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- 1. International Journal For Research & Development in Technology Volume: 2, Issue: 4, Oct -2014 ISSN (Online):- 2349-3585 21 Copyright 2014- IJRDT www.ijrdt.org Segmentation Of Medical Images Using Metric Topology – A Region Growing Approach Gnanambal Ilango1, B. Shanthi Gowri 2 , G. Rohith 3 1 Department of Mathematics,Government Arts College,Coimbatore, India. 2 Department of Mathematics,Sri Krishna College of Engineering and Technology 3 Department of Mechatronics Engineering,Sri Krishna College of Engineering and Technology,Coimbatore,India. Abstract— A metric topological approach to the region growing based segmentation is presented in this article. Region based growing techniques has gained a significant importance in the medical image processing field for finest of segregation of tumor detected part in the image. Conventional algorithms were concentrated on segmentation at the coarser level which failed to produce enough evidence for the validity of the algorithm. In this article a novel technique is proposed based on metric topological neighbourhood also with the introduction of new objective measure entropy, apart from the traditional validity measures of Accuracy, PSNR and MSE. This measure is introduced to prove the amount of information lost after segmentation is reduced to greater extent which elucidates the effectiveness of the algorithm. This algorithm is tested on the well known benchmarking of testing in ground truth images in par with the proposed region based growing segmented images. The results validated show the validation of effectiveness of the algorithm. Index Terms— Metrics, Metric Topological Neighbourhoods, Seeded Region Growing, Segmentation, Accuracy, PSNR, MSE, Entropy. I. INTRODUCTION The interpretation of group of connected pixels with similar properties into larger regions based on the predefined criteria collectively termed as region growing based segmentation, has gained a magnificent importance in medical image processing field. The main goal of image segmentation is domain independent partitioning of an image into a set of disjoint regions that are visually different, homogeneous and meaningful with respect to some characteristics or computed property such as gray level, texture or colour to enable interpretation of the image. Region growing based segmentation has got the better tradeoff than the edge based techniques owing to the fact that the edges are difficult to detect in noisy conditions. The interpretation lies in the isolation of the strongest region of interest with respect to the highest gray scale value. This attempts to segregate the particular group of pixels that are indifferent to the nominal range of values in the histogram. The continuous path of gray scale connected to the two points of the image requires a pre requisite of predefined variance (threshold) failing to fulfill will lead to the improper segregation. Based on this fact several algorithms were experimented. Yi-Ta Wu , Frank Y. Shih , Jiazheng Shi and Yih-Tyng Wu [12] developed a top-down region dividing based approach which combines the advantages of both histogram-based and region-based approaches and showed that it is efficient for segmentation without distorting the spatial structure. Geng- Cheng Lin , Wen-June Wang , Chung-Chia Kang and Chuin- Mu Wang [1] proposed a novel fuzzy knowledge based seeded region growing for multispectral MR images and proved that this method is more efficient than the functional MRI of the brain automated segmentation tool, k-means and support vector machine methods. Maria Kallergi , Kevin Woods, Laurence P. Clarke , Wei Qian and Robert A . Clark [7] developed local thresholding and region growing algorithms and applied to digitized mammograms and proved that computerized parenchymal classification of digitized mammograms is possible and independent of exposure. Pastore J., Bouchet A., Moler E. and Ballarin, V. [9] described an automatic segmentation of computerized axial tomography images with tumors by means of alternating sequential filters of mathematical morphology and connected components extraction based on continuous topology concepts. Gnanambal Ilango and R. Marudhachalam [2] presented an automatic method relevant to medical image segmentation by means of fuzzy hybrid filters for denoising and topological concepts to extract connected components and edge detection. Tamas Sandor , David Metcalf and Young-Jo Kim [11] described an automated procedure, based on the principles of region growing and nearest neighbour classification to extract continuous areas from brain CT scans and showed that it is a fast and reasonably accurate method for segmenting brain tissue. Sang Uk Lee and Seok Yoon Chung [10] compared different thresholding techniques for segmentation and concluded that image performances are different. Junchai Gao , Zhiyong Lei , Zemin Wang and Keding Yan [5] proposed a threshold and edge detection fused segmentation algorithm which considers not only the adjacent uniformity but also the local contrast.
