光流估計是一種根據影像序列中的亮度變化估計物體移動資訊的方法，在影像追蹤、動作分析、自動駕駛、影像插幀等領域都有廣泛的應用。傳統變分光流模型採用正則項維持流場的平滑性，其中 TV 正則化因為能夠保持銳利的流場邊緣而被廣泛使用，然而 TV 正則化容易造成流場出現階梯效應，導致流場內部產生不自然的分段常數現象。為了解決上述問題，我們提出了一種自適應 H1-L1 光流模型，在 H1 平滑項中引入自適應參數隨著梯度的大小調整流場的擴散係數，並且在資料項使用具穩健性的 L1 norm 以減少離群值和輕微光照變化的影響，資料項由亮度恆定假設和梯度恆定假設構成，以提升對光照變化的適應能力。我們利用輔助變數將正則項和資料項解耦成去雜訊子問題和閾值收縮子問題，透過變分法推導出去雜訊子問題的 Euler-Largrange 方程，在離散化後使用逐次超鬆弛迭代法求解，而閾值收縮子問題有逐點的閉式解。我們以交替最小化方法迭代更新各子問題，並採用多尺度的扭曲策略逐層求解。數值實驗結果顯示，所提出的方法能有效降低傳統 TV 模型所造成的階梯效應，並在保留運動邊界的同時提升流場平滑性。在光照變化的測試影像中，本方法亦展現出較佳的穩健性與視覺效果。;Optical flow estimation is a method for estimating object motion information from brightness variations in image sequences. It has been widely applied to image tracking， motion analysis， autonomous driving， video frame interpolation， and other related fields. Traditional variational optical flow models usually employ a regularization term to maintain the smoothness of the flow field. Among them， total variation regularization has been widely used because of its ability to preserve sharp motion boundaries. However， TV regularization may lead to the staircasing effect， resulting in unnatural piecewise constant structures inside the flow field. To address this problem， we propose an adaptive H1-L1 optical flow model. In the H1 regularization term， an adaptive parameter is introduced to adjust the diffusion coefficient of the flow field according to the magnitude of the gradient. In the data term， a robust L1 norm is adopted to reduce the influence of outliers and slight illumination variations. The data term consists of the brightness constancy assumption and the gradient constancy assumption， thereby improving the adaptability of the model to illumination changes. For the numerical scheme， auxiliary variables are introduced to decouple the regularization term and the data term into a denoising subproblem and a thresholding subproblem. The Euler–Lagrange equation for the denoising subproblem is derived using the calculus of variations. After discretization， the resulting equation is solved using the successive over-relaxation method， and the thresholding subproblem admits a pointwise closed-form solution. The subproblems are then iteratively updated by an alternating minimization strategy， and a multi-scale warping strategy is adopted to solve the problem layer by layer. Numerical experimental results show that the proposed method can effectively reduce the staircasing effect caused by traditional TV-based models while preserving motion boundaries and improving the smoothness of the flow field. For test images with illumination variations， the proposed method also demonstrates better robustness and visual performance.
