數位影像合成是一門相當重要且實用的課題，例如在動畫或電影的製作中，常常需要從原來的圖案中將特定的人物、物品抽出，並將他們合成在新的背景圖案裡，因此在最近幾年在這個領域中受到相當的重視，許多相關的研究探討合成影像時會遇到的問題和解決的方法。
在本篇論文中，我們提出一個以頻域分析方法為基本架構的演算法，並用之來建立透明物體的光線模型。這個光線模型將根據輸入的影像來計算透明物體的折射及反射特性，使用者可利用此資訊將物體合成到任何新的背景影像。在分析時，作為光源的液晶螢幕被分割成數個大小相同的橫向條狀區域和垂直方向條狀區域，每一個區域代表一個光源的發射位置。在這些位置中我們分別指定一個固定頻率，一個頻率訊息的形成是由多張不同的影像依序變化所產生。我們由數位相機記錄這一連串隨時間變化的影像，然後時域的資訊轉換成頻域資訊。在頻域的資訊中，每個頻率的成分接可以被分離出來，因此可以找出光源的位置和光線衰減度。
本論文的貢獻主要在於提出一個更精準的演算法來忠實呈現物體的折射及反射特性，我們引用在醫學影像的重建投影求解的Kaczmarz方法來求得更精確的光源位置和衰減度，並佐以好的初始值預測計算來避免掉進local minimum。另外，我們使用空間座標轉換的作法來求得合成後影像的背景區域的色彩分佈，這個方法不僅可以減少電腦的計算量而且也可以保持合成後影像的解析度。在實驗的結果裡，我們證明不管由視覺效果或是PSNR的比較，我們的結果均優於之前的研究，實驗中也藉由合成視訊的產生來驗證其對物體移動、旋轉、放大縮小合成能力的有效性。

The paper proposes a new environment matting algorithm to model the appearance of transparent object under different background. The frequency-domain analysis is used as the basis to compute the relationship between the area of foreground object and background image. Meanwhile, the Kaczmarz method is applied to obtain more accurate weight matrix. The compositing quality increases if the iteration number of projection increases, however, the consuming time is proportional to the iteration number. We will show that the proposed algorithm can maintain the quality even the high threshold is set to reduce the iteration.
The experimental results show that our algorithm can effectively improve the quality of compositing picture and has higher PSNR than previous method, either from the visual evaluation or PSNR table. Besides, we also demonstrate the compositing results by applying the computed lighting model to a video sequence with moving, rotating, and scaling the foreground object.

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