A fuzzy approach to the evaluation of image complexity

The inherently multidimensional problem of evaluating the complexity of an image is of a certain relevance in both computer science and cognitive psychology. Computer scientists usually analyze spatial dimensions in order to deal with automatic vision problems, such as feature extraction. Psychologists seem more interested in the temporal dimension of complexity, as a means to explore attentional models. Is it possible to define, by merging both approaches, a more general index of visual complexity? The aim of this paper is the definition of objective measures of image complexity that fits with the so named perceived time. Towards the end we have defined a fuzzy mathematical model of visual complexity, based on fuzzy measures of entropy; the results obtained by applying this model to a set of pictorial images present a strong correlation with the outcomes of an experiment with human subjects, based on variation of subjective temporal estimations associated with changes in visual attentional load, which is also described herein.

[1]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[2]  Mateu Sbert,et al.  An Information-Theoretic Framework for Image Complexity , 2005, CAe.

[3]  F Masulli,et al.  Ambiguity and structural information in the perception of reversible figures , 1989, Perception & psychophysics.

[4]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[5]  Maurizio Cardaci The mental clock model , 2000 .

[6]  Sisir Roy,et al.  Fuzzy Measures for Image Distances Corresponding Author , .

[7]  Emanuel Leeuwenberg,et al.  An Outline of Coding Theory , 1983 .

[8]  David E. Irwin Information integration across saccadic eye movements , 1991, Cognitive Psychology.

[9]  Vito Di Gesù,et al.  Detection of regions of interest via the Pyramid Discrete Symmetry Transform , 1996, TFCV.

[10]  John K. Tsotsos,et al.  Neurobiology of Attention , 2005 .

[11]  Ahmed Bouridane,et al.  Scale Adaptive Complexity Measure of 2D Shapes , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[12]  Abel G. Oliva,et al.  Gist of a scene , 2005 .

[13]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 1997, Texts in Computer Science.

[14]  R. Yager ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval , 1979 .

[15]  Dennis W. Ruck,et al.  Science of Artificial Neural Networks , 1992 .

[16]  James C. Bezdek,et al.  Measuring fuzzy uncertainty , 1994, IEEE Trans. Fuzzy Syst..

[17]  R. Ornstein The Psychology of Consciousness , 1972 .

[18]  Christopher M. Brown Advances in computer vision , 1987 .

[19]  I. Mario,et al.  Image complexity measure: a human criterion free approach , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[20]  A. Kaufman,et al.  Introduction to the Theory of Fuzzy Subsets. , 1977 .

[21]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[22]  A. Kolmogorov Three approaches to the quantitative definition of information , 1968 .

[23]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.

[24]  Maria Petrou,et al.  The Differentiating Filter Approach to Edge Detection , 1994 .

[25]  Jiu-Lun Fan,et al.  Some new fuzzy entropy formulas , 2002, Fuzzy Sets Syst..

[26]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[27]  Sankar K. Pal,et al.  Fuzzy Mathematical Approach to Pattern Recognition , 1986 .

[28]  James C. Bezdek,et al.  Quantifying Different Facets of Fuzzy Uncertainty , 2000 .

[29]  Michael L. Mack,et al.  Identifying the Perceptual Dimensions of Visual Complexity of Scenes , 2004 .

[30]  M. Marinaro,et al.  Visual Attention Mechanisms , 2002, Springer US.

[31]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[32]  Massimo Riani,et al.  Boltzmann distributions and neural networks: models of unbalanced interpretations of reversible patterns , 1992, Defense, Security, and Sensing.

[33]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[34]  A. Bonaert Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[35]  Vito Di Gesù,et al.  Symmetry operators in computer vision , 1996 .

[36]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.