Histogram Thresholding Using Fuzzy and Rough Measures of Association Error

• Published in: IEEE transactions on image processing Vol. 18; no. 4; pp. 879 - 888
• Main Authors: Sen, D., Pal, S.K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Edge extraction; Entropy; Error analysis; Errors; Exact sciences and technology; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; histogram thresholding; Histograms; Image edge detection; Image processing; Image segmentation; index of fuzziness; Information, signal and communications theory; Methodology; Partitioning algorithms; Region 1; Robustness; rough entropy; segmentation evaluation; Set theory; Signal processing; Studies; Telecommunications and information theory; Performance evaluation; Histogram; Tree algorithm; Error estimation; Image processing; Background; Threshold detection; Roughness; Entropy; Robust estimation; Tree structure; index of fuzziness; rough entropy; Image segmentation; Rough set theory; segmentation evaluation; Fuzzy set theory; Edge extraction; histogram thresholding; Multilevel system
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2009.2012890

This paper presents a novel histogram thresholding methodology using fuzzy and rough set theories. The strength of the proposed methodology lies in the fact that it does not make any prior assumptions about the histogram unlike many existing techniques. For bilevel thresholding, every element of the histogram is associated with one of the two regions by comparing the corresponding errors of association. The regions are considered ambiguous in nature, and, hence, the error measures are based on the fuzziness or roughness of the regions. Multilevel thresholding is carried out using the proposed bilevel thresholding method in a tree structured algorithm. Segmentation, object/background separation, and edge extraction are performed using the proposed methodology. A quantitative index to evaluate image segmentation performance is also proposed using the median of absolute deviation from median measure, which is a robust estimator of scale. Extensive experimental results are given to demonstrate the effectiveness of the proposed methods in terms of both qualitative and quantitative measures.