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Perceptual Indiscernibility, Rough Sets, Descriptively Near Sets, and Image Analysis

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Part of the Lecture Notes in Computer Science book series (TRS,volume 7255)

Abstract

The problem considered in this paper is how to discern and compare similarities in perceptually indiscernible objects in visual rough sets that are disjoint. The solution to the problem stems from the introduction of probe functions, object description, near set theory, perceptual systems, and perceptual indiscernibility relations. This leads to a new form of image analysis.

Keywords

  • Description
  • image analysis
  • near sets
  • perceptual indiscernibility relation
  • perceptual system
  • visual rough sets

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) research grant 185986.

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References

  1. Aggarwal, C.C., Hinneburg, A., Keim, D.A.: On the Surprising Behavior of Distance Metrics in High Dimensional Space. In: Van den Bussche, J., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 420–434. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  2. Benjamin Jr., L.T.: A Brief History of Modern Psychology. Blackwell Publishing, Malden (2007)

    Google Scholar 

  3. Beyer, K., Goldstein, J., Ramakrishnan, R., Shaft, U.: When Is Nearest Neighbor Meaningful? In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 217–235. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  4. Black, M.J., Kimia, B.B.: Guest editorial: Computational vision at brown. International Journal of Computer Vision 54(1-3), 5–11 (2003)

    CrossRef  Google Scholar 

  5. Borkowski, M.: 2D to 3D Conversion with Direct Geometrical Search and Approximation Spaces. Ph.D. thesis (2007)

    Google Scholar 

  6. Borkowski, M., Peters, J.F.: Matching 2D Image Segments with Genetic Algorithms and Approximation Spaces. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 63–101. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  7. Caicedo, J.C., González, F.A., Triana, E., Romero, E.: Design of a Medical Image Database with Content-Based Retrieval Capabilities. In: Mery, D., Rueda, L. (eds.) PSIVT 2007. LNCS, vol. 4872, pp. 919–931. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  8. Chatzichristofis, S.A., Arampatzis, A.: Late fusion of compact composite descriptors for retrieval from heterogeneous image databases. In: Proceedings of the 5th International Multi-Conference on Computing in the Global Information Technology, ICCGI. IEEE Computer Society (2010)

    Google Scholar 

  9. Chatzichristofis, S.A., Boutalis, Y.S.: CEDD: Color and Edge Directivity Descriptor: A Compact Descriptor for Image Indexing and Retrieval. In: Gasteratos, A., Vincze, M., Tsotsos, J.K. (eds.) ICVS 2008. LNCS, vol. 5008, pp. 312–322. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  10. Chatzichristofis, S.A., Boutalis, Y.S.: FCTH: Fuzzy color and texture histogram - a low level feature for accurate image retrieval. In: Proceedings of the 9th International Workshop on Image Analysis for Multimedia Interactive Services. IEEE Computer Society (2008)

    Google Scholar 

  11. Choraś, R.S., Andrysiak, T., Choraś, M.: Integrated color, texture and shape information for content-based image retrieval. Pattern Analysis & Applications 10(4), 333–343 (2007)

    CrossRef  Google Scholar 

  12. Christoudias, C., Georgescu, B., Meer, P.: Synergism in low level vision. In: Proceedings of the 16th International Conference on Pattern Recognition, vol. 4, pp. 150–156 (2002)

    Google Scholar 

  13. Comaniciu, D.: Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(5), 603–619 (2002)

    CrossRef  Google Scholar 

  14. Cover, T.M., Thomas, J.A.: Elements of information theory. John Wiley & Sons, Inc., New York (1991)

    CrossRef  MATH  Google Scholar 

  15. Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley (2001)

    Google Scholar 

  16. Fechner, G.T.: Elements of Psychophysics, vol. I. Hold, Rinehart & Winston, London, UK (1966); H.E. Adler’s trans. of Elemente der Psychophysik (1860)

    Google Scholar 

  17. Ferrer, M.A., Morales, A., Ortega, L.: Infrared hand dorsum images for identification. IET Electronic Letters 45(6), 306–308 (2009)

    CrossRef  Google Scholar 

  18. Gabbouj, M.: MUVIS a system for content-based indexing and retrieval in multimedia databases (2010), http://muvis.cs.tut.fi/index.html

  19. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentice-Hall, Toronto (2002)

    Google Scholar 

  20. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Person/Prentice Hall, Upper Saddle River (2008)

    Google Scholar 

  21. Grigorova, A., De Natale, F.G.B., Dagli, C., Huang, T.S.: Content-based image retrieval by feature adaptation and relevance feedback. IEEE Transactions on Multimedia 9(6), 1183–1192 (2007)

