- 學位論文
應用於影像解模糊的區域高斯分佈模型
Local Gaussian Distribution Models for Image De-blurring
摘要
影像解模糊採用先驗模型以解決不適定性問題。使用先驗模型解模糊的方法以加權因數來控制先驗正則化(regularization)的強度，而這加權因數通常被設為一常數。在這我們提出一個做法：將加權因數依各個影像像素的區域統計分佈而去調整加權因數的大小。這種依像素的區域統計分佈而去調整加權因數的方法可使影像解模糊的效果更好。我們提出了區域高斯分佈模型，可將解模糊目標函數的加權因數最佳化。我們共提出五種區域高斯分佈模型: 1. 超拉普拉斯(hyper-Laplacian)模型, 2. 分區調整模型, 3. Alpha-beta模型, 4. 查找表模型, 5. 布氏(Burr)直方圖模型。將區域高斯分佈模型與其他影像解模糊方法比較，區域高斯分佈模型可在結構相似性指標得較高的分數，在視覺效果上也有較佳的表現。 影像梯度直方圖在影像處理研究上有很多應用，但是來自戶外大自然的影像梯度直方圖很難用一個統計分佈去完全描述。我們提出用K-L散度來當量測統計分佈與梯度直方圖是否匹配的匹配指數。我們發現布氏(Burr)統計分佈比其他統計分佈更適合用於描述影像梯度直方圖。我們將布氏統計分佈應用於我們的布氏直方圖區域高斯分佈模型。在影像解模糊時，我們不必儲存整個參考梯度直方圖，而只需儲存三個布氏分佈參數就可取得參考梯度直方圖。有了參考梯度直方圖和模糊影像的梯度，我們就能用“梯度匹配”的方法去產生原始影像的估計梯度。有了原始影像的估計梯度，我們就能產生依各個影像像素的區域統計分佈而去調整的加權因數。這是我們如何將布氏統計分佈應用於影像梯度分佈的匹配。其他影像處理研究應該也可應用布氏(Burr)統計分佈與影像梯度分佈的良好匹配性。
並列摘要
Image de-blurring utilizes the norm prior to solve the ill-posed problem. Most of the norm prior based image de-blurring methods use weighting factors to control the strength of the regularization. We present an idea is to make these weighting factors adaptive to pixel-wise local statistical distribution. By using these adaptive weighting factors, we can achieve better performance in image de-blurring. We propose a series of Local Gaussian Distribution Models (LGDM), that can be used to optimize the weighting factors in the objective function of image de-blurring. Five LGDMs are introduced here: hyper-Laplacian LGDM, region adaptive LGDM, alpha-beta LGDM, lookup table based LGDM, and Burr Histogram LGDM. We compare our methods with other state-of-the-art image de-blurring approaches. Our approach shows better in performance. The image gradient histogram has a lot of applications in image processing research. However, the image gradient histogram from natural scene is a curve too complex to be fully described by a statistical distribution. We propose to use the K-L divergence [15] (Kullback-Leibler divergence) as the matching index to measure the match between the statistical distribution and the gradient histogram. We find the Burr distribution outperforms other distributions by a great margin. This good matching feature of the Burr distribution is applied to our Burr histogram LGDM. Instead of storing whole reference gradient histogram for image de-blurring, we can use three optimized Burr distribution parameters to represent the reference histogram. With the reference histogram and the gradient of blurred image, we can use the Histogram Matching method [16] to produce an estimated gradient latent image. This demonstrates one area to apply the Burr distribution for gradient distribution approximation. There should be other image processing research which can utilize the good matching feature of the Burr distribution.