Segmentation Of Medical Images Using Topological Concepts .
IOSR Journal of Mathematics (IOSR-JM)e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 4 Ver. IV (Jul-Aug. 2014), PP 01-07www.iosrjournals.orgSegmentation of Medical Images Using Topological ConceptsBased Region Growing Method1B. Shanthi Gowri1, Gnanambal Ilango2Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore – 641 008,Tamil Nadu, India.2Department of Mathematics, Government Arts College, Coimbatore - 641 018, Tamil Nadu, India.Abstract : Image segmentation is an important task in the field of image processing. Medical imagesegmentation plays a vital role in assisting the radiologists to visualize and analyze the region of interest inmedical images. Region growing is a very useful technique for image segmentation. Region growing method ofsegmentation which is based on the classification of pixels into connected components by selecting a seed andgrouping its neighbours with the seed based on the gray levels of the neighbours. In this article, we propose anew seeded region growing segmentation algorithm based on metric topological - neighbourhoods of differentmetrics and grouping criterion for segmentation of region of interest from the medical images. The qualities ofsegmented images are measured by the evaluation measure ‘Accuracy ’.Keywords: Metrics, Region Growing, Segmentation, Topological Neighbourhoods.I.IntroductionSegmentation of medical images like MRI, ultrasound image, CT, X-ray is a hotspot and focus ofimage processing techniques. Medical image segmentation is the most important technique to visualize theaffected region of interest for the radiologists to access patients for diagnosis and treatment of diseases. Imagesegmentation is a process of partitioning a digital image into disjoint regions of connected pixels that arehomogeneous with respect to some characteristics such as gray level or colour. Some of the imagesegmentation methods based on the above techniques are edge detection, thresholding, region growing, regionsplitting and merging, clustering, watershed algorithm etc.,Jiang Guangyou et al., [1] introduced a threshold segmentation algorithm based on neighbourhoodcharacteristics described in a mathematical way and obtained a good segmentation effect through the contrast.Chantal Revol et al., [2] proposed a new minimum variance region growing algorithm with a homogeneitycriterion based on an adequate tuning between spatial neighbourhood and histogram neighbourhood throughspecial morphological operations and gave the result as this algorithm is an efficient solution for difficultsegmentation problems. Yi-Ta Wu et al., [3] developed a top-down region dividing based approach whichcombines the advantages of both histogram-based and region-based approaches and showed that it is efficientfor segmentation without distorting the spatial structure. Maria Kallergi et al., [4] developed local thresholdingand region growing algorithms and applied to digitized mammograms and proved that computerizedparenchymal classification of digitized mammograms is possible and independent of exposure. Pastore, J. et al.,[5] described an automatic segmentation of computerized axial tomography images with tumors by means ofalternating sequential filters of mathematical morphology and connected components extraction based oncontinuous topology concepts. Gnanambal Ilango and R. Marudhachalam [6] presented an automatic methodrelevant to medical image segmentation by means of fuzzy hybrid filter for denoising and topological conceptsto extract connected components and edge detection. Tamas sandor et al.,[7] described an automated procedurebased on the principles of region growing and nearest neighbour classification to extract continuous areas frombrain CT scans and showed that it is fast and reasonably accurate method for segmenting brain tissue. Acomparative performance study of thresholding techniques for segmentation was investigated by Sang Uk Leeand Seok Yoon Chung [8] and proved that the performances are image dependent. Junchai Gao et al., [9]proposed a threshold and edge detection fused segmentation algorithm and showed that it is an effective andpractical image segmentation algorithm which considers not only the adjacent uniformity but also the localcontrast. M.M. Abdelsamea [10] proposed an automatic seeded region growing algorithm for cellular imagesegmentation and gave the result as it can overcome the oversegmentation problem and is less noisy. Anautomatic method of morphological segmentation and region growing to detect the centre and boundaries of theabnormal object of the medical images accurately was proposed by K. Martin Sagayam et al.,[11]. Dinesh D.Patil and Sonal G. Deore [12] compared the different image segmentation techniques like edge detection,thresholding, region growing, region splitting and merging, clustering, watershed and fast region mergingmethods and gave the conclusion as neither a single method is good for all types of images nor all methods areequally good for a particular type of image.www.iosrjournals.org1 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing MethodIn this article, a new seeded region growing