- 2. International Journal For Research & Development in Technology Paper Title:- Segmentation of Medical Images Using Metric Topology- A Region Growing Approach (Vol.2, Issue-4) ISSN(O):- 2349-3585 22 Copyright 2014- IJRDT www.ijrdt.org In this article, a new seeded region growing segmentation algorithm is proposed based on metric topological – neighbourhoods of different metrics and grouping criterion.This work is organized as follows: Seeded region growing method of segmentation, Basic definitions, Proposed segmentation Algorithm, Method of evaluation of segmentation, Experimental work, Result analysis, Conclusion and the Figures and Tables of the experimental results. II. SEEDED REGION GROWING METHOD OF SEGMENTATION Region based segmentation is a classical method. This method tries to extract the object that is connected based on some predefined criterion. This criterion may 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 that groups pixels in the 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 and set up a stopping rule. (iii) Grow region by appending to the seed, those neighbouring pixels that have predefined properties similar to seed pixel. (iv) Stop region growing when no more pixels meet the criterion for inclusion in that region. Here from the histogram of the image, the gray level of the region of interest is selected. Considering the gray level of the region of interest, a seed point is selected as a point having maximum number of – neighbourhoods of different metrics. For the similarity criterion, a grouping criterion is defined based on metric and gray level difference. The connected region of interest is grown by including the – neighbours of the seed point satisfying the grouping criterion with the seed point. The quality of the segmented region of interest from the medical images for the proposed algorithm is compared with the ground truth images and the results are analysed. III.BASIC DEFINITIONS Definition 1[8] A metric on a set is a function having the following properties: ( ) ( ) ( ) ( ) ( ) ( ) Given a metric on , the number ( ) is called as the distance between and in the metric . For a given , consider the set ( ) * ( ) + ( ) of all points y whose distance from is less than . Here ( ) is called the - ball centered at If is a metric on the set , then the collection of all - balls ( ) for and , is a basis for a topology on , called metric topology induced by . A set is open in the metric topology induced by iff for each , there is a such that ( ) . If is a topological space, is said to be metrizable if there exists a metric on the set that induces the topology of . A metric space is a metrizable space together with a specific metric that gives the topology of . Definition 2[4] 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-ordinates ( ) is called the intensity or gray level of the image at that point. If and the intensity values of are all finite, discrete quantities, we call the image a digital image. A digital image is composed of a finite number of elements ( ) each of which has a particular location and value. These elements are called picture elements or pixels. Definition 3[3] Let , where *( ) + be the set of spatial co-ordinates of an image. For any metric space ( ) any and any , consider the set ( ) * ( ) + . ( ) is called the (open) - neighbourhood of in . ( ) is an open ball centered at . Definition 4[6] Let ( ) ( ) . Consider the functions i. , defined by ( ) | | | |. Then ( ) is a metric space. The metric is called the City – Block metric or Manhattan metric. ii. , defined by ( ) * | | | | + . Then ( ) is a metric space. The metric is called the Chessboard metric. Definition 5[3] For any point , the 4 - neighbourhood of denoted by ( ) is defined as ( ) * ( ) + ( ) is also denoted by ( ) and the 8 - neighbourhood of denoted by ( ) is defined as ( ) * ( ) + ( ) is also denoted by ( ). Definition 6[3] For any point , the 4 - neighbours of are ( ) * + and the 8 - neighbours of are ( ) * +. Definition 7[3] Let where *( ) +. Let ( ) ( ) . Consider the function defined by ( ) | | | | . ( ) is a metric space. For any point , the neighbourhood of is defined as ( ) * ( ) +. Hence the neighbourhood of is ( ) * ( ) + and the neighbourhood of is ( ) * ( ) +. The
