Applying Weighted Generalized Mean Aggregation and Learning Rule to Edge Detection of Images

Abstract

在這篇論文中，我們運用廣義加權平均建立區間值模糊關係，進行灰階影像邊緣偵測，並推導參數的學習法則以達成影像邊緣偵測。 我們的邊緣偵測方法包含三個部分。第一部分，在 滑動視窗中，我們利用上限與下限建構子計算中心像素和其八鄰域像素的加權平均集成運算，建立區間值模糊關係，及可指出相對應像素強度值變化程度的W模糊關係。第二部分，我們藉著離散型梯度演算法的概念進行加權平均參數的學習與更新，並引入口袋演算法(pocket algorithm)獲得最佳的參數集合。最後，我們運用後處理技術，包括增強邊緣的連接性並移除孤立的像素，以獲得較好的邊緣影像。從六張添加隨機雜訊的灰階合成影像訓練結果顯示，我們的方法產生較穩定且強健的邊緣偵測;並且我們的方法對自然影像的邊緣偵測，比著名的Canny邊緣偵測器顯示出更清楚的細節。

In this paper, we apply generalized weighted mean to construct interval-valued fuzzy relations for grayscale image edge detection and derive the learning formulas for parameters in order to decrease the edge detection error. The proposed detector consists of three stages. In the first stage, we use the upper and lower constructors to calculate the weighted mean aggregations of the central pixel and its eight neighbor pixels in each sliding window. Then we construct the interval-valued fuzzy relation and its associated W-fuzzy relation indicating the degree of intensity variation between the center pixel and its neighborhood. In the second stage, we update the weighting parameters of the mean which can be learned by the gradient method casted in discrete formulation and utilize pocket algorithm to obtain the optimal parameter set for all training images. Finally, we use post-processing techniques to strengthen the connectivity of edges and remove isolated pixels for obtaining better edge images. Our method produces a more stable and robust edge images on synthetic images and nature images as well, in comparison with the well-known Canny edge detector.