Abstract
The problem considered in this article is how to solve the image correspondence problem in cases where it is important to measure changes in the contour, position, and spatial orientation of bounded regions. This article introduces a computational intelligence approach to the solution of this problem with anisotropic (direction dependent) wavelets and a tolerance near set approach to detecting similarities in pairs of images. Near sets are a recent generalization of rough sets introduced by Z. Pawlak during the early 1980s. Near sets resulted from a study of the perceptual basis for rough sets. Pairs of sets containing objects with similar descriptions are known as near sets. The proposed wavelet-based image nearness measure is compared with F. Hausdorff and P. Mahalanobis image distance measures. The results of three wavelet-based image resemblance measures for several well-known images, are given. A direct benefit of this research is an effective means of grouping together (classifying) images that correspond to each other relative to minuscule similarities in the contour, position, and spatial orientation of bounded regions in the images, especially in videos containing image sequences showing varied object movements. The contribution of this article is the introduction of an anisotropic wavelet-based measure of image resemblance using a near set approach.
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V. Bruce, P. R. Green, M. A. Georgeson, Visual perception: physiology, psychology, and ecology, Psychology Press, Hove, East Sussex, UK, 1996.
E. J. Candès, D. L. Donoho, Curvelets – a surprisingly effective nonadaptive representation for objects with edges (1999). URL http://www-stat.stanford.edu/~donoho/Reports/1999/curveletsurprise.pdf
E. J. Candès, D. L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise-c2 singularities., Comm. Pure Appl. Math. 57 (2002) 219–266.
M. N. Do, M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing 14 (12) (2005) 2091–2106.
G. Brunner, Structure features for content-based image retrieval and classification problems, Ph.d. diss., Albert-Ludwigs-Universität Freiburg (2006).
H. Fashandi, J. Peters, S. Ramanna, l2 norm length-based image similarity measures: Concrescence of image feature histogram distances, Signal and Image Processing, (2009), in press.
J. Angulo, J. Serra, Morphological color size distribution for image classification and retrieval, in: Proc. Advanced Concepts for Intelligent Vision Systems, Ghent, Belgium, 2002.
T. Deselares, Features for image retrival, Phd diss., Rheinisch-Westfalische Technische Hochschule Aachen (2003).
W. Bartol, J. Miró, K. Pióro, F. Rosselló, On the coverings by tolerance classes, Inf. Sci. Inf. Comput. Sci. 166 (1–4) (2004) 193–211.
M. Geetha, S. Palanivel, Video classification and shot detection for video retrieval applications, International Journal of Computational Intelligence Systems 2 (1) (2009) 39–50.
S. N. Gerasin, V. V. Shlyakhov, S. V. Yakovlev, Set coverings and tolerance relations, Cybernetics and Sys. Anal. 44 (3) (2008) 333–340.
C. Gope, N. Kehtarnavaz, Affine invariant comparison of point-sets using convex hulls and hausdorff distances, Pattern Recogn. 40 (1) (2007) 309–320.
A. E. Hassanien, A. Abraham, J. F. Peters, G. Schaefer, C. Henry, Rough sets and near sets in medical imaging: A review, IEEE Transactions on Information Technology in Biomedicine (2009) digital object identifier:10.1109/TITB.2009.2017017, in press. URL http://ieeexplore.ieee.org/xpl/tocpreprint.jsp?isnumber=4358869&punumber=4233
F. Hausdorff, Dimension und äusseres mass, Math. Ann. 79 (1919) 157–179.
C. Henry, J. Peters, Near set evaluation and recognition (near) system, Tech. rep., Computationa Intelligence Laboratory, University of Manitoba, UM CI LABORATORY TECHNICAL REPORT No. TR-2009-015 (2000). URL http://wren.ee.umanitoba.ca/images/ci\_reports/reportci-2009-015.pdf
C. Henry, J. Peters, Perception-based image analysis, Int. J. of Bio-Inspired Computation 2 (2), in press.
C. Henry, J. F. Peters, Image pattern recognition using approximation spaces and near sets, in: Proc. of the Eleventh International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computer (RSFDGrC 2007), Joint Rough Set Symposium (JRS07), Lecture Notes in Artificial Intelligence, vol. 4482, 2007.
C. Henry, J. F. Peters, Near set index in an objective image segmentation evaluation framework, in: GEOgraphic Object Based Image Analysis: Pixels, Objects, Intelligence, University of Calgary, Alberta, 2008.
C. Henry, J. F. Peters, Near sets, Wikipedia. URL http://en.wikipedia.org/wiki/Near_sets
J. Ilonen, Supervised local image feature detection, Phd diss., Lappeenrannan teknillinen yliopisto, Lappeenranta (2007).
K. Jänich, Topology, Springer-Verlag, Berlin, 1984.
J. Kämäräinen, Feature extraction using gabor filters, Phd diss., Lappeenrannan teknillinen yliopisto, Lappeenranta (2003).
P. Mahalanobis, On tests and measures of group divergence i. theoretical formulae, J. and Proc. Asiat. Soc. of Bengal 26 (1930) 541–588.
P. Mahalanobis, On the generalized distance in statistics, Proc. Nat. Institute of Science (Calcutta) 2 (1936) 49–55.
S. G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999.
A. Meghdadi, J. Peters, S. Ramanna, Tolerance classes in measuring image resemblance, Intelligent Analysis of Images & Videos, (2009), in press.
E. Orłowska, Semantics of vague concepts. applications of rough sets, Tech. Rep. 469, Institute for Computer Science, Polish Academy of Sciences (1982).
