Several improvements and extensions to our basic methodology are possible. The framework follows a modular processing pipeline, in which any module involved could be replaced, inter-changed, or improved. Accordingly, the extensions to the current work could be adopted in the following directions: Seed point Extraction, Contour Evidence Extraction, Contour Estimation, Post-processing and Evaluation.
The seed point extraction method combines the bounded erosion with FRS transform to detect seed points. The method is efficient and highly accurate, provided that the objects are convex and symmetric. As another limitation, the performance of the detected seed points strictly depends on the initial parameter defining the range of radii. To overcome these shortcomings, it would be valuable to explore and apply methods that are more robust to shape changes and are not parametrization dependent.
In the contour evidence extraction method, the task of extracting contour evidences is performed by the edge-to-marker association method and works based on the distance and the divergence criteria. However, it was found that mixing the parameter of distance and divergence criteria is critical, as with the problems of several overlapped objects, the high weighting rate of divergence degrades the performance of edge-to-marker association. Therefore, for further improvement additional constraints will need to be investigated to resolve this problem. In addition, this step is considered to be the most time consuming step in the algorithm.
The contour estimation method utilizes the numerically stable version of direct ellipse fitting for the task of contour estimation, as previously mentioned in Section 3.4.1, and this is sensitive to outliers and may result in ellipses with low eccentricity. Obviously, this kind of formulation could not be a comprehensive solution for every scenario, and it would be worthwhile to promote the current fitting algorithm to the one that is robust to the outliers. In addition, the current model of contour fitting solely relies on elliptical approximation and may fail to reach satisfactory results when the shape of objects differ substantially from ellipse. This is in parallel with several real world applications, where the object models do not strictly follow elliptical patterns, motivating the replacing of the ellipse fitting model by a more sophisticated approach, e.g. hypersquadratics and closed B-spline curve.
The post-processing for false positive elimination only examines the object sizes, but dose not consider the redundant objects. This is the case when two different ellipses are related to a single object. The further extensions to post-processing will be left for future research.
The evaluations were limited to synthetic data and 11 distinct real microscopic images. It would be worthwhile to evaluate the proposed method with different image datasets and various imaging settings. This would be required to verify the generalizability of the proposed method.
6 Conclusions
The work described in this thesis was concerned with the problem of multiple overlapping object segmentation with an emphasis on convex-shape objects. Under the heading of a modular frame-work consisting of seed point extraction, contour evidence extraction, and contour estimation, several state-of-art techniques applied to each individual component were reviewed and studied.
For the evaluation purpose, the competing methods were experimented the synthetic data and the real microscopic image data.
Considering the evaluation results obtained at each particular task and in an effort to improve the overlapping object segmentation, a contour-based method for segmentation of overlapping objects was introduced. The method proposed particularly follows a five modular segmentation pipe line. First, the grayscale image binarization is performed using global thresholding followed by morphological opening to smooth the object boundaries. Second, the object seed point are extracted through a combined approach of bounded erosion and Fast Radial Transform. Third, given the estimated object seed points, the visible parts of object boundaries are extracted as per the edge-to-marker association method. Fourth, ellipse fitting is applied to estimate the primary segmentation results. Finally, a post-processing step using a priori knowledge about the size of the objects is applied for false positive elimination.
To validate the effectiveness of the proposed method, it was compared to the other two existing methods, Nano Particle Segmentation (NPS) and Concave-point Contour Based Segmentation (CBCS), both on the synthetic and real microscopic image data. Experimental results revealed that the proposed approach is efficient and reliable, and outperformed the existing approaches.
References
[1] Jordi Freixenet and Xavier Mu. Yet another survey on image segmentation: Region and boundary information integration. In7th European Conference on Computer Vision (ECCV), pages 408–422, 2002.
[2] Nikhil R Pal and Sankar K Pal. A review on image segmentation techniques. Pattern Recognition, 26(9):1277–1294, 1993.
[3] Dzung L Pham, Chenyang Xu, and Jerry L Prince. Current methods in medical image segmentation 1. Annual review of biomedical engineering, 2(1):315–337, 2000.
[4] H.P. Narkhede. Review of image segmentation techniques.International Journal of Science and Modern Engineering, 1(8):54–61, 2013.
[5] P. Quelhas, M. Marcuzzo, A.M. Mendonca, and A. Campilho. Cell nuclei and cytoplasm joint segmentation using the sliding band filter. IEEE Transactions on Medical Imaging, 29(8):1463–1473, 2010.
