A narrow band interval type-2 fuzzy approach for image segmentation

• With the extension of traditional fuzzy sets into interval type-2 fuzzy sets, uncertain knowledge or information of an image will be well described by uncertain membership values.
• Pixels within a small selected region are updated at each iteration, which enables the contour to evolve gradually and reduces the computational cost on the employment of the interval type-2 fuzzy set.
• The spatial constraint providing more image details has been intensively used in image segmentation algorithms. In the proposed model, the weighted fuzzy factor which takes both spatial and gray constraints into consideration is designed for computing the type-2 fuzzy membership value.

Traditional fuzzy sets capture vagueness through precise numeric membership degrees. This poses a dilemma of excessive precision in describing uncertain phenomenon. Interval type-2 fuzzy sets have shown its effectiveness in handling uncertainties in comparison to the traditional fuzzy sets. In this paper, the interval type-2 fuzzy approach is introduced into the framework of active contour model, which effectively segment images with large uncertainties. However, the computational cost is largely increased by employing the interval type-2 fuzzy set. Therefore, we try to update the pixels within a narrow band region near the contour boundary for reducing the computational cost caused by employing the interval type-2 fuzzy set. Moreover, both spatial and gray constraints are taken into consideration when calculating the fuzzy membership value to retain more image details. Experimental results on synthetic and real images show that the proposed method is effective and efficient, and is relatively independent of initial conditions.