Differential Evolution (DE) is used with 2D Otsu method for optimizing the thresholding value of an image for segmentation in less computation time and less computation complexity，and results will be compared with 2D Otsu method and with 2D Otsu with PSO (Particle Swarm Otimization). In first section of the paper introduction of 2D Otsu method，in second sectionK. Deep et al.(E ds.):Pr oceedings of the I附rnational Conference on Soc Pro S 2011，AISC 131，pp，891~springerlinkcom © Springer India 2012892 S. Kumar ， M. Pant ， and A.K. Rayintroduction of Differential Evolution ， and then the proposed algorithm and finally results and conclusion.2 2D Otsu Method2.1 Two-Dimensional HistogramAn image with size MxN can be represented by a 2D gray level intensity function f(x ， y). The value of 开x ， y) is the gray level ， ranging from 0 to L-l ， where L is thenumber of distinct gray levels. In a 2D thresholding method ， the gray level of a pixel and its local average gray level are both used. The local average gray level is also divided into the same L values ， let g 衍， y) be the function of the local average gray level [3].(0，0)T L-1 S[，-1x Fig.1. Two dimensional HistogramLet be the total number of occurrence (frequency) of the pair (i ，j) which reprsents pixel (x ， y)with f(x ， y)=i and g(x ， y)=j ， 0~二ηl 三M X N ， then the joint probability mass function pij is given byp ，=」L'J MXN where i ，j = 0， 1，2，... L-l \‘自，，FJ FJ 唱Ei /'目飞、LL>ij = 1 (2)The 2D histogram of the image is Pij. Figure 1 shows the top view of 2D histogram.It covers a square region with size Ll. The x-coordinate (i) represents gray level and the coordinate U) represents the local average gray leve l. The 2DSegmentation of CT Lung Images Based on 2D Otsu Optimized 893 Histogram is divided into four quadrants at a vector 侣， T)， where 0~二(S ，T)三 L -1. The dash dot line is the diagonal of 2D histogram. The pixels interior to the objects or the background should contribute mainly to the near-diagonal elements because of the homogeneity. Because of the pixels interior to the objects and background ， the gray level of a pixel and its local average gray level are simila r. For pixels in the neighborhood of an edge between the objects and the background ， the gray level of a pixel differs fairly from its local average gray leve l. Therefore ， quadrants 1 and 2 contain the distributions of background and object classes ， whereas the off diagonal quadrants 3 and 4 contain the distributions of pixels near edges and noises [3].Now suppose that the pixels are partitioned into two classes CO and Cl (background and objects) by a threshold pair(s ， t)， then the probabilities of class occurrence are given by向(s ，t)=IIpij Pl(S ，t) = I I Pij (3) (4)And the corresponding class mean levels areT (2.f=oz;=oI Pilzf=oz;=ol pz j\T flo = (µ00，µ01)' = I-o-~-J-~ • OJ ，-o-~-J-~- • OJ I飞Po Po J(5) T (2.:二:+1z;二:+1i pzlz:二:+1z;二:+1j pz 八T µ1 = (µ10'µ11)1 = ，OJ I\Pl Pl J (6) The total mean level vector of 2D Histogram is11-11-1 1-1 1-1\TflT =(川In? = (II i.Pij ，IIjPij ) (7)Because of assumption that the occurrences of image data in off-diagonal quadrants of 2D histogram can be neglected ， it is easy to be verified thatPo + Pl ""1，µT "" Poµ。