A Discrete Tchebichef Transform Approximation for Image and Video Coding

Oliveira, Paulo A. M.; Cintra, Renato J.; Bayer, Fábio M.; Kulasekera, Sunera; Madanayake, Arjuna

doi:10.1109/lsp.2015.2389899

Cited by 26 publications

(34 citation statements)

References 31 publications

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“…To the best of our knowledge, the only DTT approximation archived in literature was proposed in [42]. That approximation was obtained by means of a parameterization of integer functions combined with a normalization of transformation matrix columns.…”

Section: Related Workmentioning

confidence: 99%

“…That approximation was obtained by means of a parameterization of integer functions combined with a normalization of transformation matrix columns. The derived approximation in [42] furnishes good coding capabilities, but it lacks orthogonality or near-orthogonality properties. As a consequence, the forward and inverse transformations are quite distinct and possess unbalanced computational complexities.…”

Section: Related Workmentioning

confidence: 99%

“…The proposed approximations were compared with their corresponding exact DTT in terms of coding performance as measured according to the coding gain and the transform efficiency. For N = 8, we also include in our comparisons the DTT approximation proposed in [42]. The coding performance of the proposed approximations was evaluated according to the figures of merit Cg and η.…”

Section: Performance Assessmentmentioning

confidence: 99%

“…The additive and total arithmetic complexity of the proposed approximation are 45.5% and 58.9% lower than the exact transform, respectively. Although, the computational cost of the proposed approximation is slightly higher than the forward DTT approximation in [42], it is important to notice that the inverse transformation in [42] is relatively more complex. Considering the combination of forward and inverse transformation, the design in [42] requires 49 additions, whereas the proposed design requires 48 additions.…”

Section: Fast Algorithm and Arithmetic Complexitymentioning

confidence: 99%

“…Usually, approximations are multiplierless, requiring only addition and bit-shifting operations for its computation. In [42], a multiplierless approximation for the 8-point DTT is proposed. To the best of our knowledge, this is the only DTT aproximation archived in literature.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Low-Complexity Image and Video Coding Based on an Approximate Discrete Tchebichef Transform

Oliveira

Cintra

Bayer

et al. 2017

IEEE Trans. Circuits Syst. Video Technol.

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The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The DTT transform kernel does not depend on the input data and fast algorithms can be developed to real time applications. However, the DTT fast algorithm presented in literature possess high computational complexity. In this work, we introduce a new low-complexity approximation for the DTT. The fast algorithm of the proposed transform is multiplication-free and requires a reduced number of additions and bit-shifting operations. Image and video compression simulations in popular standards shows good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows 43.1% reduction of configurable logic blocks and ASIC place and route realization shows 57.7% reduction in the area-time figure when compared with the 2-D version of the exact DTT. KeywordsApproximate transforms, discrete Tchebichef transform, fast algorithms, image and video coding * Paulo A. M. Oliveira is with the Signal Processing Group,

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Performance Assessmentmentioning

confidence: 99%

Section: Fast Algorithm and Arithmetic Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Low-Complexity Image and Video Coding Based on an Approximate Discrete Tchebichef Transform

Oliveira

Cintra

Bayer

et al. 2017

IEEE Trans. Circuits Syst. Video Technol.

Self Cite

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Fast and accurate computation of high‐order Tchebichef polynomials

Abdulhussain

Mahmmod

Baker

et al. 2022

Concurrency and Computation

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Summary Discrete Tchebichef polynomials (DTPs) and their moments are effectively utilized in different fields such as video and image coding, pattern recognition, and computer vision due to their remarkable performance. However, when the moments order becomes large (high), DTPs prone to exhibit numerical instabilities. In this article, a computationally efficient and numerically stable recurrence algorithm is proposed for high order of moment. The proposed algorithm is based on combining two recurrence algorithms, which are the recurrence relations in the n$$ n $$ and x$$ x $$‐directions. In addition, an adaptive threshold is used to stabilize the generation of the DTP coefficients. The designed algorithm can generate the DTP coefficients for high moment's order and large signal size. By large signal size, we mean the samples of the discrete signal are large. To evaluate the performance of the proposed algorithm, a comparison study is performed with state‐of‐the‐art algorithms in terms of computational cost and capability of generating DTPs with large polynomial size and high moment order. The results show that the proposed algorithm has a remarkably low computation cost and is numerically stable, where the proposed algorithm is 27prefix×$$ \times $$ times faster than the state‐of‐the‐art algorithm.

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