    CrossRef  Google Scholar 

  22. Guldogan, E.: Improving Content-Based Image Indexing and Retrieval Performance. Ph.d. dissertation (2009)

    Google Scholar 

  23. Gupta, S., Patnaik, K.: Enhancing performance of face recognition systems by using near set approach for selecting facial features. Journal of Theoretical and Applied Information Technology 4(5), 433–441 (2008)

    Google Scholar 

  24. Haralick, R.M.: Textural features for image classification. IEEE Transactions on Systems, Man, and Cybernetics SMC-3(6), 610–621 (1973)

    CrossRef  MathSciNet  Google Scholar 

  25. Haralick, R.M.: Statistical and structural approaches to texture. Proceedings of the IEEE 67(5), 786–804 (1979)

    CrossRef  Google Scholar 

  26. Hassanien, A.E., Abraham, A., Peters, J.F., Schaefer, G., Henry, C.: Rough sets and near sets in medical imaging: A review. IEEE Transactions on Information Technology in Biomedicine 13(6), 955–968 (2009)

    CrossRef  Google Scholar 

  27. Hausdorff, F.: Grundzüge der mengenlehre. Verlag Von Veit & Comp., Leipzig (1914)

    MATH  Google Scholar 

  28. Hausdorff, F.: Set theory. Chelsea Publishing Company, New York (1962)

    Google Scholar 

  29. Henry, C.: Near set Evaluation And Recognition (NEAR) system. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Analysis Foundations and Applications, pp. 7-1 – 7-22. CRC Press, Taylor & Francis Group (2010), http://wren.ee.umanitoba.ca

  30. Henry, C., Peters, J.F.: Image Pattern Recognition Using Near Sets. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 475–482. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  31. Henry, C., Peters, J.F.: Near set index in an objective image segmentation evaluation framework. In: Proceedings of the GEOgraphic Object Based Image Analysis: Pixels, Objects, Intelligence, pp. 1–8 (2008)

    Google Scholar 

  32. Henry, C., Peters, J.F.: Perception based image classification. Tech. rep., Computational Intelligence Laboratory, University of Manitoba, UM CI Laboratory Technical Report No. TR-2009-016 (2009)

    Google Scholar 

  33. Henry, C., Peters, J.F.: Perception-based image classification. International Journal of Intelligent Computing and Cybernetics 3(3), 410–430 (2010), Emerald Literati Network 2011 Award for Excellence

    CrossRef  MathSciNet  Google Scholar 

  34. Henry, C., Peters, J.F.: Perception image analysis. International Journal of Bio-Inspired Computation 2(3/4), 271–281 (2010)

    CrossRef  Google Scholar 

  35. Henry, C.J.: Near Sets: Theory and Applications. Ph.D. thesis (2010), https://mspace.lib.umanitoba.ca/handle/1993/4267

  36. Hergenhahn, B.R.: An Introduction to the History of Psychology. Wadsworth Publishing, Belmont (2009)

    Google Scholar 

  37. Howarth, P., Ruger, S.: Robust texture features for still-image retrieval. IEE Proceedings Vision, Image, & Signal Processing 152(6), 868–874 (2005)

    CrossRef  Google Scholar 

  38. Kasson, J.M., Plouffe, W.: An analysis of selected computer interchange color spaces. ACM Transactions on Graphics 11(4), 373–405 (1992)

    CrossRef  MATH  Google Scholar 

  39. Kendall, D.G., Barden, D., Crane, T.K., Le, H.: Shape and Shape Theory. John Wiley & Sons Ltd., Chichester (1999)

    CrossRef  MATH  Google Scholar 

  40. Khotanzad, A., Hong, Y.H.: Invariant image reconstruction by Zernike moments. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(5), 489–497 (1990)

    CrossRef  Google Scholar 

  41. Kim, W.Y., Kim, Y.S.: A region-based shape descriptor using Zernike moments. Signal Processing: Image Communication 16, 95–102 (2000)

    CrossRef  Google Scholar 

  42. Kiranyaz, S.: Advanced Techniques for Content-Based Management of Multimedia Databases. Ph.d. dissertation (2005)

    Google Scholar 

  43. Li, J., Wang, J.Z.: Automatic linguistic indexing of pictures by a statistical modeling approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(9), 1075–1088 (2003)

    CrossRef  Google Scholar 

  44. Maji, P., Pal, S.K.: Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 114–134. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  45. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, California (1999)

