Journal of Intelligent & Fuzzy Systems 28 (2015) 2269–2277 DOI:10.3233/IFS-141509 IOS Press 2269 Fuzzy mathematical morphology using triangular operators and its application to images Tamalika Chaira ∗ Centre for Biomedical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India Abstract. This paper presents a fuzzy morphological approach to detect the edges of real time images in order to preserve their features. Edge detection on these kinds of images is a difficult task where the edges/regions are vaguely visible. Especially, when these images are mixed with noise, detection becomes much more difficult. In this method, real time images are considered to be intuitionistic as the structures are not clear. Non membership degrees of an intuitionistic fuzzy image are computed using Sugeno type intuitionistic fuzzy generator. Then it uses triangular operators (product t-norms and conorms, Hamacher and Dombi t-norms and t-conorms) for computing morphological dilation and erosion. The method highlights almost all the edges of both normal (without noise) images and noisy images and the gradient images almost do not contain noise. Experiments have been performed qualitatively and quantitatively on several medical and human face images using triangular operators (product t-norms and conorms, Hamacher and Dombi t- norms and t-conorms) and the results are compared with gradient images using i) fuzzy morphology with Lukasiewicz t-norms and t-conorms, ii) fuzzy morphology with product t-norms and t-conorms, iii) median filter based edge detection method, and iii) interval valued fuzzy relation based edge detection method. It is observed that the gradient image using fuzzy morphology with Hamacher t-norm and t-conorm performs better in noisy environment. Keywords: Atanassov’s’s intuitionistic fuzzy set, sugeno type generator, hamacher t- norm and t-conorm, product t-norm and t-conorm, interval valued fuzzy relation, fuzzy morphology, gradient image 1. Introduction Edge detection is an essential and fundamental part in image processing application because edges represent important contour features in an image. Over the years different methods are proposed to extract the edges of the image. For example Sobel, Prewitt, Roberts [11], Canny [7] operators are used to find gradient image. Laplacian operator [11] uses a second-order differential operator to find edge points based on the zero-crossing properties. ∗ Corresponding author. Tamalika Chaira, Centre for Biomedical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. Tel.: +91 11 2659 7242; Fax: +91 11 2658 2037; E-mail: tchaira@yahoo.com. Mathematical morphology is a type of mathematical theory that can be used to process and analyze images. Mathematical morphology has been used in edge detec- tion for finding contour features in an image. Bouchet et al. [5] proposed a top-hat mathematical morpholog- ical operator to extract thin edge features of an image. Hidalgo et al. [12] proposed a method that uses Top- hat transformation to highlight certain features of an image. He [13] also proposed discrete t norms and its application to images. Zhao et al. [22] proposed a mor- phological edge detection algorithm that works in noisy environment. Pahsa [17] suggested dilation and erosion using Sakawa and Yumine’s membership function. Xu [19] enhanced and detected the edges of an image using median filter. There is also a work by Bustince et al. [3] 1064-1246/15/$35.00 © 2015 – IOS Press and the authors. All rights reserved