Fast implementation for symmetric non-separable transforms based on grids

Lu, Keng-Shih; Ortega, Antonio

doi:10.1109/icassp.2017.7952929

Cited by 7 publications

(11 citation statements)

References 16 publications

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“…First, symmetries are often present in both real-world data and residual signals. For example, in [13] the authors worked with graphs estimated from interpixel correlation in residual blocks after HEVC predictive coding. They showed that the considered blocks exhibit different kinds of symmetry, pointing out that there exist potentially efficient 2D GFTs generated by symmetric grids.…”

Section: Preliminaries and Previous Workmentioning

confidence: 99%

“…A second important argument is that all the introduced graphs are associated to a GFT that admits a fast transform implementation. Indeed, in [13] the authors have shown that butterflybased speedup methods can be exploited when all the edges (and self loops) of G are symmetric about the diagonal, anti-diagonal, updown and left-right symmetries. Lower computational complexity of transforms is of course a crucial requirement for all true image/video compression systems.…”

Section: Preliminaries and Previous Workmentioning

confidence: 99%

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Symmetry-Based Graph Fourier Transforms: Are They Optimal For Image Compression?

Gnutti

Guerrini

Leonardi

et al. 2021

2021 IEEE International Conference on Image Processing (ICIP)

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Traditional block-based transforms are based on applying a single transform to all blocks. As an alternative, better performance in image and video processing and representation can be achieved by choosing one among a discrete set of transforms for each block. As an example, our recently proposed set of multiple transforms called Symmetry-Based Graph Fourier Transforms (SBGFTs) have shown good performance in terms of energy compaction, improving HEVC intra coding performance when used to replace the Discrete Cosine Transform (DCT). This paper further explores the performance of the SBGFTs in a multiple transforms, non-linear approximation perspective, by comparing them with two alternative sets of orthogonal transforms, namely, the Karhunen-Loève Transform (KLT) and the Sparse Orthonormal Transform (SOT). Experimental results confirm that SBGFTs achieve superior representation ability in this context as well, suggesting that they could assume a central role in image compression.

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Section: Preliminaries and Previous Workmentioning

confidence: 99%

Section: Preliminaries and Previous Workmentioning

confidence: 99%

Symmetry-Based Graph Fourier Transforms: Are They Optimal For Image Compression?

Gnutti

Guerrini

Leonardi

et al. 2021

2021 IEEE International Conference on Image Processing (ICIP)

Self Cite

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“…11. While [29] applies different node re-ordering rules for different types of symmetric grid, in this work we can simply describe grid symmetries by the involutions shown in Table II, to provide a more straightforward derivation of fast GFTs on symmetric grids. For application, it has been shown in [46] that GFTs with exact or partial symmetry properties can enhance compression efficiency with respect to the DCT.…”

Section: Symmetric Grid Graphsmentioning

confidence: 99%

“…Motivated by these fast algorithms, in this paper our goal is to explore more general classes of graphs with fast GFTs. In our preliminary work [28], [29], we have introduced two classes of graphs, symmetric line and grid graphs, whose GFTs have a butterfly stage for fast implementation. This work extends and generalizes the results of [28], [29] to graphs that are bipartite or have more general symmetry properties.…”

Section: Introductionmentioning

confidence: 99%

“…In our preliminary work [28], [29], we have introduced two classes of graphs, symmetric line and grid graphs, whose GFTs have a butterfly stage for fast implementation. This work extends and generalizes the results of [28], [29] to graphs that are bipartite or have more general symmetry properties. A more detailed outline of this paper will be presented in Section I-B.…”

Section: Introductionmentioning

confidence: 99%

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Fast Graph Fourier Transforms Based on Graph Symmetry and Bipartition

Ortega

2019

IEEE Trans. Signal Process.

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The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does not have a fast algorithm. In this work, we develop new approaches to accelerate the GFT computation. In particular, we show that Haar units (Givens rotations with angle π 4) can be used to reduce GFT computation cost when the graph is bipartite or satisfies certain symmetry properties based on node pairing. We also propose a graph decomposition method based on graph topological symmetry, which allows us to identify and exploit butterfly structures in stages. This method is particularly useful for graphs that are nearly regular or have some specific structures, e.g., line graphs, cycle graphs, grid graphs, and human skeletal graphs. Though butterfly stages based on graph topological symmetry cannot be used for general graphs, they are useful in applications, including video compression and human action analysis, where symmetric graphs, such as symmetric line graphs and human skeletal graphs, are used. Our proposed fast GFT implementations are shown to reduce computation costs significantly, in terms of both number of operations and empirical runtimes.

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