    MATH  Google Scholar 

  46. Mallat, S., Zhong, S.: Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(7), 710–732 (1992)

    CrossRef  Google Scholar 

  47. Małyszko, D., Stepaniuk, J.: Standard and Fuzzy Rough Entropy Clustering Algorithms in Image Segmentation. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 409–418. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  48. Malyszko, D., Stepaniuk, J.: Rough fuzzy measures in image segmentation and analysis. In: Pal, S.K., Peters, J.F. (eds.) Rough Fuzzy Analysis Foundations and Applications, pp. 11-1–11-25. CRC Press, Taylor & Francis Group (2010) ISBN 13: 9781439803295

    Google Scholar 

  49. Marcus, S.: Tolerance rough sets, Cech topologies, learning processes. Bulletin of the Polish Academy of Sciences: Technical Sciences 42(3), 471–487 (1994)

    MATH  Google Scholar 

  50. Marti, J., Freixenet, J., Batlle, J., Casals, A.: A new approach to outdoor scene description based on learning and top-down segmentation. Image and Vision Computing 19, 1041–1055 (2001)

    CrossRef  Google Scholar 

  51. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Visison, vol. 2, pp. 416–423 (2001), http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/

  52. Meghdadi, A.H., Peters, J.F., Ramanna, S.: Tolerance Classes in Measuring Image Resemblance. In: Velásquez, J.D., Ríos, S.A., Howlett, R.J., Jain, L.C. (eds.) KES 2009. LNCS, vol. 5712, pp. 127–134. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  53. Mrózek, A., Mrózek, L.: Rough sets in image analysis. Foundations of Computing and Decision Sciences F18(3-4), 268–273 (1993)

    Google Scholar 

  54. Muja, M.: FLANN - Fast Library for Approximate Nearest Neighbors (2009), http://www.cs.ubc.ca/~mariusm/index.php/FLANN/FLANN

  55. Muja, M., Lowe, D.G.: Fast approximate nearest neighbors with automatic algrorithm configuration. In: Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP), pp. 331–340 (2009)

    Google Scholar 

  56. Mushrif, M., Ray, A.K.: Color image segmentation: Rough-set theoretic approach. Pattern Recognition Letters 29(4), 483–493 (2008)

    CrossRef  Google Scholar 

  57. Naimpally, S.A.: Near and far. A centennial tribute to Frigyes Riesz. Siberian Electronic Mathematical Reports 6, A.1–A.10 (2009)

    Google Scholar 

  58. Naimpally, S.A., Warrack, B.D.: Proximity spaces. In: Cambridge Tract in Mathematics No. 59. Cambridge University Press, Cambridge (1970)

    Google Scholar 

  59. Nallaperumal, K., Banu, M.S., Christiyana, C.C.: Content based image indexing and retrieval using color descriptor in wavelet domain. In: International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2007), vol. 3, pp. 185–189 (2007)

    Google Scholar 

  60. Nieminen, J.: Rough tolerance equality and tolerance black boxes. Fundamenta Informaticae 11, 289–296 (1988)

    MathSciNet  MATH  Google Scholar 

  61. Orłowska, E.: Semantics of vague concepts. Applications of rough sets. Tech. Rep. 469, Institute for Computer Science, Polish Academy of Sciences (1982)

    Google Scholar 

  62. Orłowska, E.: Semantics of vague concepts. In: Dorn, G., Weingartner, P. (eds.) Foundations of Logic and Linguistics. Problems and Solutions, pp. 465–482. Plenum Pres, London (1985)

    Google Scholar 

  63. Orłowska, E.: Incomplete information: Rough set analysis. In: Studies in Fuzziness and Soft Computing, vol. 13. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  64. Pal, N.R., Pal, S.K.: Entropy: A new definition and its applications. IEEE Transactions on Systems, Man, and Cybernetics 21(5), 1260–1270 (1991)

    CrossRef  Google Scholar 

  65. Pal, N.R., Pal, S.K.: Some properties of the exponential entropy. Information Sciences 66, 119–137 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  66. Pal, S.K., Mitra, P.: Multispectral image segmentation using rough set initialized em algorithm. IEEE Transactions on Geoscience and Remote Sensing 11, 2495–2501 (2002)

    CrossRef  Google Scholar 

  67. Pal, S.K., Peters, J.F.: Rough Fuzzy Image Analysis: Foundations and Methodologies. CRC Press, Boca Raton (2010)

    MATH  Google Scholar 

  68. Pal, S.K., Shankar, B.U., Mitra, P.: Granular computing, rough entropy and object extraction. Pattern Recognition Letters 26(16), 401–416 (2005)

