Treffer: A convex optimization algorithm for gradient histogram specification

M.Phil. ; The goal of gradient-histogram specification is to find an image whose edge image has a histogram that matches a given gradient-histogram as much as possible. Mignotte has proposed a non-convex model for the problem [M. Mignotte. An energy-based model for the image edge-histogram specification problem. IEEE Transactions on Image Processing, 21(1):379–386, 2012]. In his work, gradient magnitudes of an input image are first modified by histogram specification to match the given gradient-histogram. Then, a non-convex model is minimized to find an output image whose gradient histogram matches the modified gradient-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this thesis, instead of considering gradient magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently. ; 梯度直方圖規範的目標是盡可能找到邊緣圖像具有與預定義的梯度直方圖匹配的直方圖的圖像。 Mignotte提出了梯度直方圖規範的非凸 模型[M. Mignotte. An energy-based model for the image edge-histogram specification problem. IEEE Transactions on Image Processing, 21(1):379– 386, 2012]。在他的工作中，輸入圖像的梯度絕對值通過預定義的梯度直方圖通過直方圖規範來修改。然後，非凸目標函數被最小化以獲得輸出圖像。目標函數的非凸性阻礙了計算和包含附加約束。我們直接考慮梯度並提出基於梯度的凸模型，而不是考慮梯度絕對值。此外，我們在基於不同應用的模型中增加了其他約束。我們的模型的凸性允許我們使用交替方向乘法器或快速迭代收縮閾值算法來有效地計算輸出圖像。我們考慮了邊緣保留平滑的幾個應用，包括細節誇張，邊緣提取，圖像抽象和文檔干擾去除。數值結果表明，我們的方法可以成功地產生體面的結果。 ; Chan, Cheuk Kit Kelvin. ; Thesis M.Phil. Chinese University of Hong Kong 2018. ; Includes bibliographical references (leaves ...