- 3. International Journal For Research & Development in Technology Paper Title:- Segmentation of Medical Images Using Metric Topology- A Region Growing Approach (Vol.2, Issue-4) ISSN(O):- 2349-3585 23 Copyright 2014- IJRDT www.ijrdt.org neighbours of are ( ) * + and the neighbours of are ( ) * +. Definition 8[3] Let where *( ) + . Let ( ) ( ) . Consider the function defined by ( ) | | | | . ( ) is a metric space. For any point p, the - neighbourhood of p is defined as ( ) * ( ) +. Hence the - neighbourhood of p is defined as ( ) * ( ) + and the - neighbourhood of p is defined as ( ) * ( ) + . The - neighbours of p are ( ) * + and the - neighbours of p are ( ) * +. Definition 9[3] Let where {*( )+ *( )+ } . Let ( ) ( ) . Consider the function defined by ( ) ,| | | | - . ( ) 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 ( ) * ( ) +. ( ) is also denoted by ( ) . The neighbours of are ( ) * + and the neighbours of p are ( ) * +. Definition 10 Grouping criterion: Let be an image in levels of gray and a topology associated with and let Let be a metric on . Define such that (( )) where is the maximum of the gray level difference between and the elements of . Let Given a fixed , an element is said to belong to if ( ) for some and (( )) IV.PROPOSED SEGMENTATION ALGORITHM VHLT ALGORITHM Let be an image in levels of gray. Step I: From the histogram of the image , select the gray level for 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 vertical neighbours with gray level difference less than which is very small. If more than one point has the maximum number of vertical neighbours then choose any one of those points as the seed point. Let * + where is the seed point of the region of interest. Step III: Choose If a point where such that ( ) (( )) -----(1) then include in and rename it as . Repeat Step III again and again for the elements of till no point satisfying the condition (1). That is all the vertical neighbours of are obtained. Step IV: If a point where such that ( ) where (( )) -----(2) then include in and rename it as . Repeat Step IV again and again for the elements of till no point satisfying the condition (2). That is all the horizontal neighbours of are obtained. Step V: If a point where such that ( ) where (( )) ------(3) then include in and rename it as . Repeat Step V again and again for the elements of till no point satisfying the condition (3). That is all the LT neighbours of are obtained. The set is the segmented region of interest. V.EVALUATION MEASURES (i) Let be the set of pixels in the image. Define the ground truth as the set of pixels that were labeled as tumor by the expert. Similarly define the segmented tumor as the set of pixels that were labeled as tumor by the algorithm. ̅and ̅ the set of pixels that were labeled as non- tumor by the experts and algorithm respectively. The true positive ( ) 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 algorithm. The true negative ( ) set is defined as ̅ ̅, i.e., the set of pixels common to ̅ and ̅. i.e., the set of pixels that were labeled 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 non-tumor by the algorithm. The false positive ( ) set is defined as ̅
- 4. International Journal For Research & Development in Technology Paper Title:- Segmentation of Medical Images Using Metric Topology- A Region Growing Approach (Vol.2, Issue-4) ISSN(O):- 2349-3585 24 Copyright 2014- IJRDT www.ijrdt.org , i.e., the set of pixels common to ̅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 as Accuracy = ( ) ( ) ( ) ( ) ( ) ( ) . (ii) The Mean Square Error (MSE) is defined as ∑ ∑ ‖ ( ) ( )‖ Where I(i,j) = Input image and K(i,j) = Segmented image. The Peak Signal to Noise Ratio (PSNR) is defined as the ratio of peak signal power to noise power in logarithmic scale. Since the MSE represents the noise power and peak signal power, it is unity in case of normalized image signal. PSNR = [ ] where MaxI = Maximum possible pixel value of the image. The typical values of PSNR in a lossy image is between 20 and 50 db. (iii) For the validation in terms of amount of information retained after segmentation subjected to accurate recovery of information, a new parameter which can be introduced is the Entropy. Entropy (E) which is the amount of information per pixel in the source is formulated as E = ∑ where = Number of image pixels expressed in bits. VI. EXPERIMENTAL WORK In this work, magnetic resonance images of brain affected by tumor are taken. The seed point of the region of interest is selected using the histogram of the image and metric topological - neighbourhoods . The region of interest is grown from the seed point using the metric topological - neighbourhoods ( ) ( ) ( ) and the grouping criterion. The proposed region growing segmentation algorithm is implemented using MATLAB 7.0. The performances of the proposed