    CrossRef  Google Scholar 

  69. Pavel, M.: Fundamentals of Pattern Recognition. Marcel Dekker, Inc., NY (1993)

    MATH  Google Scholar 

  70. Pawlak, M.: Image analysis by moments: reconstruction and computational aspects. Wydawnictwo Politechniki, Wrocław (2006)

    MATH  Google Scholar 

  71. Pawlak, Z.: Classification of objects by means of attributes. Tech. Rep. PAS 429, Institute for Computer Science, Polish Academy of Sciences (1981)

    Google Scholar 

  72. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  73. Pawlak, Z., Peters, J.F.: Jak blisko (how near). Systemy Wspomagania Decyzji I 57, 109 (2002)

    Google Scholar 

  74. Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Information Sciences 177, 41–73 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  75. Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  76. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  77. Peters, J.F.: Classification of objects by means of features. In: Proceedings of the IEEE Symposium Series on Foundations of Computational Intelligence (IEEE SCCI 2007), pp. 1–8 (2007)

    Google Scholar 

  78. Peters, J.F.: Near sets. General theory about nearness of objects. Applied Mathematical Sciences 1(53), 2609–2629 (2007)

    MathSciNet  MATH  Google Scholar 

  79. Peters, J.F.: Near sets. Special theory about nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)

    MathSciNet  MATH  Google Scholar 

  80. Peters, J.F.: Classification of perceptual objects by means of features. International Journal of Information Technology & Intelligent Computing 3(2), 1–35 (2008)

    Google Scholar 

  81. Peters, J.F.: Discovering affinities between perceptual granules. l 2 norm-based tolerance near preclass approach. Advances in Man-Machine Interactions and Soft Computing 59, 43–54 (2009)

    CrossRef  Google Scholar 

  82. Peters, J.F.: Discovery of perceptually near information granules. In: Yao, J.T. (ed.) Novel Developments in Granular Computing: Applications of Advanced Human Reasoning and Soft Computation. Information Science Reference, Hersey (2009) (in press)

    Google Scholar 

  83. Peters, J.F.: Fuzzy Sets, Near Sets, and Rough Sets for Your Computational Intelligence Toolbox. In: Hassanien, A.-E., Abraham, A., Herrera, F. (eds.) Foundations of Comput. Intel. Vol. 2. SCI, vol. 202, pp. 3–25. Springer, Heidelberg (2009)

    Google Scholar 

  84. Peters, J.F.: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 1(4), 239–245 (2009)

    CrossRef  Google Scholar 

  85. Peters, J.F.: Corrigenda and addenda: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 2(5), 310–318 (2010)

    CrossRef  Google Scholar 

  86. Peters, J.F.: How near are zdzisław pawlak’s paintings? Merotopic distance between regions-of-interest. In: Skowron, A., Suraj, Z. (eds.) Commemorating Zdzisław Pawlak’s Life and Work, pp. 1–19. Springer, Berlin (2011) (communicated)

    Google Scholar 

  87. Peters, J.F., Borkowski, M.: k-means indiscernibility over pixels (2004)

    Google Scholar 

  88. Peters, J.F., Puzio, L.: Anisotropic wavelet-based image nearness measure. International Journal of Computational Intelligence Systems 2-3, 168–183 (2009)

    CrossRef  Google Scholar 

  89. Peters, J.F., Puzio, L., Szturm, T.: Measuring nearness of rehabilitation hand images with finely-tuned anisotropic wavelets. In: Choraś, R.S., Zabludowski, A. (eds.) Image Processing & Communication Challenges, pp. 342–349. Academy Publishing House, Warsaw (2009)

    Google Scholar 

  90. Peters, J.F., Ramanna, S.: Affinities between perceptual granules: Foundations and perspectives. In: Bargiela, A., Pedrycz, W. (eds.) Human-Centric Information Processing Through Granular Modelling, pp. 49–66. Springer, Berlin (2009)

    CrossRef  Google Scholar 

  91. Peters, J.F., Shahfar, S., Ramanna, S., Szturm, T.: Biologically-inspired adaptive learning: A near set approach. In: Frontiers in the Convergence of Bioscience and Information Technologies (2007)

    Google Scholar 

  92. Peters, J.F., Wasilewski, P.: Foundations of near sets. Info. Sci. 179(18), 3091–3109 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  93. Poincaré, H.: Science and Hypothesis. The Mead Project, Brock University (1905), L.G. Ward’s translation

    Google Scholar 

  94. Poincaré, H.: Mathematics and Science: Last Essays. Kessinger Publishing, N.Y (1963), J.W. Bolduc’s trans. of Dernières Pensées (1913)

