Rough Fuzzy Image Analysis
Foundations and Methodologies

A new CRC Press book on rough fuzzy image analysis, foundations and applications is currently in press (available here).

This book introduces the foundations and applications in the state-of-art of rough-fuzzy image analysis. Fuzzy sets1 and rough sets2 as well as a generalization of rough sets called near sets3 provide important as well as useful stepping stones in various approaches to image analysis that are given in the chapters of this book. These three types of sets and various hybridizations provide powerful frameworks for image analysis.

Image analysis focuses on the extraction of meaningful information from digital images. This subject has its roots in studies of space and the senses by J.H. Poincaré during the early 1900s, studies of visual perception and the topology of the brain by E.C. Zeeman and picture processing by A.P. Rosenfeld4. The basic picture processing approach pioneered by A.P. Rosenfeld was to extract meaningful patterns in given digital images representing real scenes as opposed to images synthesized by the computer. Underlying picture processing is an interest in filtering a picture to detect given patterns embedded in digital images and approximating a given image with simpler, similar images with lower information content (this, of course, is at the heart of the near set-based image analysis). This book calls attention to the utility that fuzzy sets, near sets and rough sets have in image analysis. One of the earliest fuzzy set-based image analysis studies was published in 1982 by S.K. Pal5. The spectrum of fuzzy set-oriented image analysis studies includes edge ambiguity, scene analysis, image enhancement using smoothing, image description, motion frame analysis, medical imaging, remote sensing, thresholding and image frame analysis.

The application of rough sets in image analysis was launched in a seminal paper published in 1993 by A. Mrózek and L. Plonka6. Near sets are a recent generalization of rough sets that have proven to be useful in image analysis and pattern recognition7.

This volume fully reflects the diversity and richness of rough fuzzy image analysis both in terms of its underlying set theories as well as its diverse methods and applications. From the lead chapter by J.F. Peters and S.K. Pal, it can be observed that fuzzy sets, near sets and rough sets are, in fact, instances of different incarnations of Cantor sets. These three types of Cantor sets provide a foundation for what A. Rosenfeld points to as the stages in pictorial pattern recognition, i.e., image transformation, feature extraction and classification. The chapters by P. Maji and S.K. Pal on rough-fuzzy clustering and by D. Malyszko on rough-fuzzy measures point to the utility of hybrid approaches that combine fuzzy sets and rough sets in image analysis.

The chapters by D. Sen, S.K. Pal on rough set-based image thresholding, H. Fashandi, J.F. Peters on rough set-based mathematical morphology and M.M. Mushrif, A.K. Ray on image segmentation, illustrate how image analysis can be carried out with rough sets by themselves. Tolerance spaces and a perceptual systems approach in image analysis can be found in the papers by A.H. Meghdadi, J.F. Peters, S. Shahfar, and S. Ramanna (these papers carry forward the work on visual perception by J.H. Poincar´e and E.C. Zeeman). A rich harvest of applications of rough fuzzy image analysis can be found in the papers by C. Henry, A.E. Hassanien, A.H. Meghdadi, L. Miroslaw, T. Nakashima, G. Schaefer, S. Shahfar, and W. Tarnawski. Finally, a complete, downloadable implementation of near sets in image analysis called NEAR is presented by C. Henry.

Volume Editors:
Sankar K. Pal, Machine Intelligence Unit, Indian Statistical Institute, Calcutta, India, email:
James F. Peters, University of Manitoba, Canada, email:

1See, e.g., Zadeh, L.A., Fuzzy sets. Information and Control (1965), 8 (3) 338-353; Zadeh, L.A., Toward a theory of fuzzy granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems 90 (1997), 111-127. See, also, Rosenfeld, A., Fuzzy digital topology, in Bezdek, J.C., Pal, S.K., Eds., Fuzzy Models for Pattern Recognition, IEEE Press, 1991, 331-339; Banerjee, M., Kundu, M.K., Maji, P., Content-based image retrieval using visually significant point features, Fuzzy Sets and Systems 160, 1 (2009), 3323-3341; set
2See, e.g., Peters, J.F., Skowron, A.: Zdzis_law Pawlak: Life andWork, Transactions on Rough Sets V, (2006), 1-24; Pawlak, Z., Skowron, A.: Rudiments of rough sets, Information Sciences 177 (2007) 3-27; Pawlak, Z., Skowron, A.: Rough sets: Some extensions, Information Sciences 177 (2007) 28-40; Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning, Information Sciences 177 (2007) 41-73.; set
3See, e.g., Peters, J.F., Puzio, L., Image analysis with anisotropic wavelet-based nearness measures, Int. J. of Computational Intelligence Systems 79, 3-4 (2009), 1-17; Peters, J.F., Wasilewski, P., Foundations of near sets, Information Sciences 179, 2009, 3091-3109; sets. See, also,
4See, e.g., Rosenfeld, A.P., Picture processing by computer, ACM Computing Surveys 1, 3 (1969), 147-176
5 Pal, S.K., A note on the quantitative measure of image enhancement through fuzziness, IEEE Trans. on Pat. Anal. & Machine Intelligence 4, 2 (1982), 204-208.
6 Mrózek, A., Plonka, L., Rough sets in image analysis, Foundations of Computing and Decision Sciences 18, 3-4 (1993), 268-273.
7See,e.g., Gupta, S., Patnik, S., Enhancing performance of face recognition by using the near set approach for selecting facial features, J. Theor. Appl. Inform. Technol. 4, 5 (2008), 433-441; Henry, C., Peters, J.F., Perception-based image analysis, Int. J. Bio-Inspired Comp. 2, 2 (2009), in press; Peters, J.F., Tolerance near sets and image correspondence, Int. J. of Bio-Inspired Computation 4, 1 (2009), 239-245.