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Computación y Sistemas

versión impresa ISSN 1405-5546

Comp. y Sist. vol.10 no.3 México ene./mar. 2007




A Fuzzy Approach on Image Complexity Measure


Enfoque Difuso Para la Medición de la Complejidad de Imágenes


Mario Ignacio Chacón Murguía, Alma Delia Corral Sáenz and Rafael Sandoval Rodríguez


Chihuahua Institute of Technology, DSP & Vision Laboratory
Av. Tecnológico 2909
Chihuahua, Chih., México C.P. 31310 Tel.4–13–74–74 Ext 112 y 114


Article received on March 08, 2007; accepted on April 26, 2007



This paper describes a novel fuzzy based approach to determine the complexity of an image which is independent of a human perception criterion. The proposed method determines the complexity of an image based on the analysis of its edge level percentages. First, the method determines the complexity class of an image from among three classes, Little Complex, More or Less Complex, and Very Complex using centroids obtained from a fuzzy clustering process. Second, the membership value for that class is computed by a set of interval mapping functions. The method is very robust and consistent since it does not incorporate any a priori human evaluation of complexity. Results of the method show a correlation with human complexity values obtained in an independent evaluation test; however, the values obtained with our method are consistent and not subject to the viewer's subjectivity. The paper also shows promising results in applying the method to an application of determining the edges of images when compared with a crisp image complexity method.

Keywords: Image complexity, Fuzzy logic, Image processing.



Este artículo describe un nuevo enfoque basado en lógica difusa para determinar la complejidad de una imagen, el cual es independiente del criterio de la percepción humana. El método propuesto determinar la complejidad de una imagen mediante el análisis de los porcentajes de niveles de bordes de la imagen. El método determina primero la clase de complejidad de la imagen entre tres clases, Poco Compleja, Más o Menos Compleja y Muy Compleja usando centros de grupos obtenidos mediante un proceso de agrupamiento difuso. Después, el grado de pertenencia a esa clase es calculado mediante un conjunto de funciones de mapeo de intervalos. El método es muy robusto y consistente ya que no incorpora ninguna evaluación humana a priori de la complejidad. Los resultados del método muestran una correlación con los valores de complejidad asignados por observadores humanaos en una prueba de evaluación independiente, sin embargo, los valores obtenidos con el método propuesto son consistentes y no sujetos a la subjetividad del visor. El artículo presenta también resultados promisorios in la aplicación del método para la determinación de bordes de imágenes cuando se compara con un método de complejidad rígido.

Palabras clave: Complejidad de Imagen, Lógica Difusa, Procesamiento de Imágenes.





The authors appreciate the support of COSNET, and SEP–DGEST for the support of this research under grant 445.05–P.



1. Zadeh L.: Outline of a New Approach to the Analysis of Complex Systems and Processes, IEEE Tran. On Systems, Man, & Cybernetics 3(1) (1973) 28–44.        [ Links ]

2. Mendel J.: Fuzzy Logic Systems for Engineering: A Tutorial, Proceedings of the IEEE 83(3) (1995) 345–377.        [ Links ]

3. Kandel A., and Byatt W.: Fuzzy, Sets, Fuzzy Algebra, and Fuzzy Statistics, Proceedings of the IEEE 66(12) (1978) 1619–1639.        [ Links ]

4. Freeman J.: The Modeling of spatial relations, Computer Graphics and Image Processing 4 (1975) 156–171.        [ Links ]

5. Krishnapuram R., Keller J. M., and Ma Y.: Quantitative Analysis of Properties and Spatial Relations of Fuzzy Image Regions, IEEE Trans, on Fuzzy Systems 1(3) (1993) 222–233.        [ Links ]

6. Miyajima K., and Ralescu A.: Spatial Organization in 2D Segmented Images: Representation and Recognition of Primitive Spatial Relations, Fuzzy Sets and Systems 65(2/3) (1994) 225–236.        [ Links ]

7. Matsakis P., and Wendling L.: A New Way to Represent the Relative Position Between Areal Objects, IEEE Trans. on Pattern Analysis and Machine Intelligence 21(7) (1999) 634–643.        [ Links ]

8. Matsakis P., Keller J., Wendling L., Marjamaa J., and Sjahputera O., Linguistic Description of Relative Positions in Images, IEEE Trans. on Systems, Man and Cybernetics Part B 31(4) (2001) 573–588.        [ Links ]

9. Bloch L: ECVision– Specific Action Contribution to CCV Ontology: Dealing with Imprecise Spatial Information in Cognitive Vision (Unpublished manuscript, Ecole Nationale Supérieure des Télécommunications Département Traitement du Signal et des images, Paris France, 2003).        [ Links ]

10. Matsakis P., and Andréfouet S.: The fuzzy Between Line Between Among and Surround. In Proceeding of the 2002 IEEE International Conference on Fuzzy Systems, May 2002, 1596–1601.        [ Links ]

11. Bloch L: Fuzzy Spatial Relationships for Image Processing and Interpretation: a Review, Image and Vision Compute, 23 (2005) 89–110.        [ Links ]

12. Krishnapuram R., and Keller J. M.: Fuzzy Set Theoretic Approach to Computer Vision: An Overview. In: Proceedings of the FUZZ–IEEE, 1992, 135–142.        [ Links ]