algorithm are evaluated using the segmentation evaluation measures Accuracy, MSE, PSNR and Entropy. VII.RESULT ANALYSIS AND DISCUSSION The magnetic resonance images of brain affected by tumor are segmented using the proposed region growing segmentation algorithm based on metric topological - neighbourhoods and the grouping criterion. The experimental results show that the quality of segmentation by the VHLT algorithm is 98.6% or more. PSNR values are in the nominal range 20 – 50 db. The difference between the entropy values of the original and segmented images is negligibly small i.e. less than 0.01. Table 1 shows the entropy values of the original and segmented images. Table 2 shows the accuracy ,quality of segmentation, PSNR and MSE values. Fig 1 shows the ground truth images. Fig 2 shows the original magnetic resonance images of brain affected by tumor, the corresponding segmented region and the segmented region with boundary using the proposed VHLT region growing segmentation algorithm respectively. VIII. CONCLUSION In this work, a new region growing segmentation algorithm based on metric topological - neighbourhoods and grouping criterion is introduced. To demonstrate the performance of the proposed region growing segmentation algorithm, experiments have been conducted on magnetic resonance images of brain affected by tumor. The performance of the proposed segmentation algorithm is measured using the segmentation evaluation measure „Accuracy‟. The experimental results indicate that the quality of segmentation by the proposed VHLT algorithm is 98.6% or above. The new parameter Entropy is validated between the original and segmented images. The amount of information present in the original image approaches the segmented portion which proves the effectiveness of algorithm by retaining the essential information without loss of data. This retains maximum fidelity of image. Further, the observed objective measure PSNR meet the nominal range of 20-50 db. This work is a new metric topological approach for region growing segmentation of magnetic resonance images. FIGURES Fig 1 – Ground Truth Images Fig 2 – Segmentation by VHLT Algorithm
- 5. International Journal For Research & Development in Technology Paper Title:- Segmentation of Medical Images Using Metric Topology- A Region Growing Approach (Vol.2, Issue-4) ISSN(O):- 2349-3585 25 Copyright 2014- IJRDT www.ijrdt.org Table 1 – Entropy Values Table 2 - Accuracy , Quality, PSNR and MSE values. ACKNOWLEDGEMENT The first author thank The University Grants Commission, India for its financial support to carry out this work. REFERENCES [1] Geng-Cheng Lin , Wen-June Wang , Chung-Chia Kang and Chuin-Mu Wang, “Multispectral MR images segmentation based on fuzzy knowledge and modified seeded region growing”, Magnetic Resonance Imaging , 30, pp. 230- 246, 2012 . [2] Gnanambal Ilango and R. Marudhachalam, “Topological Concepts Applied to Image Segmentation”, Journal of Advanced Studies in Topology, Vol. 4, No. 1, pp. 128-132, 2013. [3] Gnanambal Ilango and B. Shanthi Gowri, “ - Neighbourhood Median Filters to Remove Speckle Noise from CT-Images,” International Journal of Applied Information Systems, Vol.4, No. 10, pp.40-46, 2012. [4] R. Gonzalez and R. Woods, Digital Image Processing, Adison-Wesley, New York, 1992. [5] Junchai Gao , Zhiyong Lei , Zemin Wang and Keding Yan , “Region growth segmentation based on dual - cores”, Energy Procedia, 13, pp.4567-4571, 2011. [6] R. Klette and A. Rosenfeld, Digital Geometry, Kaufmann, San Fransisco, 2004. [7] Maria Kallergi , Kevin Woods, Laurence P. Clarke , Wei Qian and Robert A . Clark , “Image segmentation in digital mammography: Comparison of local thresholding and region growing algorithms”, Computerized Medical Imaging and Graphics , Vol 16 . No.5, pp. 323-331, 1992. [8] James R. Munkres, Topology, Prentice-Hall of India, 2007. [9] Pastore J., Bouchet A., Moler E. and Ballarin, V., “Topological Concepts applied to Digital Image Processing”, JCS&T, Vol. 6, No. 2, pp. 80-84, 2006. [10] Sang Uk Lee and Seok Yoon Chung, “A comparative performance study of several global thresholding techniques for segmentation”, Computer Vision , Graphics and Image processing , 52 , pp. 171 – 190, 1990 . [11] Tamas Sandor , David Metcalf and Young-Jo Kim, “Segmentation of brain CT images using the concept of Region Growing”, Int J Biomed Comput, 29, pp. 133-147, 1991. [12] Yi-Ta Wu , Frank Y. Shih , Jiazheng Shi and Yih- Tyng Wu , “A top-down region dividing approach for image segmentation”, Pattern Recognition, 41, pp. 1948-1960, 2008.