segmentation algorithm is proposed to segment the regionof interest from the medical images. This algorithm is based on metric topological - neighbourhoods ofdifferent metrics and grouping criterion. This work is organized as follows: Section II explains the seeded regiongrowing method of segmentation, Section III gives the basic definitions, Section IV provides the proposedsegmentation algorithm, Section V explains the method of evaluation of segmentation, Section VI deals with theexperimental work, Section VII discusses the result analysis, Section VIII gives the conclusion and Section IXgives the table and figures of the experimental results.II.Seeded Region Growing Method Of SegmentationImage segmentation algorithms are mainly based on two properties, detecting discontinuities andsimilarities. The first category is based on the abrupt changes in intensity and the second category is based ongrouping the set of similar pixels satisfying predefined criterion. Region based segmentation is a classicalmethod which comes under the second category. This method tries to extract the object that is connected basedon some predefined criterion. This criterion can be based on the intensity information and edges in the image.One of the region based segmentation methods is the Seeded Region Growing method. This is a procedure thatgroups pixels in whole image into sub regions based on predefined criterion and processed in four steps. (i)Select a seed pixel in the original image. (ii) Select a set of similarity criterion such as gray level or colour andset up a stopping rule. (iii) Grow region by appending to the seed, those neighbouring pixels that havepredefined properties similar to seed pixel. (iv) Stop region growing when no more pixels meet the criterion forinclusion in that region.Here from the histogram of the image, the gray level of the region of interest is selected. Consideringthe gray level of the region of interest, a seed point is selected as a point having maximum number of metrictopological– neighbourhood. For the similarity criterion, a grouping criterion is defined based on metric andgray level difference. The connected region of interest is grown by including the – neighbours of the seedpoint satisfying the grouping criterion with the seed point. The qualities of the segmented region of interest fromthe medical images by the proposed algorithm is compared with the ground truth images and the results areanalyzed.Definition 3.1[13]A metric on a set is a functionIII.Basic Definitionshaving the following properties:Given a metric on , the numberis called as the distance between and in the metric .For a given, consider the setof all points y whosedistance from is less than . Hereis called the - ball centered at If is a metric on the set ,then the collection of all - ballsforand, is a basis for a topology on , calledmetric topology induced by . A set is open in the metric topology induced by iff for each y U , thereis asuch that. If is a topological space,is said to be metrizable if there exists ametric on the set that induces the topology of . A metric space is a metrizable space together with aspecific metric that gives the topology of .Definition 3.2[14]An image may be defined as a two-dimensional function, where and are spatial (plane)coordinates, and the amplitude of at any pair of co-ordinatesis called the intensity or gray level of theimage at that point. Ifand the intensity values of are all finite, discrete quantities, we call the image adigital image. A digital image is composed of a finite number of elementseach of which has aparticular location and value. These elements are called picture elements or pixels.Definition 3.3[15]Let, wherebe the set of spatialco-ordinates of an image. For any metric space, anywww.iosrjournals.organd any, consider the set2 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing Method.is called the (open)- neighbourhood ofin.is. Then (isan open ball centered at .Definition 3.4[16]Let. Consider the functionsi., defined bya metric space. The metricis called the City – Block metric or Manhattan metric.ii., defined by(is a metric space. The metricis called the Chessboard metric.Definition 3.5[15]For any point,the4-neighbourhoodofdenoted. Thenbyisdefinedis also denoted byneighbourhood ofdenoted byis also denoted byand the 8 -is defined as.Definition 3.6[15]For any point , the 4 - neighbours ofareasareand the 8 - neighbours of.Definition 3.7[15]Letwhere. Consider the function.neighbourhood ofneighbourhood ofdefined byis a metric space. For any pointis defined asis defined asand the.are, the. Hence theis defined asneighbours ofLetand theneighbourhood ofis also denoted byneighbours ofare.The.Definition 3.8Letwhere.Considerthe.neighbourhood ofneighbourhood ofdefinedis a metric space. For any pointis defined asand the. Theneighbours ofareby, the. Hence theis defined asis defined asand thefunctionLetneighbours ofneighbourhood ofare.Definition 3.9Letwhere. Consider the functionwww.iosrjournals.orgLetdefined by3 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing Method.neighbourhood ofneighbourhood ofis a metric space. For any pointis defined as. Hence theis defined asand theis