Irrational Scaling, Interpolation, and Decimation for Digital Signal and Image Processing Applications
Date Issued
2004
Date
2004
Author(s)
Kao, Meng-Ping
DOI
en-US
Abstract
Scaling has always been an important topic in the field of digital signal processing, since its applications are so widespread and extensive. For example, interpolation, decimation and warping of a digital image, sampling rate conversion of a digital signal, and wavelet transform based filter banks are all closely related to scaling.
The operation of scaling entirely depends on the scaling factor, which controls the ratio between the original signal and the scaled signal. In general, scaling factor can be either rational or irrational numbers. We named the operation on both rational and irrational factors, i.e. real factors, the generalized scaling. For a long time, there is no steadfast definition for generalized scaling, since everyone could justify his opinions from different points of view.
In this paper, I propose a new algorithm to realize the generalized scaling using linear operations in the frequency domain. Compared to previous methods, this algorithm is entirely linear such that it can be well applied to the design of Perfect Reconstruction Filter Banks (PR FB). Furthermore, both one dimensional and two dimensional FB cases are explored in this paper.
In addition, after a fine modification of the above algorithm, it can be utilized in image warping, which is a common problem in multi-projection applications. The term “warping” is different from scaling in that the former one is a non-linear operation while the later is linear. Through image warping, we can arbitrarily change the shape of a digital image.
At the end of this paper, I put more emphases on DCT compressed domain manipulations, which are similar to generalized scaling in main concepts. I propose a new scheme to efficiently implement the block size conversion between different DCT’s. This scheme can be useful in image resizing for which the image is compressed in the DCT domain, such as JPEG and MPEG.
Subjects
任意變形
內插
完整回復濾波器串
快速離散餘弦轉換
nonuniform filter bank
interpolation
decimation
perfect reconstruction
direct DCT domain computation
radix-3 dct
irrational scaling
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-93-R91942027-1.pdf
Size
23.31 KB
Format
Adobe PDF
Checksum
(MD5):506df3ffbc6ed60bcd3384a70c74a965