Histograms for Fuzzy Color Spaces

In this paper we introduce two kinds of fuzzy histograms on the basis of fuzzy colors in a fuzzy color space and the notion of gradual number by Dubois and Prade. Fuzzy color spaces are a collection of fuzzy sets providing a suitable, conceptual quantization with soft boundaries of crisp color spaces. Gradual numbers assign numbers to values of a relevance scale, typically [0,1]. Contrary to convex fuzzy subsets of numbers (called fuzzy numbers, but corresponding to fuzzy intervals as an assignment of intervals to values of [0,1]), they provide a more precise representation of the cardinality of a fuzzy set. Histograms based on gradual numbers are particularly well-suited for serving as input to another process. On the contrary, they are not the best choice when showing the information to a human user. For this second case, linguistic labels represented by fuzzy numbers are a better alternative, so we define linguistic histograms as an assignment of linguistic labels to each fuzzy color. We provide a way to calculate linguistic histograms based on the compatibility between gradual numbers and linguistic labels. We illustrate our proposals with some examples.

[1]  Daniel Sánchez,et al.  RL-numbers: An alternative to fuzzy numbers for the representation of imprecise quantities , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[2]  John Domingue,et al.  Artificial Intelligence: Methodology, Systems, and Applications, 12th International Conference, AIMSA 2006, Varna, Bulgaria, September 12-15, 2006, Proceedings , 2006, AIMSA.

[3]  Eduard Montseny,et al.  Obtaining the relevant colors of an image through stability-based fuzzy color histograms , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[4]  Didier Dubois,et al.  A Discussion of Indices for the Evaluation of Fuzzy Associations in Relational Databases , 2003, IFSA.

[5]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1993 .

[6]  Nikolaos D. Doulamis,et al.  Fuzzy histograms for efficient visual content representation: application to content-based image retrieval , 2001, IEEE International Conference on Multimedia and Expo, 2001. ICME 2001..

[7]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[8]  Daniel Sánchez,et al.  A new approach for defining a fuzzy color space , 2010, International Conference on Fuzzy Systems.

[9]  Kai-Kuang Ma,et al.  Fuzzy color histogram and its use in color image retrieval , 2002, IEEE Trans. Image Process..

[10]  Witold Pedrycz,et al.  Fuzzy Logic and Applications , 2013, Lecture Notes in Computer Science.

[11]  Maciej Wygralak.  Cardinalities of Fuzzy Sets , 2003 .

[12]  Thomas A. Runkler.  Fuzzy histograms and fuzzy chi-squared tests for independence , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[13]  Naotoshi Sugano,et al.  Color-naming system using fuzzy set theoretical approach , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[14]  Madjid Fathi,et al.  Knowledge-based fuzzy color processing , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

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

[16]  Bernard De Baets,et al.  Fuzzy Sets and Systems — IFSA 2003 , 2003, Lecture Notes in Computer Science.

[17]  D. Dubois,et al.  Fuzzy cardinality and the modeling of imprecise quantification , 1985 .

[18]  Didier Dubois,et al.  Gradual elements in a fuzzy set , 2008, Soft Comput..

[19]  T. John Stonham,et al.  Fuzzy colour category map for the measurement of colour similarity and dissimilarity , 2005, Pattern Recognit..

[20]  Daniel Sánchez,et al.  A probabilistic definition of a nonconvex fuzzy cardinality , 2002, Fuzzy Sets Syst..

[21]  Yong Yu,et al.  Deep into Color Names: Matching Color Descriptions by Their Fuzzy Semantics , 2006, AIMSA.

[22]  I. Andreadis,et al.  New fuzzy model for morphological colour image processing , 2002 .

[23]  Takashi Mitsuishi,et al.  Color construction using dual fuzzy system , 2003, The 3rd International Workshop on Scientific Use of Submarine Cables and Related Technologies, 2003..

[24]  Daniel Sánchez,et al.  Fuzzy Quantification Using Restriction Levels , 2009, WILF.

[25]  Daniel Sánchez,et al.  A novel histogram definition for fuzzy color spaces , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).