[6] Bahram Parvin, Qing Yang, Ju Han, Hang Chang, Bjorn Rydberg, and Mary Helen Barcellos-Hoff. Iterative voting for inference of structural saliency and characterization of subcellular events. IEEE Transactions on Medical Imaging, 16(3):615–623, 2007.
[7] Wen-Hui Zhang, Xiaoya Jiang, and Yin-Mingzi Liu. A method for recognizing overlapping elliptical bubbles in bubble image. Pattern Recognition Letters, 33(12):1543 – 1548, 2012.
[8] Jie Shu, Hao Fu, Guoping Qiu, Philip Kaye, and Mohammad Ilyas. Segmenting overlapping cell nuclei in digital histopathology images. In35th International Conference on Medicine and Biology Society (EMBC), pages 5445–5448, 2013.
[9] Chiwoo Park, Jianhua Z Huang, Jim X Ji, and Yu Ding. Segmentation, inference and classification of partially overlapping nanoparticles.IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(3):669–681, 2013.
[10] Nobuyuki Otsu. A threshold selection method from gray-level histograms. Automatica, 11(285-296):23–27, 1975.
[11] J. Kittler and J. Illingworth. Minimum error thresholding. Pattern Recognition, 19(1):41 – 47, 1986.
[12] Mehmet Sezgin and Bulent Sankur. Survey over image thresholding techniques and quan-titative performance evaluation. Journal of Electronic Imaging, 13(1):146–168, 2004.
[13] Thresholding (image processing). http://en.wikipedia.org/w/index.php?
title=Thresholding_(image_processing)&oldid=606970852, 2014.
[Online; Accessed August -2014].
[14] N Senthilkumaran and R Rajesh. Edge detection techniques for image segmentation–a sur-vey of soft computing approaches. International Journal of Recent Trends in Engineering, 1(2):250–254, 2009.
[15] John Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):679–698, 1986.
[16] Judith MS Prewitt. Object enhancement and extraction. Picture processing and Psychopic-torics, 10(1):15–19, 1970.
[17] Lawrence Gilman Roberts. Machine Percption of Three-Dimensional Soups. PhD thesis, Massachusetts Institute of Technology, 1963.
[18] Canny edge detector demos. http://robotics.eecs.berkeley.edu/
~sastry/ee20/cademo.html, 1996. [Online; Accessed August -2014].
[19] Rolf Adams and Leanne Bischof. Seeded region growing. IEEE Transaction on Pattern Analysis and Machine Intelligence, 16(6):641–647, 1994.
[20] S. L. Horowitz and T. Pavlidis. Picture Segmentation by a directed split-and-merge proce-dure. Proceedings of the 2nd International Joint Conference on Pattern Recognition, pages 424–433, 1974.
[21] ABM Faruquzzaman, Nafize Rabbani Paiker, Jahidul Arafat, and M Ameer Ali. A survey report on image segmentation based on split and m erge algorithm. IIETECH Journal of Advanced Computations, 2(2):86–108, 2008.
[22] Fernand Meyer and Serge Beucher. Morphological segmentation. Journal of Visual Com-munication and Image Representation, 1(1):21–46, 1990.
[23] Vicente Grau, AUJ Mewes, M Alcaniz, Ron Kikinis, and Simon K Warfield. Improved watershed transform for medical image segmentation using prior information.IEEE Trans-actions on Medical Imaging, 23(4):447–458, 2004.
[24] Allan Hanbury. Image segmentation by region based and watershed algorithms. Wiley Encyclopedia of Computer Science and Engineering, 2008.
[25] Splitting and merging. http://homepages.inf.ed.ac.uk/rbf/CVonline/
LOCAL_COPIES/MARBLE/medium/segment/split.htm, 1996. [Online; Ac-cessed August -2014].
[26] Digital image processing, chapter 5, part 3. http://user.engineering.uiowa.
edu/~dip/lecture/segmentation3.html, 2003. [Online; Accessed August -2014].
[27] Tim McInerney and Demetri Terzopoulos. Deformable models in medical image analysis:
a survey. Medical Image Analysis, 1(2):91 – 108, 1996.
[28] Michael Kass, Andrew Witkin, and Demetri Terzopoulos. Snakes: Active contour models.
International Journal of Computer Vision, 1(4):321–331, 1988.
[29] David Mumford and Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42(5):577–685, 1989.
[30] Da Chen, Dengwang Li, and Mingqiang Yang. Active contour for noisy image segmenta-tion based on contourlet transform. Journal of Electronic Imaging, 21(1):013009–1, 2012.
[31] Faliu Yi and Inkyu Moon. Image segmentation: A survey of graph-cut methods. In Inter-national Conference on Systems and Informatics (ICSAI), 2012.
