Advanced Image Compression Techniques by Triangular and Trapezoidal Segmentations

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. esults 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.