13. Huntsberger T., Rangarajan C., and Jayaramamurthy S.: Representation of Uncertainty in Computer Vision Using Fuzzy Sets, IEEE Trans. On Computers C–35(2) (1986) 145–155.        [ Links ]

14. Lashkia V.: Defect Detection in X–ray Images Using Fuzzy Reasoning, Image and Vision Computer 19 (2001) 261–269.        [ Links ]

15. Pal S., and Sarbadhikari S.: Fuzzy Geometrical Features for Identifying Distorted Overlapping Fingerprints. In: Proceedings of the International Conference on Information, Communication and Signal, 1997, 1527–1531.        [ Links ]

16. Hata Y., Kobashi S., Hirano S., Kitagaki H., and Mori E.: Automated Segmentation of Human Brain MR Images Aided by Fuzzy Information Granulation and Fuzzy Inference, IEEE Trans. On System, Man, and Cybernetics C–30(3) (2000) 381–395.        [ Links ]

17. Ahmed M., Yamany S., Mohamed N., Farag A., and Moriarty T.: A Modified Fuzzy C–Means Algorithm for Bias field estimation and Segmentation of MRI Data, IEEE Trans. On Medical Imaging 21(3) (2002) 193–199.        [ Links ]

18. Park J., and Yae H.: Analysis of Active Features selection in Optic Nerve Data Using Labeled Fuzzy C–means Clustering. In: Proceedings of the IEEE International Joint Conference on Neural Networks, May 2002, 1178–1182.        [ Links ]

19. Ralescu A., and Shanaham J., Perceptual Organization for Inferring Object Boundaries in an Image, Pattern Recognition 32 (1999) 1923–1933.        [ Links ]

20. Johnson J., Olshausen R.: Time course of Neural Signatures of Object Recognition, Journal of Vision 3 (2003) 499–512.        [ Links ]

21. Boyle J., Maeder A., and Boles W., Visual Perception. In: 9th International Conference on Neural Information Processing of low Quality Images, Vol 1, November, 2002, 153–157.        [ Links ]

22. Peters II R., and Strickland R.: Image Complexity Metrics for Automatic Target Recognizers. In: ATR System and Technology Conference, October 1990, 1–17.        [ Links ]

23. Krishnapuram R., Medassani S., Jung S., Choi Y., and Balasubramaniam R., Content–Based Image Retrieval Based on a Fuzzy Approach, IEEE Transactions on Knowledge and Data Engineering 16(10) (2004) 1185–1199.        [ Links ]

24. Puniene J., Punys V., and Punys J., Ultrasound and Angio Image Compression by Cosine and Wavelet Transforms, International Journal of Medical Informatics 64(2–3) (2001)473–481.        [ Links ]

25. X. Yang, and C. Zhou, Analysis of the Complexity of Remote Sensing Image and Its Role on Image Classification. In: Proceedings of the IEEE Geoscience and Remote Sensing Symposium (IGARSS 2000), July 2000, 2179–2181.        [ Links ]

26. Seong Y. K., Choi Y., and Choi T., Scene–based Watermarking Method for Copy Protection Using Image Complexity and Motion Vector Amplitude. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, 409 – 412.        [ Links ]

27. Auffarth B., Muto Y., and Kunii Y.: An artificial system for visual perception in autonomous Robots. In: Proceedings of the IEEE International Conference on Intelligent Engineering Systems, September 2005, 211–216.        [ Links ]

28. Zadeh L.: Fuzzy Logic = Computing with Words, IEEE Trans. on Fuzzy Systems 4(2) (1996) 103–111.        [ Links ]

29. Hata Y., Kobashi S., Hirano S., Kitagaki H., and Mori E.: Automated Segmentation of Human Brain MR Images Aided by Fuzzy Information Granulation and Fuzzy Inference, IEEE Transactions on System Man, and Cybernetics C–30(3) (2000) 381–395.        [ Links ]

30. Chacón M., Aguilar L., and Delgado A.: Fuzzy Adaptive Edge Definition Based on the Complexity of the Image. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, December 2001, 675–678.        [ Links ]

31. Milanese R., Pun T., Gil S., and Bost J.–M.: Exploiting Dynamic Aspects of Visual Perception for Object Recognition. In: Proceedings of the Perception to Action Conference, 1994, 193–205.        [ Links ]

32. Freeman W. J.: A Neurobiological Theory of Meaning in Perception. In: Proceedings of the International Joint Conference, July 2003, 1373–1378.        [ Links ]

33. Chacón M., and Aguilar L.: A Fuzzy Approach to Edge Level Detection. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, December 2001, 809–812.        [ Links ]

34. Bezdek J. and Pal K.: Fuzzy Models for Pattern Recognition, Methods that Search for Structures in Data ( IEEE Press 1991).        [ Links ]

35. Pakhira M., Bandyopadhyay S., and Maulik U.: Validity Index for Crisp and Fuzzy Cluster, Pattern Recognition 31 (2004) 487–501.        [ Links ]

36. Corral A. D.: Modeling edge perception using fuzzy logic, Master Thesis, Chihuahua Institute of Technology, Mexico (2003).        [ Links ]

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