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Edge Detection Approach Based on Type-2 Fuzzy Images
Claudia I. Gonzalez, Patricia Melin, Juan R. Castro and Oscar Castillo

This paper presents a new fuzzy edge detection method applied on fuzzy images. The aim of this approach is that each pixel value in a digital image can be extended to be a fuzzy number; therefore, the images can be fuzzified using interval type-2 (IT2 FS), general type-2 (GT2 FS) and type-1 fuzzy sets (T1 FS). In an image processing system when an image is captured by any acquisition hardware, there are diverse factors that could introduce noise to the image (distance, environment and lighting) and consequently add uncertainty, varying the brightness or color information; so, in this approach the idea is to have a better handling of the imprecision that could exist in each numerical pixel.

Due to the fact that we are not sure if each pixel value is precise, we can add a level of uncertainty in the image processing and handle each crisp pixel as a fuzzy pixel. We are presenting results using different types of membership functions (MFs), Triangular and Trapezoidal for the T1 and IT2 FS. For the GT2 FS we use two types of MFs: Triangular on the primary MF and Gaussian in the secondary MFs and Trapezoidal on the primary MF and Gaussian in the secondary MFs. The parameters for the IT2 and GT2 MFs are obtained using a Genetic Algorithm. According with the results, we provide statistical evidence to confirm that the results achieved by the GT2 FS have a significant advantage with respect to the T1 and IT2 FS.

Keywords: Interval type-2 fuzzy sets, type-1 fuzzy sets, general type-2 fuzzy sets, fuzzy edge detection, fuzzy images.

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