貝氏推論法於影像對比加強之研究

Abstract

在本篇論文中，我們提出一套以貝氏推論法為基礎的影像對比加強方法來處理亮度對比不足的影像。本論文從攝影取像的角度出發，並將影像對比加強的問題模擬成一個後置機率最大化估測的問題(Maximum A Posterior Estimation, MAP estimation)。在後置機率最大化的問題中，其基本概念為根據目前的所觀測的低對比影像資訊，推測出一相對應的高對比影像，而其最重要的核心步驟就是建立可能性模型(likelihood model)和預先模型(prior model)。在我們的做法中，可能性模型描述了低對比影像和高對比影像之間的機率關係， 而預先模型則是描述了一個高對比影像的機率統計特性。我們根據攝影取像的相關原則以及高低對比影像之間相關性(correlation)的統計特性來建立可能性模型；預先模型則是根據影像的區域亮度的分佈特性以及自然影像的統計特性來加以建立。由於我們的推論步驟同時考慮了取像過程的影響和原始影像的特性，因此所提出架構可較傳統的方式達到更佳的影像對比處理效果。 在我們的論文架構中，一旦將可能性模型和預先模型的架構完成後，我們就會採用適當的最佳化求解法來求出後置機率最大化估測問題的最佳解。然而，由於整體估測問題的維度相當高，求出最佳解的過程將相當費時。舉例而言，一張300200大小的影像所需的處理時間可能長達十分鐘左右，這麼大的計算量將會造成演算法於實際應用上的困難。因此在論文的第二部分，我們也提出一個簡單的概念及相對應的求解法來試著簡化演算法的複雜度，以減少演算法求解所需的運算時間。所提簡化方法假設低對比影像和高對比影像的關係可以一個亮度轉換函數來描述，根據此假設，配合者投影求解的概念，所提方法可以快速有效率的求出最佳解。模擬結果顯示，我們不但可以大幅地簡化原始演算法的運算步驟以符合一般使用者使用上的需求，也能呈現相當不錯的對比加強處理效果。 在我們演算法中，有數個參數的選擇會影響到對比加強處理的結果，因此，如何根據影像的特性，選出一組最適合於此張影像的參數設定，也是一個相當重要的課題。因此在論文中，我們也討論了影像內容和參數設定之間的關係。在此部分，我們藉由統計分析的技巧，建立影像特性和參數間的關係。藉由此分析的結果，針對任一輸入影像，我們都可以大致預測出適當的參數，並根據此參數之設定來執行影像對比加強的運算。 總結來說，在本論文中我們提出並驗證了以貝氏推論為基礎的影像對比加強方式。透過貝氏推論的架構，我們將影像的特徵、取像的原則等不同的資訊，系統化地結合在一起。另外，我們也討論了演算法的簡化和參數的選擇等議題。模擬結果顯示本論文所提出的貝氏推論演算法的確可以穩定且有效地改善影像的對比值。

In this dissertation, an efficient Bayesian framework is proposed for image contrast enhancement. Starting from the image acquisition pipeline process, we model the image enhancement problem as a Maximum A Posteriori (MAP) estimation problem. The goal of MAP estimation is to infer a high-contrast image based on the observed low-contrast image and some well defined likelihood and prior models. In the proposed MAP inference framework, the likelihood model represents the relationship between the observed image and the desired image. On the other hand, the prior model describes some expected statistical properties of the desired high-contrast image. In the design of the likelihood model, we consider the correlations between low-contrast images and their corresponding high-contrast images. On the other hand, we design the prior model based on the observed image and some statistical properties of natural images. Since our framework has systematically considered several major factors that influence the quality of the acquired image, the proposed algorithm can effectively enhance the contrast level of the input image in a natural-looking way, while without producing apparent artifacts. In the proposed MAP framework, a high-contrast image is derived by applying a suitable optimization solver to the aforementioned MAP estimation problem. However, it is extremely time-consuming to find the optimal solution due to the large number of unknown variables in the MAP problem. Take a 300 by 200 image as an example, the processing time could be longer than 10 minutes! This long processing time makes the proposed MAP-based algorithm impractical for typical image editing applications. Hence, in the second part of the dissertation, we discuss how to simplify the MAP estimation process to meet the requirement of practical applications. By assuming that the relationship between the desired image and the observed image can be modeled as an intensity mapping function, the dimensionality of the original MAP estimation problem is greatly reduced. Simulation results show that the simplified MAP-based approach can greatly reduce the computational complexity of the original MAP-based algorithm, while without causing apparent degradation of visual quality. For the proposed algorithm, the selection of model parameters is important. In the dissertation, we also discuss the proper selection of parameters for image enhancement. In this issue, we try to describe the relationship between image contents and the selection of parameters. With the help of some statistical analyses, we could effectively choose suitable values of the parameters for contrast enhancement. In summary, in this dissertation, we verify the feasibility of the proposed algorithm for image contrast enhancement. The proposed framework properly integrate various kinds of information into a unified inference process. Besides, we also discuss the simplification of the algorithm and selection of parameter in order to fit for practical applications. Simulations results have demonstrated the feasibility of the proposed framework in providing flexible and effective image contrast enhancement.