    MATH  Google Scholar 

  95. Polkowski, L.: Rough Sets. Mathematical Foundations. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  96. Polkowski, L., Skowron, A., Zytkow, J.: Tolerance based rough sets. In: Lin, T.Y., Wildberger, A.M. (eds.) Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, pp. 55–58. Simulation Councils, Inc., San Diego (1995)

    Google Scholar 

  97. Ramanna, S., Meghdadi, A.H.: Measuring resemblances between swarm behaviours: A perceptual tolerance near set approach. Fundamenta Informaticae 95, 533–552 (2009)

    MathSciNet  Google Scholar 

  98. Ramanna, S., Peters, J.F.: Nearness of associated rough sets; Case study in image analysis. In: Peters, G., Lingras, P., Slezak, D., Yao, Y. (eds.) Selected Methods and Applications of Rough Sets in Management and Engineering, pp. 181–206. Springer, Berlin (2012)

    CrossRef  Google Scholar 

  99. Rucklidge, W.: Efficient Visual Recognition Using Hausdorff Distance. Springer (1996)

    Google Scholar 

  100. Sen, D., Pal, S.K.: Generalized rough sets, entropy, and image ambiguity measures. IEEE Transactions on Systems, Man, and Cybernetics - Part B 39(1), 117–128 (2009)

    CrossRef  Google Scholar 

  101. Shahfar, S.: Near Images: A Tolerance Based Approach to Image Similarity and Its Robustness to Noise and Lightening. M.sc. thesis (2011)

    Google Scholar 

  102. Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: Lin, T.Y., Wildberger, A.M. (eds.) Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, pp. 18–21. Simulation Councils, Inc., San Diego (1995)

    Google Scholar 

  103. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  104. Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., Jain, R.: Content-based image retrieval at the end of the early years. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(12), 1349–1380 (2000)

    CrossRef  Google Scholar 

  105. Sossinsky, A.B.: Tolerance space theory and some applications. Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications 5(2), 137–167 (1986)

    MathSciNet  Google Scholar 

  106. Szturm, T., Peters, J.F., Otto, C., Kapadia, N., Desai, A.: Task-specific rehabilitation of finger-hand function using interactive computer gaming. Archives of Physical Medicine and Rehabilitation 89(11), 2213–2217 (2008)

    CrossRef  Google Scholar 

  107. Tamura, H., Shunji, M., Yamawaki, T.: Textural features corresponding to visual perception. IEEE Transactions on Systems, Man, and Cybernetics 8(6), 460–473 (1978)

    CrossRef  Google Scholar 

  108. Teh, C.H., Chin, R.T.: On image analysis by the methods of moments. IEEE Transactions on Pattern Analysis and Machine Intelligence 10(4), 496–513 (1988)

    CrossRef  MATH  Google Scholar 

  109. Toharia, P., Robles, O.D., Rodríguez, Á., Pastor, L.: A Study of Zernike Invariants for Content-Based Image Retrieval. In: Mery, D., Rueda, L. (eds.) PSIVT 2007. LNCS, vol. 4872, pp. 944–957. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  110. Wang, J.Z., Li, J., Wiederhold, G.: SIMPLIcity: Semantics-sensitive integrated matching for picture libraries. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(9), 947–963 (2001)

    CrossRef  Google Scholar 

  111. Weber, M.: Leaves dataset: Images taken in and around caltech. Computational Vision at California Institute of Technology (2003), www.vision.caltech.edu/archive.html (permission received July 2008)

  112. Wolski, M.: Perception and classification. A Note on near sets and rough sets. Fundamenta Informaticae 101, 143–155 (2010)

    MathSciNet  MATH  Google Scholar 

  113. Zagoris, K.: img(Anaktisi) (2010), http://orpheus.ee.duth.gr/anaktisi/

  114. Zeeman, E.C.: The topology of the brain and the visual perception. In: Fort, K.M. (ed.) Topoloy of 3-manifolds and Selected Topices, pp. 240–256. Prentice Hall, New Jersey (1965)

    Google Scholar 

  115. Zervas, G., Ruger, S.M.: The curse of dimensionality and document clustering. In: IEE Colloguium on Microengineering in Optics and Optoelectronics, vol. 187, pp. 19/1–19/3 (1999)

    Google Scholar 

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Henry, C.J. (2012). Perceptual Indiscernibility, Rough Sets, Descriptively Near Sets, and Image Analysis. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XV. Lecture Notes in Computer Science, vol 7255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31903-7_3

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