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Relative Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation
November 2002 (vol. 24 no. 11)
pp. 1485-1500

Disclaimer
A claim of priority in research and publication appeared on page 1486 in the paper "Relative Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation" by J.K. Udupa, P.K. Saha, and R.A. Lotufo (IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 11, pp. 1485-1500, Nov. 2002) with respect to the paper "Multiseeded Segmentation Using Fuzzy Connectedness" by G.T. Herman and B.M. Carvalho (IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 5, pp. 460-474, May 2001). Furthermore, the wording of this claim suggests professional misconduct on the part of G.T. Herman and B.M. Carvalho.
Responsibility for the content of published papers rests with the authors. The peer review process is intended to determine the overall significance of the technical contribution of a manuscript. The peer review process does not provide a way to validate every statement in a manuscript. In particular, the IEEE has not validated the claim referred to in the first paragraph above. The IEEE regrets publishing this unauthenticated statement and the pain that such publication may have caused to G.T. Herman and B.M. Carvalho.

Abstract—The notion of fuzzy connectedness captures the idea of "hanging-togetherness" of image elements in an object by assigning a strength of connectedness to every possible path between every possible pair of image elements. This concept leads to powerful image segmentation algorithms based on dynamic programming whose effectiveness has been demonstrated on 1,000s of images in a variety of applications. In the previous framework, a fuzzy connected object is defined with a threshold on the strength of connectedness. In this paper, we introduce the notion of relative connectedness that overcomes the need for a threshold and that leads to more effective segmentations. The central idea is that an object gets defined in an image because of the presence of other co-objects. Each object is initialized by a seed element. An image element c is considered to belong to that object with respect to whose reference image element c has the highest strength of connectedness. In this fashion, objects compete among each other utilizing fuzzy connectedness to grab membership of image elements. We present a theoretical and algorithmic framework for defining objects via relative connectedness and demonstrate utilizing the theory that the objects defined are independent of reference elements chosen as long as they are not in the fuzzy boundary between objects. An iterative strategy is also introduced wherein the strongest relative connected core parts are first defined and iteratively relaxed to conservatively capture the more fuzzy parts subsequently. Examples from medical imaging are presented to illustrate visually the effectiveness of relative fuzzy connectedness. A quantitative mathematical phantom study involving 160 images is conducted to demonstrate objectively the effectiveness of relative fuzzy connectedness.

[1] Z.H. Cho, J.P. Jones, and M. Sing, Foundation of Medical Imaging. New York: John Wiley&Sons, 1993.
[2] N.R. Pal and S.K. Pal, “A Review of Image Segmentation Techniques,” Pattern Recignition, vol. 26, pp. 1277-1294, 1993.
[3] J.K. Udupa and S. Samarasekera, “Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation,” Graphic Models Image Processing, vol. 58, pp. 246-261, 1996.
[4] S.P. Raya, “Low-Level Segmentation of 3D Magnetic Resonance Brain Images—A Rule-Based System,” IEEE Trans. Medical Imaging, vol. 9, no. 3, pp. 327-337, 1990.
[5] L. Gong and C. Kulikowski, “Composition of Image Analysis Processes through Object-Centered Hierarchical Planning,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 997-1009, 1995.
[6] M. Kamber, R. Singhal, D. Collins, G. Francis, and A. Evans, “Model-Based 3D Segmentation of Multiple Sclerosis Lesions in Magnetic Resonance Brain Images,” IEEE Trans. Medical Imaging, vol. 4, pp. 442-453, 1995.
[7] J. Gee, M. Reivich, and R. Bajcsy, “Elastically Deforming 3D Atlas to Match Anatomical Brain Images,” J. Computer Assisted Tomography, vol. 17, pp. 225-236, 1993.
[8] G. Christensen, R. Rabbitt, and M. Miller, “3-D Brain Mapping Using a Deformable Neuroanatomy,” Physical Medical Biology, vol. 39, pp. 609-618, 1994.
[9] U. Montanari, “On the Optimal Detection of Curves in Noisy Pictures,” Comm. ACM, vol. 15, no. 5, pp. 335-345, 1971.
