在本論文裡，提出一個有別於傳統的順向三維離散餘弦轉換與逆向三維離散餘弦轉換的新架構。就計算度而言，有效率的三維離散餘弦轉換對，使得公式更簡明並且具有系統性的架構，三維離散餘弦轉換對，對於其他應用的發展具有一種高度潛能。透過所提出的三維離散餘弦轉換對，二維影像/三維視訊放大與縮小的應用，在這論文裡也被提出。新的演算法有效地消除波紋和方塊效應，並且保持原先像素之間的特性。同時，由於離散餘弦轉換本身的偶函數特性，所提出的影像放大演算法證明了所被期望的對稱特質。因此，無論在資料壓縮、影像處理和視訊編碼領域，三維離散餘弦轉換對都能提供許多的應用。實驗結果顯示，所提出的機制在三維離散餘弦轉換對與對於序列、影像、視訊放大/縮小的演算上確實有良好的效果，就像所期望的。

　　In this thesis, a novel representation of the conventional forward three-dimensional (3-D) discrete cosine transform (DCT) and the inverse 3-D DCT are proposed. The pair of the computationally efficient 3-D DCT makes the formulation be more concise and with a systematic structure, which has a high potential on developments of other applications via the 3-D DCT pair. Applications for enlargement and reduction of images/videos implemented by the proposed 3-D DCT transform pair are presented in this paper also. These new algorithms effectively eliminate ripple and blocky effects and maintain the original characteristic. Moreover, due to the essentially even-function property of the DCT, the proposed enlargement of an image demonstrates the desired symmetric property. As a result, they can provide numerous applications whatever in data compression, image processing and video coding as well. Simulation results show that proposed mechanisms enable good performances for the proposed 3-D DCT pair and scaling algorithms of sequences, images and videos as expected.

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