光流估計是電腦視覺中的一項基礎問題，旨在量化影像序列中相鄰影格之間物體的運動。光流通常以向量場的形式表示，每個向量描述像素從一幀移動至下一幀的位移。傳統方法大多依賴於亮度恆定假設，即假設像素在運動過程中其亮度不變。然而，當光照分佈不均時，該假設往往無法成立，導致估計精度顯著下降。在本文中，我們提出一種新穎的 TV-L2 變分模型，旨在解決非均勻光照條件下的光流估計問題。該模型結合了總變差正則化，用以保留運動邊界，並引入 L2 資料保真項以因應光照變化。我們進一步採用分裂 Bregman 方法有效求解相應的最佳化問題，確保整體方法兼具穩定性與計算效率。透過大量的數值實驗，我們驗證了所提模型在處理複雜光照情境時的有效性，並顯示其在準確度方面優於傳統方法。

Optical flow estimation is a fundamental problem in computer vision, aiming to quantify the motion of objects between consecutive frames in an image sequence. Optical flow is typically represented as a vector field, where each vector captures the displacement of a pixel from one frame to the next. Traditional approaches often rely on the brightness constancy assumption, which posits that the intensity of a pixel remains unchanged over time as it moves. However, this assumption frequently fails under inhomogeneous illumination conditions, where lighting variations can significantly degrade estimation accuracy. In this thesis, we present a novel TV-L2 variational model designed to address the challenges of optical flow estimation under inhomogeneous illumination. Our model integrates total variation (TV) regularization to preserve motion boundaries and an L2 data fidelity term to handle illumination variations. We propose an iterative split Bregman scheme to effectively solve the associated optimization problem, ensuring robustness and computational efficiency. Through extensive numerical experiments, we demonstrate the effectiveness of our proposed model, highlighting its accuracy in handling complex illumination scenarios compared to traditional methods.

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