[10] J. Cappelletti and A Rosenfeld, “Three-Dimensional Boundary Following,” Computer Vision Graphics and Image Processing, vol. 48, pp. 80-92, 1989.
[11] A.X. Falcão, J.K. Udupa, S. Samarasekera, and S. Sharma, “User-Steered Image Segmentation Paradigms: Live Wire and Live Lane,” Graphical Models Image Processing, vol. 60, pp. 233-260, 1998.
[12] N. Otsu, “A Threshold Selection Method from Gray-Level Histogram,” IEEE Trans. Systems, Man, and Cybernetics, vol. 9, pp. 62-66, 1979.
[13] T. Hong and A. Rosenfeld, “Compact Region Extraction Using Weighted Pixel Linking in a Pyramid,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 222-229, 1984.
[14] H. Soltanian-Zadeh, J. Windham, and D. Peck, “A Comparative Analysis of Several Transformations for Enhancement and Segmentation of Magnetic Images,” IEEE Trans. Medical Imaging, vol. 11, pp. 302-318, 1992.
[15] J.K. Udupa, L. Wei, S. Samarasekera, Y. Miki, M.A. van Buchem, and R.I. Grossman, “Multiple Sclerosis Lesion Quantification Using Fuzzy-Connectedness Principles,” IEEE Trans. Medical Imaging, vol. 16, pp. 598-609, 1997.
[16] S. Samarasekera, J.K. Udupa, Y. Miki, and R.I. Grossman, “A New Computer-Assisted Method for Enhancing Lesion Quantification in Multiple Sclerosis,” J. Computer Assisted Tomography, vol. 21, pp. 145-151, 1997.
[17] Y. Miki, R.I. Grossman, J.K. Udupa, M.A. van Buchem, L. Wei, M.D. Philips, U. Patel, J.C. McGown, and D.L. Kolson, “Differences Between Relapsing Remitting and Chronic Progressive Multiple Sclerosis as Determined with Quantitative MR Imaging,” Radiology, vol. 210, pp. 769-774, 1999.
[18] B.L. Rice and J.K. Udupa, “Clutter-Free Volume Rendering for Magnetic Resonance Angiography Using Fuzzy Connectedness,” Int'l J. Imaging Systems and Technology, vol. 11, pp. 62-70, 2000.
[19] T. Lei, J.K. Udupa, P.K. Saha, and D. Odhner, “Artery-Vein Separation via MRA—An Image Processing Approach,” IEEE Trans. Medical Imaging, vol. 20, pp. 689-703, 2001.
[20] P.K. Saha, J.K. Udupa, E.F. Conant, D.P. Chakraborty, and D. Sullivan, “Breast Tissue Density Quantification via Digitized Mammograms” IEEE Trans. Medical Imaging, vol. 20, pp. 792-803, 2001.
[21] J.K. Udupa, J. Tian, D. Hemmy, and P. Tessier, “A Pentium PC-Based Craniofacial 3D Imaging and Analysis System,” J. Craniofacial Surgery, vol. 8, pp. 333-339, 1997.
[22] R. Cannon, J. Dave, and J. Bezdek, “Efficient Implementation of the Fuzzyc-means Clustering Algorithms,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 248-255, 1986.
[23] L. Hall, A. Bensaid, L. Clarke, R. Velthuizen, M. Silbiger, and J. Bezdek, “A Comparison of Neural Networks and Fuzzy Clustering Techniques in Segmenting Magnetic Resonance Images of the Brain,” IEEE Trans. Neural Networks, vol. 3, pp. 672-683, 1992.
[24] A. Rosenfeld, “Fuzzy Digital Topology,” Information Control, vol. 40, pp. 76-87, 1979.
[25] I. Bloch, “Fuzzy Connectivity and Math. Morphology,” Pattern Recognition Letters, vol. 14, pp. 483-488, 1993.
[26] S. Dellepiane and F. Fontana, “Extraction of Intensity Connectedness for Image Processing,” Pattern Recognition Letters, vol. 16, pp. 313-324, 1995.