[32] The robust tool for natural image segmentation and matting. www.juew.org/
projects/RobustMatting/index.html, 2006. [Online; Accessed August -2014].
[33] Tony Chan and Wei Zhu. Level set based shape prior segmentation. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), pages 1164–
1170 vol. 2, 2005.
[34] Daniel Freedman and Tao Zhang. Interactive graph cut based segmentation with shape priors. InIEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, pages 755–762, 2005.
[35] Thomas Schoenemann and Daniel Cremers. Globally optimal image segmentation with an elastic shape prior. InIEEE International Conference on Computer Vision (ICCV), pages 1–6, 2007.
[36] Manuel Werlberger, Thomas Pock, Markus Unger, and Horst Bischof. A variational model for interactive shape prior segmentation and real-time tracking. InScale Space and Vari-ational Methods in Computer Vision, volume 5567 ofLecture Notes in Computer Science, pages 200–211, 2009.
[37] Ian Jolliffe. Principal component analysis. Wiley Online Library, 2005.
[38] Tammy Riklin-Raviv, Nahum Kiryati, and Nir Sochen. Prior-based segmentation and shape registration in the presence of perspective distortion. International Journal of Computer Vision, 72(3):309–328, 2007.
[39] Anil K Jain, Yu Zhong, and Marie-Pierre Dubuisson-Jolly. Deformable template models:
A review. Signal Processing, 71(2):109–129, 1998.
[40] Ramesh Jain, Rangachar Kasturi, and Brian G Schunck. Machine Vision. McGraw-Hill, Inc., New York, NY, USA, 1995.
[41] Remco C. Veltkamp and Michiel Hagedoorn. Principles of Visual Information Retrieval.
Springer, 2001.
[42] George C. Stockman and Ashok K. Agrawala. Equivalence of hough curve detection to template matching. Communications of the ACM, 20(11):820–822, 1977.
[43] Timothy F Cootes, Christopher J Taylor, David H Cooper, and Jim Graham. Active shape models-their training and application. Computer Vision and Image Understanding, 61(1):38–59, 1995.
[44] Timothy F Cootes, Gareth J Edwards, and Christopher J Taylor. Active appearance models.
In5th European Conference on Computer Vision (ECCV), pages 484–498. 1998.
[45] Mikael Rousson and Nikos Paragios. Shape priors for level set representations. In 7th European Conference on Computer Vision (ECCV), pages 78–92, 2002.
[46] A Tsai, Jr. Yezzi, A, III Wells, W., C. Tempany, D. Tucker, A Fan, W.E. Grimson, and A Willsky. Model-based curve evolution technique for image segmentation. InIEEE Com-puter Society Conference on ComCom-puter Vision and Pattern Recognition (CVPR), 2001.
[47] Michael E Leventon, W Eric L Grimson, and Olivier Faugeras. Statistical shape influence in geodesic active contours. InIEEE Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, pages 316–323, 2000.
[48] Yousef Al-Kofahi, Wiem Lassoued, William Lee, and Badrinath Roysam. Improved auto-matic detection and segmentation of cell nuclei in histopathology images. IEEE Transac-tions on Biomedical Engineering, 57(4):841–852, 2010.
[49] Carlos Arteta, Victor Lempitsky, J Alison Noble, and Andrew Zisserman. Learning to detect partially overlapping instances. InIEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3230–3237, 2013.
[50] Marti A. Hearst, ST Dumais, E Osman, John Platt, and Bernhard Scholkopf. Support vector machines. Intelligent Systems and Their Applications, 13(4):18–28, 1998.
[51] Tiago Esteves, Pedro Quelhas, Ana Maria Mendonça, and Aurélio Campilho. Gradient con-vergence filters and a phase congruency approach for in vivo cell nuclei detection.Machine Vision and Applications, 23(4):623–638, 2012.
[52] Hidefumi Kobatake and Shigeru. Hashimoto. Convergence index filter for vector fields.
IEEE Transactions on Image Processing, 8(8):1029–1038, 1999.
[53] Jun Wei, Yoshihiro Hagihara, and Hidefumi Kobatake. Detection of cancerous tumors on chest x-ray images -candidate detection filter and its evaluation. InInternational Confer-ence on Image Processing (ICIP), 1999., pages 397–401 vol.3, 1999.
[54] CarlosS. Pereira, Hugo Fernandes, AnaMaria Mendonça, and Aurélio Campilho. Detection of lung nodule candidates in chest radiographs. InPattern Recognition and Image Analysis, volume 4478 ofLecture Notes in Computer Science, pages 170–177, 2007.
