多焦影像融合是影像處理領域中一項被廣泛研究的技術，其目的在將具有不同焦深的多幅來源影像合併為單一輸出影像，並保留每個輸入影像的清晰區域，使我們能獲得完整且銳利的視覺資訊。本文聚焦於研究基於一階梯度的變分影像融合模型，並探索了幾種從輸入影像中選擇梯度特徵的策略。我們分別使用不同的選擇標準來提取代表性梯度結構，並將其整合到一個變分框架中，該框架使用分裂Bregman迭代法進行求解。我們針對各種梯度選取方法在變分模型下的表現進行比較，透過客觀品質評估指標與視覺觀察來評估每種方法的性能。實驗結果表明，與傳統影像融合方法相比，合適的梯度選擇與變分融合方法相結合，能夠在多焦影像融合的任務中提高視覺清晰度並更自然地保留細節。

Multi-focus image fusion is a widely studied technique in the field of image processing. It aims to combine multiple source images with different focal depths into a single output that retains the sharp regions of each input. This thesis focuses on the first-order gradient-based variational fusion model and explores several strategies for selecting gradient features from the input images. Representative gradient structures are extracted using different selection criteria and integrated into a variational framework, which is solved using the split Bregman iteration method. The performance of each method is evaluated through both objective quality metrics and visual inspection. Experimental results show that appropriate gradient selection, when combined with a variational fusion approach, leads to improved visual clarity and better detail preservation compared to traditional fusion methods.

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