Transform Techniques

An OCA-Based Fast Algorithm For 2-D Discrete Periodized Wavelet Transform

Authors:

King-Chu Hung,
Jyh-Horng Jeng,
Yu-Jung Huang,
Chi-Wave Hung,

Page (NA) Paper number 1055

Abstract:

Abstract This paper presents a fast algorithm to perform the 2-D discrete periodized wavelet transform based on the operator correlation algorithm (OCA). The OCA-based algorithm needs half of the multiplications and bits required by the classical algorithm. The OCA-based algorithm is modular inherent. It can be easily mapped to VLSI design.

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Packed Integer Wavelet Transform Constructed By Lifting Scheme

Authors:

Chengjiang Lin,
Bo Zhang,
Yuan F Zheng,

Page (NA) Paper number 1082

Abstract:

A new method for speeding up the integer reversible wavelet transforms constructed by the lifting scheme is proposed. The proposed method packs multiple pixels (wavelet coefficients) in a single word; therefore, it can make use of the 32-bit or 64-bit computation capability of modern computers to accomplish multiple addition/subtraction operations in one instruction cycle. As a result, the proposed method can save the decomposition/reconstruction time by up to 37 percent on 32-bit machines in comparison with the original wavelet transform algorithms. Furthermore, the packed integer wavelet transform requires much less working memory.

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2-D Affine Generalized Fractional Fourier Transform

Authors:

Jian-Jiun Ding, Depart. of EE, NTU, Taipei, Taiwan (Taiwan)
Soo-Chang Pei, Depart. of EE, NTU, Taipei, Taiwan (Taiwan)

Page (NA) Paper number 1219

Abstract:

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform). It also has been generalized into the 2-D unseparable fractional Fourier transform with 4 parameters. In this paper, we will introduce the 2-D affine generalized fractional Fourier transform (AGFFT). It has even further generalized these 2-D transforms. We will show it can deal with many problems that can't be dealt by these 2-D transforms and extend their utility.

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A Fast Degradation-free Algorithm for DCT Block Extraction in the Compressed Domain

Authors:

Yoshiaki Shibata,
Zhigang Chen,
Roy H Campbell,

Page (NA) Paper number 1597

Abstract:

A fast, degradation-free solution for the DCT block extraction problem is proposed. The problem is defined as extracting a DCT block from a DCT compressed frame composed of DCT blocks. This problem is encountered in both video/image manipulations in the compressed domain and transcodecs, for example, converting from MPEG to Motion JPEG. Traditionally, solutions involve using the pixel domain manipulation or Chang's algorithm with approximations. The new solution expands Chang's algorithms, takes full advantage of a fast DCT algorithm, and exploits characteristics of the input DCT blocks without any approximation. The new DCT block extraction achieves 70% performance improvement without any degradation of image quality compared with the conventional solutions.

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Analysis of Deformational Transformations with Spatio-Temporal Continuous Wavelet Transforms

Authors:

Jonathan R. Corbett,
Jean-Pierre L Leduc,
Mingqi Kong,

Page (NA) Paper number 1733

Abstract:

This paper deals with the estimation of deformational parameters in discrete spatio-temporal signals. The parameters of concern correspond to time-varying scales. As such, they can be the coefficients of either a Taylor expansion of the scale or a given deformational transformation. At first sight, there are just a few deformational transformations that provide continuous wavelet transforms. The approach presented in this paper associates deformational transformations to motion transformations taking place in higher dimensional spaces and projected on the sensor plane. Then, finding continuous wavelet transforms becomes much more easier since numerous continuous wavelet transforms have already been defined for motion analysis. It is also known that spatio-temporal continuous wavelet transforms provide minimum-mean-squared-error estimates of motion parameters. Any deformational transformation of features embedded in a spatio-temporal signal may always be related to the projection on the sensor plane of the motion of a rigid object taking place in a higher dimensional space. This reasoning applies conversely. The associated rigid motion may be actual or virtual, may take place either on a flat space or on a curved space immersed in higher dimensions. Continuous wavelet transforms for the estimation of deformational parameters may be then deduced from those already existing in motion analysis.

