應用廣義模糊加權平均集成運算於影像脈衝雜訊去除

Abstract

本論文應用加權平均集成運算建立的區間值模糊關係進行灰階影像和彩色影像的雜訊點偵測。在一開始，我們使用兩個加權參數，對整張影像以 視窗內中心像素和其八鄰域像素進行加權平均集成運算並得到模糊關係影像。最後經由門檻值作用後，進而判斷像素是否為雜訊點。此外，為了減少誤判雜訊或像素之個數，我們在訓練階段中針對加權參數與門檻值推導出一套遞迴反覆的學習機制，最後我們將口袋演算法嵌入至學習機制中，藉此訓練出最佳的加權參數與門檻值，讓非雜訊點與雜訊點的誤判個數能夠最小化。 測試階段可以分為3個部分：分別為影像直方圖統計、雜訊點偵測、影像修復。首先我們先計算測試影像直方圖之峯處並找出可能的雜訊點群。接著，針對這些可能的雜訊點群，我們使用訓練階段所得的最佳參數進行重覆檢驗，偵測此點是否為雜訊點。除此之外，我們也使用加權平均法將訓練時所得到的資料結合起來，稱之為加權平均分數方法，以增加雜訊點偵測的正確率。換句話說，在測試階段時我們不只使用所得到的最佳參數，也使用在訓練階段所得到的資料。最後，如果像素點被判為雜訊點，此點會使用加權平均濾波器所修復。並且根據結果，相對於其他的現有的演算法，我們的方法能夠有效的偵測雜訊點並修復。

In this thesis, we have porposed weighted mean aggregation to construct interval-valued fuzzy relation for grayscale and color images noise detection. In the beginning, 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 images. In the end, the image noise map is obtained through a suitable thresholding. Moreover, to decrease the noisy and un-contaminated pixel detection error, we have derived the iterative learning mechanism of these weighting parameters of the mean aggregation and thresholds in the training stage. Finally, we embed the pocket algorithm in our learning mechanism to train the best parameter set to minimize the noisy and noise free pixel detection error. The testing stage is composed of three component: image histogram, noise detection, and image restoration. First, we calculate the histogram of the testing image to find the groups of potential noise pixels. On these possible noisy pixel groups, we make use of the best weighting parameters trained to perform the fuzzy weighted mean aggregation to double-check whether they are noise corrupted or not. Furthermore, we utilize the Weighted Average Score (WAS) method to integrate information in the training stage to enhance the accuracy of our noise detector in noise detection step. In other words, we not only use the parameters obtained by the training stage, but also use the information which is obtained during training stage. Finally, if a pixel is identified as noisy in previous step, its value will be replaced by a weighted mean filter. According to the simulation results, we have found that our proposed algorithm provide a significant improvement over other existing filers.