defined asand the. Theneighbours ofare. Definedifference betweento belong to ifa topology associated withsuch thatwhereand the elements of . Letfor someIV.neighbours ofneighbourhood ofare.Definition 3.10Grouping criterion:Letbe an image in levels of gray andmetric on, theand letLetbe ais the maximum of the gray levelGiven a fixedand, an elementis saidProposed Segmentation AlgorithmLeft Triangular AlgorithmLet be an image in levels of gray.Step I:From the histogram of the image, select the gray level of the region of interest to be segmented.Step II:Find the seed point of the region of interest. Here, the seed point is a point with maximum number of LTneighbours with gray level difference less than which is very small. If more than one point has the maximumnumber of LT neighbours then choose any one of those points as the seed point.Letwhere is the seed point of the region of interest.Step III:ChooseIf a pointwheresuch thatandthen include------ (1)inand rename it as.Repeat Step III again and again for the elements ofis, all the LT neighbours ofStep IV:If a pointwheretillno pointsatisfying the condition (1). Thatare obtained.such thatwhereand------ (2)then includeinand rename it as.Repeat Step IV again and again for the elements ofis all theStep V:If a pointneighbours ofare obtained.wheresuch thattillno pointsatisfying the condition (2). Thatwhereandthen include----- (3)inand rename it as.Repeat Step V again and again for the elements ofis all theneighbours oftillno pointsatisfying the condition (3). Thatare obtained.www.iosrjournals.org4 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing MethodThe setis the segmented region of interest.V.Evaluation MeasureLet be the set of pixels in the image. Define the ground truthas the set of pixels that werelabeled as tumor by the expert. Similarly define the segmented tumoras the set of pixels that werelabeled as tumor by the algorithm. and be the set of pixels that were labeled as non-tumor by the expert andalgorithm respectively. The true positive () set is defined as, i.e., the set of pixels common toand . i.e., the set of pixels that were labeled as tumor by the expert and algorithm. The true negative ()set is defined as, i.e., the set of pixels common to and . i.e., the set of pixels that werelabeled as non-tumor by the expert and algorithm. The false negative () set is defined as,i.e., the set of pixels common to and . i.e., the set of pixels that were labeled as tumor by the expert and nontumor by the algorithm. The false positive () set is defined as, i.e., the set of pixels commonto and . i.e., the set of pixels that were labeled as non-tumor by the expert and tumor by the algorithm.The segmentation evaluation measure ‘Accuracy’ is defined asAccuracy VI.Experimental WorkIn this work, magnetic resonance images of brain affected by tumor are taken. The seed point of theregion of interest is selected using the histogram of the image and metric topological - neighbourhoods . dpointusingthemetrictopological-and the grouping criterion. The proposed region growingsegmentation algorithm is implemented using MATLAB 7.0. The performance of the proposed algorithm isevaluated using the segmentation evaluation measure ‘Accuracy’.VII.Result Analysis And DiscussionThe magnetic resonance images of brain affected by tumor are segmented using the proposed LeftTriangular Algorithm based on metric topological - neighbourhoods and the grouping criterion.Table 1 shows the accuracy values and the percentage of the quality of segmentation of the proposedLeft Triangular Algorithm applied to magnetic resonance images of brain affected by tumor.Fig 1 shows the ground truth images. Fig 2 shows the original magnetic resonance images of brain affected bytumor, the corresponding segmented region and the segmented region with boundary respectively using theproposed Left Triangular Algorithm.VIII.ConclusionIn this work, a new region growing segmentation algorithm based on metric topological neighbourhood and grouping criterion is introduced. To demonstrate the performance of the proposed LeftTriangular Algorithm based on metric topological - neighbourhoods, the experiments have been conducted onmagnetic resonance images of brain affected by tumor. The performance of the proposed segmentationalgorithm is measured using the segmentation evaluation measure ‘Accuracy’. The experimental results indicatethat the percentage of the quality of segmentation by the proposed Left Triangular Algorithm is 98.59% or more.This work is a new metric topological approach for region growing segmentation of medical images to segmentthe region of interest.IX.Table And FiguresTable 1 - Accuracy and Qualitywww.iosrjournals.org5 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing MethodFig 1 – Ground Truth ImagesFig 2 – Segmentation by Left Triangular AlgorithmAcknowledgementsThe authors thank The University Grants Commission, India, to carry out this research work.References[1][2][3]Jiang Guangyou and Kang Gewen, A threshold segmentation algorithm based on neighbourhood characteristics, Thetenth International conference on Electronic Measurement and Instruments ,IEEE , 2011,328-331.Chantal Revol and Michel