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New Fast Algorithms Of Multidimensional Fourier And Radon Discrete Transforms

Authors:

Ekaterina Labunets, Ural State Technical University Department A&IT Ekaterinburg, Russia (Russia)
Valery Labunets, Ural State Technical University Department A&IT Ekaterinburg, Russia (Russia)
Karen O Egiazarian,
Jaakko Astola,

Page (NA) Paper number 1739

Abstract:

This paper describes a fast new n--D Discrete Radon Transform (DRT) and a fast exact inversion algorithm for it, without interpolating from polar to Cartesian coordinates or using the backprojection operator. New approach is based on the fast Nussbaumer's Polynomial Transform (NPT).

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Quantized Discrete Cosine Transform: A Combination of DCT and Scalar Quantization

Authors:

Khanh Nguyen-Phi,
Alen Docef,
Faouzi Kossentini,

Page (NA) Paper number 2039

Abstract:

A typical MPEG-2 video encoder requires that DCT and quantization be performed in most cases. In this paper, we show how to combine these two steps, reducing sunstantially the number of computations. The new nonlinear transform is called the Quantized Discrete Cosine Transform, or QDCT. We also introduce a new method to trade-off the computational complexity and the precision of the QDCT. Although the QDCT is independent of input data, better trade-offs can be obtained by making it data dependent, which is appropriate in multimedia applications such as MPEG-2 video coding. The results presented in this paper can also be extended to other linear transforms and/or other coding methods

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Wavelet-Based Image Coder with Channel-Optimized Trellis-Coded Quantization

Authors:

Tuyet-Trang Lam,
Glen P Abousleman,
Lina J Karam,

Page (NA) Paper number 2392

Abstract:

This paper presents a wavelet-based image coder optimized for transmission over binary symmetric channels (BSC). The proposed coder uses a channel-optimized trellis-coded quantization (COTCQ) stage that is designed to optimize the image coding based on the channel characteristics. This optimization is performed only at the level of the source encoder, and does not include any channel coding for error protection. Consequently, the proposed channel-optimized image coder is especially suitable for wireless transmission due to its reduced complexity. Furthermore, the improvement over TCQ-based image coders is significant. Examples are presented to illustrate the performance of the proposed COTCQ-based image coder.

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A Lossless Multi-Partitioning Successive Zero Coder For Wavelet-based Progressive Image Transmission

Authors:

Chun-Ho Cheung, City University of Hong Kong (Hong Kong)
Sheung-Yeung Wang, City University of Hong Kong (Hong Kong)
Kwok-Wai Cheung, City University of Hong Kong (Hong Kong)
Lai-Man Po, City University of Hong Kong (Hong Kong)

Page (NA) Paper number 2447

Abstract:

This paper proposed an embedded image compression algorithm called Lossless Multi-Partitioning Successive Zero Coder (LMP-SZC) using the integer wavelet transform for progressive image transmission (PIT). By dynamically adjusting the partitions based on the space-frequency domain coefficients, the algorithm can achieve lower complexity and superior coding efficiency as compared with other well-known embedded lossless wavelet-based coder even without the zerotree analysis.

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Optimum Transform Coding Of Imagery

Authors:

Glen P Abousleman,

Page (NA) Paper number 2415

Abstract:

A system is presented for transform coding of imagery. Specifically, the system uses the 2-D discrete cosine transform (DCT) in conjunction with adaptive classification, entropy-constrained trellis-coded quantization, optimal rate allocation, and adaptive arithmetic encoding. Adaptive classification, side rate reduction, and rate allocation strategies are discussed. Entropy-constrained codebooks are designed using a modified version of the generalized Lloyd algorithm. This entropy-constrained DCT-based system is shown to achieve outstanding coding performance as compared to other DCT-based systems.

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An Improved Wavelet-Based Corner Detection Technique

Authors:

Azhar Quddus,
Moustafa Mahmood Fahmy,

Page (NA) Paper number 5062

Abstract:

In this paper an improved, wavelet-based technique for corner detection, in 2-D planar curves, is presented. This boundary based technique is simple to implement and computationally efficient and exploits wavelet transform modulus maxima (WTMM) to detect corners. The proposed algorithm is robust with respect to object geometry. We also report results under AWGN noise.

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