以三角形和梯形分割為基礎的影像壓縮改良技術

Abstract

在近幾年的多媒體應用中，不規則形狀的影像壓縮已經變的越來越熱門。形狀自適應編碼的優點在於這種方法可以運用同一個不規則區塊中色彩強度的高相關性來對不規則形狀內的影像資訊做更好的壓縮，以達到更高的壓縮率。 相較於傳統基於方型區塊的影像壓縮，形狀自適應的影像編碼可產生相當少的區塊效應及變形失真的情形。這是由於基於方型區塊的影像壓縮忽略了影像的內容與特徵。 因為傳統的不規則形狀的影像壓縮大多依賴格拉姆-施密特正交化演算法來取得每一個不規則形狀區塊的正交化基底，它的運算複雜度是相當龐大的。因此，我們在這邊論文裡提出了一個創新的概念 – 以三角形和梯形分割為基礎的二維正交離散餘弦轉換，其效能較傳統的不規則形狀的離散餘弦轉換來說，在運算複雜度上較為節省。由於一個不規則形狀的區域嚴格來說是一個多邊形，而一個多邊形可以被分解成很多三角形及梯形，本篇論文提出的方法是相當適用在對不規則形狀的區域做轉換。 實驗結果顯示本篇論文提出的方法跟運用格拉姆-施密特演算法的方法都有一樣好的將能量集中在低頻的能力，而本篇論文提出的方法可以顯著的減少運算時間。另外，我們也可以運用本篇論文提出的方法產生可適於三角形和梯形的正交離散傅立葉基底、KLT基底、Legendre基底、Hadamard (Walsh)基底、及其他多項式基底。

Coding of arbitrarily shaped image region is becoming more and more popular in today’s multimedia applications. The advantage of shape-adaptive coding is that it can employ the information of arbitrarily-shaped region to exploit the high correlation of the color values within the same image segment in order to achieve a superior compression rate. Compared to the conventional block-based image coding, shape-adaptive image coding produces significantly less blocking artifacts and distortions in other forms which typically emerges in block-based image coding since its negligence of the image content and characteristics. Because early shape-adaptive image coding relies on the Gram-Schmidt process to obtain orthogonal basis for each arbitrary region, its computational complexity could be enormous. Therefore, in this thesis, we present the two-dimensional orthogonal DCT expansion in triangular and trapezoid regions which is much more economical in terms of the complexity compared to the conventional shape-adaptive transforms. Since an arbitrarily shaped region literally is a polygon and a polygon can be decomposed into several triangular or trapezoidal regions, the proposed method is highly suitable for transforming arbitrarily shaped segments. Results show that the proposed method has the energy compact ability that is as good as the results of the Gram-Schmidt method, and significantly fast computation time. In addition, the proposed method can also be used for generating the 2-D complete and orthogonal DFT basis, KLT basis, Legendre basis, Hadamard (Walsh) basis, and polynomial basis in the trapezoid and triangular regions.