影像斜邊放大後的平整程度比較

此節我們將對 Nearest Neighbor、[23]和本篇論文三種演算法作放大品質作進 一步的量化比較。我們透過比較視覺上的舒適度可以粗略地比較各演算法的放大 邊作比較。以 Nearest Neighbor、[23]和本篇論文等三種演算法將此五張影像從解 析度 648×486 放大到 1920×1080，並從放大每張後的影像中取出邊緣部分的 100 個像素座標，透過 PCA 找出近似直線。在 PCA 計算過程中我們可求得此 100 像 素座標的相關矩陣(covariance matrix)的特徵值，特徵值中較小者可表示為此 100 像素與上述近似直線的平均誤差。誤差越小我們可視為此 100 像素座標的分布越 接近一條直線。

結果如圖 4-9 所示，縱軸為特徵值，橫軸分別表示五個不同斜率，特徵值越 小表示取樣的像素與降維後直線的誤差越小。我們可以觀察到[23]與本篇論文所 提方法明顯優於 Nearest Neighbor 的放大結果。而[23]與本篇論文所提方法差異 不大，但就記憶體需求量來說，因為本篇論文因透過圖樣群的妥善設計，所以節 省了記錄連接點暫存器，在將來尋求硬體實現的前提下，可以較低的記憶體成本 達到相似的邊緣放大平整性。

(a) (b) (c)

(d) (e) 圖 4-8 分析不同斜率的斜邊放大後平整程度的測試資料。

圖 4-9 不同斜率的斜邊放大後平整程度的測試結果，PCA 計算所得較小的特徵值越 小表示越平整。 

五、結論 

在這樣情況下，或許可以靠著區塊內灰階深淺的三分法或者四分法，以彌補灰階 值高/低二分法的不足，減少以 Bi-Cubic 作內插補點的機會。但如此一來，所需 考慮的圖樣又將更為複雜，並且在顧及演算法複雜度之下，將會是一個值得努力 的方向。另一方面，因為本論文是以硬體實作為出發點，因此有朝一日若希望能 落實在硬體實作方面，勢必將面對更多時間與空間上面的限制。屆時，對現有的 演算法架構作最佳化的處理，將會是所須面對的新挑戰。 

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