[27] P.K. Saha and J.K. Udupa, “Relative Fuzzy Connectedness among Multiple Objects: Theory, Algorithms, and Applications in Image Segmentation,” Computer Vision and Image Understanding, vol. 82, pp. 42-56, 2001.
[28] J.K. Udupa, P.K. Saha, and R.A. Lotufo, “Fuzzy Connected Object Definition in Images with Respect to Co-Objects,” Proc. Int'l Soc. for Optical Eng. (SPIE) Conf. Medical Imaging, vol. 3661, pp. 236-245, 1999.
[29] P.K. Saha and J.K. Udupa, “Iterative Relative Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation,” Proc. IEEE Workshop Math. Methods in Biomedical Image Analysis, pp. 28-35, 2000.
[30] G.T. Herman and B.M. De Carvalho, “Multiseeded Segmentation Using Fuzzy Connectedness,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, pp. 460-474, 2001.
[31] A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, vol. 1,New York: Academic Press, 1975.
[32] P.K. Saha, J.K. Udupa, and D. Odhner, “Scale-Based Fuzzy Connected Image Segmentation: Theory, Algorithms, and Validation,” Computer Vision Image Understanding, vol. 77, pp. 145-174, 2000.
[33] S.M. Pizer, D. Eberly, D.S. Fritsch, and B.S. Morse, “Zoom-Invariant Vision of Figural Shape: the Mathematics of Cores,” Computer Vision and Image Understanding, vol. 69, no. 1, pp. 55-71, 1998.
[34] J.H. Elder and S.W. Zucker, Local Scale Control for Edge Detection and Blur Estimation IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 7, pp. 699-716, July 1998.
[35] P. Liang and Y.F. Wang, “Local Scale Controlled Anisotropic Diffusion with Local Noise Estimate for Image Smoothing and Edge Detection,” Proc. Int'l Conf. Computer Vision, pp. 193-200, 1998.
[36] M. Tabb and N. Ahuja, “Multiscale Image Segmentation by Integrated Edge and Region Detection,” IEEE Trans. Image Processing, vol. 6, no. 5, pp. 642-655, 1997.
[37] P.K. Saha and J.K. Udupa, “Iterative Relative Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation,” TR: MIPG-269, Medical Image Processing Group, Dept. Radiology, Univ. of Pennsylvania, Philadelphia, 2000.
[38] D.A. Bluemke, R.D. Darrow, R. Gupta, S.K. Tadikonda, and C.L. Dormoulin, “3D Contrast Enhanced Phase Contrast Angiography: Utility for Artery/Vein Separation,” ISMRM Proc., vol. 2, p. 1237, 1999.
[39] T. Lei, J.K. Udupa, P.K. Saha, D. Odhner, R. Baum, S.T. Tadikonda, and E.K. Yucel, “3D MRA Visualization and Artery-Vein Separation Using Blood-Pool Contrast Agent MS-325,” Academic Radiology, vol. 9,(suppl. 1), pp. S127-S133, 2002.
[40] J.K. Udupa and D. Odhner, “Shell Rendering,” IEEE Computer Graphics and Applications, vol. 13, no. 6, pp. 58-67, 1993.
[41] J.K Udupa, D. Odhner, S. Samarasekera, R.J. Goncalves, K. Iyer, K. Venugopal, and S. Furuie, “3DVIEWNIX: An Open, Transportable, Multidimensional, Multimodality, Multiparametric Imaging System,” Proc. Int'l Soc. for Optical Eng. (SPIE) Conf., vol. 2164, pp. 58-73, 1994.
[42] Y. Zhuge, J.K. Udupa, and P.K. Saha, “Vectorial Scale Based Fuzzy Connectedness for Segmenting Anatomical Structures in Visible Human Color Data Sets,” Proc. Int'l Soc. for Optical Eng. (SPIE), Conf. Medical Imaging, 2002.

Index Terms:
Fuzzy connectedness, image segmentation, object definition, digital topology.
Citation:
Jayaram K. Udupa, Punam K. Saha, Roberto A. Lotufo, "Relative Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 11, pp. 1485-1500, Nov. 2002, doi:10.1109/TPAMI.2002.1046162
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