E. Orłowska, Semantics of vague concepts, in: G. Dorn, P. Weingartner (eds.), Foundations of Logic and Linguistics. Problems and Solutions, Plenum Pres, London/NY, 1985, pp. 465–482.
M. Pavel, Fundamentals of Pattern Recognition, 2nd ed., Marcel Dekker, Inc., N.Y., U.S.A., 1993.
Z. Pawlak, Classification of objects by means of attributes, Tech. Rep. PAS 429, Institute for Computer Science, Polish Academy of Sciences (1981).
Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (1982) 341–356.
Z. Pawlak, J. Peters, Jak blisko (how near), Systemy Wspomagania Decyzji I (2002,2007) 57,109.
Z. Pawlak, A. Skowron, Rudiments of rough sets, Information Sciences 177 (2007) 3–27.
J. Peters, Classification of objects by means of features, in: Proceedings of the IEEE Symposium Series on Foundations of Computational Intelligence (IEEE SCCI 2007), Honolulu, Hawaii, 2007.
J. Peters, Near sets. general theory about nearness of objects, Applied Mathematical Sciences 1 (53) (2007) 2609–2629.
J. Peters, Near sets. special theory about nearness of objects, Fundamenta Informaticae 76 (2007) 1–27.
J. Peters, Classification of perceptual objects by means of features, Int. J. of Info. Technology & Intell. Computing 3 (2) (2008) 1–35.
J. Peters, Discovery of perceptually near information granules, in: J. T. Yao (ed.), Novel Developements in Granular Computing: Applications of Advanced Human Reasoning and Soft Computation, Information Science Reference, Hersey, N.Y., USA, 2009, p. in press.
J. Peters, Tolerance near sets and image correspondence, Int. J. of Bio-Inspired Computation 4 (1) (2009) 239–445.
J. Peters, L. Puzio, Measuring nearness of rehabilitation hand images with finely-tuned anisotropic wavelets, in: 1st Int. Conf. on Image Processing & Communications, Bydgoszcz, Poland, 2009.
J. F. Peters, Fuzzy sets, near sets, and rough sets for your computational intelligence toolbox, in: A.-E. Hassanien, A. Abraham, F. Herrera (eds.), Foundations of Computational Intelligence, Volume 2, Approximate Reasoning Series: Studies in Computational Intelligence, Vol. 202, Springer-Verlag, Berlin, 2009, iSBN: 978-3-642-01532-8.
J. F. Peters, L. Puzio, T. Szturm, Measuring nearness of rehabilitation hand images with finely-tuned anisotropic wavelets, Int. Conf. on Image Processing & Communication (2009) submitted.
J. F. Peters, S. Ramanna, Affinities between perceptual granules: Foundations and perspectives, in: A. Bargiela, W. Pedrycz (eds.), Human-Centric Information Processing Through Granular Modelling, Springer-Verlag, Berlin, 2008, pp. 49–66.
J. F. Peters, P. Wasilewski, Foundations of near sets, Information Sciences. An International Journal (2009) digital object identifier: doi:10.1016/j.ins.2009.04.018, in press. URL http://dx.doi.org/10.1016/j.ins.2009.04.018
H. Poincaré, The topology of the brain and the visual perception, Prentice Hall, New Jersey, 1965, in K.M. Fort, Ed., Topology of 3-manifolds and Selected Topics, 240–256.
L. Puzio, Adaptive edge extraction method for images, Ph.D. thesis, Military University of Technology in Warsaw (2008).
L. Puzio, A. Walczak, 2-d wavelet with position controlled resolution, in: Medical Imaging, vol. 5959, SPIE, Warsaw, 2005.
L. Puzio, A. Walczak, Adaptive edge detection method for images, Opto-Electronics Review 16 (1) (2008) 60–67.
C. Rogers, Hausdorff Measures, Cambridge, UK, Cambridge U Press, 1970.
W. Rucklidge, Efficient Visual Recognition Using the Hausdorff Distance, Springer-Verlag, Berlin, 1996.
C. Sanderson, K. Paliwal, Fast feature extraction method for robust face verification, Electronics Letters 38 (25) (2002) 1648–1650.
M. Schroeder, M. Wright, Tolerance and weak tolerance relations, Journal of Combinatorial Mathematics and Combinatorial Computing 11 (1992) 123–160.
Y. A. Shreider, Tolerance spaces, Cybernetics and Systems Analysis 6 (12) (1970) 153–758.
A. Skowron, J. Stepaniuk, Tolerance Approximation Spaces, Fundamenta Informaticae 27 (2/3) (1996) 245–253.
A. Sossinsky, Tolerance space theory and some applications, Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications 5 (2) (1986) 137–167.
V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, P. L. Dragotti, Directionlets: Anisotropic Multidirectional representation with separable filtering, IEEE Transactions on Image Processing 15 (7) (2006) 1916–1933.
V. D. Witte, S. Schulte, E. Kerre, New vector ordering in the redgreenblue colour model with application to morphological image magnification, International Journal of Computational Intelligence Systems 1 (2) (2008) 103–115.
E. Zeeman, The topology of the brain and the visual perception, Prentice Hall, New Jersey, 1965, in K.M. Fort, Ed., Topology of 3-manifolds and Selected Topics, 240–256.
Z. Zheng, H. Hu, Z. Shi, Tolerance Relation Based Granular Space, Lecture Notes in Computer Science 3641 (2005) 682.
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Anisotropic Wavelet-Based Image Nearness Measure
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Peters, J.F., Puzio, L. Anisotropic Wavelet-Based Image Nearness Measure. Int J Comput Intell Syst 2, 168–183 (2009). https://doi.org/10.2991/ijcis.2009.2.3.1
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DOI: https://doi.org/10.2991/ijcis.2009.2.3.1