Applying Weighted Mean Aggregation to Edge Detection of Images

This paper applies weighted mean to construct interval-valued fuzzy relations for grayscale image edge detection. This fuzzy relation image shows the changes in intensity values between a 3x3 window central pixel and its eight neighbor pixels. We employ two weighting parameters, and perform the weighted mean aggregation for the central pixel and its eight neighbor pixels in a sliding window across the image to lead to the fuzzy edge images. Finally, the image edge map is obtained through a threshold operation. Moreover, to decrease the edge detection error, weighting parameters of the mean can be learned by the gradient method caste in discrete formulation. By the training results of eight grayscale synthetic images with adding random noises, we have shown that the integration of interval-valued fuzzy relations with the weighted mean aggregation algorithm will produce a more robust response in detecting the image edge. Finally, by applying the optimal edge detection parameters to natural images, we have found that it is better compared to the well-known Canny edge detector.