Jourlin, A new minimum variance region growing algorithm for image segmentation,Pattern Recognition Letters, 18, 1997, 249-258.Yi-Ta Wu , Frank Y. Shih , Jiazheng Shi and Yih-Tyng Wu, A top-down region dividing approach for imagesegmentation, Pattern Recognition, 41, 2008, 1948-1960.www.iosrjournals.org6 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing 6]Maria Kallergi, Kevin Woods, Laurence P. Clarke, Wei Qian and Robert A. Clark, Image segmentation in digitalmammography; Comparison of local thresholding and region growing algorithms, Computerized Medical Imagingand Graphics , Vol 16(5), 1992, 323-331.Pastore J., Bouchet A., Moler E. and Ballarin, V., Topological Concepts applied to Digital Image Processing,JCS&T, Vol. 6, No. 2, 2006, 80-84.Gnanambal Ilango and R. Marudhachalam, Topological Concepts Applied to Image Segmentation, Journal ofAdvanced Studies in Topology, Vol. 4, No. 1, 2013,128-132.Tamas Sandor, David Metcalf and Young-Jo Kim, Segmentation of brain CT images using the concept of RegionGrowing, Int J Biomed Comput, 29, 1991, 133-147.Sang Uk Lee and Seok Yoon Chung, A comparative performance study of several global thresholding techniques forsegmentation, Computer Vision, Graphics and Image processing, 52, 1990, 171 - 190.Junchai Gao , Zhiyong Lei , Zemin Wang and Keding Yan, Region growth segmentation based on dual - cores,Energy Procedia, 13, 2011, 4567-4571.M.M. Abdelsamea, An Automatic Seeded Region Growing for 2D Biomedical Image Segmentation, Proceedings ofthe International Conference on Environment and Bioscience, 21, 2011, 1-5.K. Martin Sagayam, V. Ayyappan, and S. Palani, Automatic Morphological Segmentation and Region GrowingMethod of Diagnosing Medical Images, International Journal of Information & Computation Technology, Vol 2(6),2012, 173 - 180 .Dinesh D. Patil and Sonal G. Deore , Medical Image Segmentation: A Review, International Journal of ComputerScience and Mobile Computing, 2, 2013, 22-27.James R. Munkres, Topology (Prentice-Hall of India, 2007).R. Gonzalez, and R. Woods, Digital Image Processing (New York, Adison-Wesley, 1992).Gnanambal Ilango and B. Shanthi Gowri, - Neighbourhood Median Filters to Remove Speckle Noise from CTImages, International Journal of Applied Information Systems, Vol. 4, No. 10, 2012, 40-46.R. Klette and A. Rosenfeld, Digital Geometry (San Fransisco, Kaufmann, 2004).www.iosrjournals.org7 Page
Segmentation of Medical Images Using Topological Concepts Based Region Growing Method www.iosrjournals.org 4 Page . is a metric space. For any point , the neighbourhood of is defined as . Hence the neighbourhood of is defined as and the neighbourhood of is defined as .
The accurate segmentation of medical images is one of the most important tasks in diverse medical applications. In the recent literature, a plentiful of general approaches has been proposed on medical image segmentation [33]. The medical image segmentation methods available in the literature can be divided into eight categories.
liver, pancreas etc. The segmentation of the part in image is to be done accurately. Especially in medical images, the segmentation result has to be accurate. In this proposed work, the brain MRI images segmentation using fuzzy c means clustering (FCM) and discrete wavelet transform (DWT).
Fig. 1.Overview. First stage: Coarse segmentation with multi-organ segmentation withweighted-FCN, where we obtain the segmentation results and probability map for eachorgan. Second stage: Fine-scaled binary segmentation per organ. The input consists of cropped volume and a probability map from coarse segmentation.
Internal Segmentation Firewall Segmentation is not new, but effective segmentation has not been practical. In the past, performance, price, and effort were all gating factors for implementing a good segmentation strategy. But this has not changed the desire for deeper and more prolific segmentation in the enterprise.
Internal Segmentation Firewall Segmentation is not new, but effective segmentation has not been practical. In the past, performance, price, and effort were all gating factors for implementing a good segmentation strategy. But this has not changed the desire for deeper and more prolific segmentation in the enterprise.
segmentation research. 2. Method The method of segmentation refers to when the segments are defined. There are two methods of segmentation. They are a priori and post hoc. Segmentation requires that respondents be grouped based on some set of variables that are identified before data collection. In a priori segmentation, not only are the
Segmentation of Medical Ultrasound Images Using Convolutional Neural Networks with Noisy Activating Functions (a) (b) Figure 1. One example of (a) the medical ultrasound images in the dataset, and (b) segmentation of the image by trained human volunteers. The segmented nerves are represented in red.
Medical Image Segmentation Using Active Contours Serdar Kemal Balci Abstract—Medical image segmentation allow medical doctors to interpret medical images more accurately and more efficiently. We aim to develop a medical image segmentation procedure in order to reduce medical doctors’ data examination and interpretation time.