[55] Robert M Haralick, S Zhuang, Charlotte Lin, and J Lee. The digital morphological sampling theorem. IEEE Transactions on Acoustics, Speech and Signal Processing, 37(12):2067–2090, 1989.
[56] Azriel Rosenfeld. Measuring the sizes of concavities.Pattern Recognition Letters, 3(1):71–
75, 1985.
[57] Azriel Rosenfeld and John L. Pfaltz. Sequential operations in digital picture processing.
Jornal of the ACM, 13(4):471–494, 1966.
[58] Gareth Loy and Alexander Zelinsky. Fast radial symmetry for detecting points of interest.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(8):959–973, 2003.
[59] Sonal Kothari, Qaiser Chaudry, and May D Wang. Automated cell counting and cluster segmentation using concavity detection and ellipse fitting techniques. InIEEE International Symposium on Biomedical Imaging (ISBI), pages 795–798, 2009.
[60] M. Pilu, A.W. Fitzgibbon, and R.B. Fisher. Ellipse-specific direct least-square fitting. In International Conference on Image Processing (ICIP), pages 599–602 vol.3, 1996.
[61] Andrew Fitzgibbon, Maurizio Pilu, and Robert B Fisher. Direct least square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(5):476–480, 1999.
[62] Radim Halır and Jan Flusser. Numerically stable direct least squares fitting of ellipses. In 6th International Conference in Central Europe on Computer Graphics and Visualization (WSCG), volume 98, pages 125–132, 1998.
[63] Eliseo Stefano Maini. Enhanced direct least square fitting of ellipses. International Journal of Pattern Recognition and Artificial Intelligence, 20(6):939–953, 2006.
[64] Radim Halir. Robust bias-corrected least squares fitting of ellipses. In 8th International Conference in Central Europe on Computer Graphics and Visualization (WSCG), 2000.
[65] Dilip K Prasad, Maylor KH Leung, and Chai Quek. Ellifit: An unconstrained, non-iterative, least squares based geometric ellipse fitting method. Pattern Recognition, 46(5):1449–
1465, 2013.
[66] Sung Joon Ahn, Wolfgang Rauh, and Hans-Jürgen Warnecke. Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition, 34(12):2283–2303, 2001.
[67] Paul D Sampson. Fitting conic sections to ”very scattere” data: An iterative refinement of the bookstein algorithm. Computer Graphics and Image Processing, 18(1):97–108, 1982.
[68] Hyungjun Park and Joo-Haeng Lee. B-spline curve fitting based on adaptive curve refine-ment using dominant points. Computer-Aided Design, 39(6):439–451, 2007.
[69] H Haron, A Rehman, DIS Adi, SP Lim, and T Saba. Parameterization method on b-spline curve. Mathematical Problems in Engineering, vol. 2012, Article ID 640472, 22 pages, 2012.
[70] Hyungjun Park. Choosing nodes and knots in closed b-spline curve interpolation to point data. Computer-Aided Design, 33(13):967–974, 2001.
[71] Xiao-Li Meng and Donald B Rubin. Maximum likelihood estimation via the ecm algorithm:
A general framework. Biometrika, 80(2):267–278, 1993.
[72] Qilong Zhang and Robert Pless. Segmenting multiple familiar objects under mutual oc-clusion. InIEEE International Conference on Image Processing (ICIP), pages 197–200, 2006.
[73] Sahirzeeshan Ali and Anant Madabhushi. An integrated region-, boundary-, shape-based active contour for multiple object overlap resolution in histological imagery. IEEE Trans-actions on Medical Imaging, 31(7):1448–1460, 2012.
[74] Tony F Chan and Luminita A Vese. Active contours without edges. IEEE Transactions on Image Processing, 10(2):266–277, 2001.
[75] Thomas Kailath. The divergence and bhattacharyya distance measures in signal selection.
IEEE Transactions on Communication Technology, 15(1):52–60, 1967.
[76] Seung seok Choi and Sung hyuk Cha. A survey of binary similarity and distance measures.
Journal of Systemics, Cybernetics and Informatics, 8(1):43–48, 2010.
[77] Microscopic image data analysis for nanoparticle size and shape information. http://
www.eng.fsu.edu/~chiwoo.park/, 2012. [Online; Accessed August -2014].
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Figure A1.1.Image # 01: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.2.Image # 02: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.3.Image # 03: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.4.Image # 04: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.5.Image # 05: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.6.Image # 06: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.7.Image # 07: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.8.Image # 08: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.9.Image # 09: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.10.Image # 10: (a) Segmentation result; (b) Size distribution comparison.
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Figure A1.11.Image # 11: (a) Segmentation result; (b) Size distribution comparison.