Graph Fourier Transform with Negative Edges for Depth Image Coding

Su, Weng-Tai; Cheung, Gene; Lin, Chia-Wen

doi:10.48550/arxiv.1702.03105

Cited by 1 publication

(7 citation statements)

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“…Then, for each signal, they perform an exhaustive search choosing the best GFT in ratedistortion terms. Furthermore, a new graph transform, called signed graph Fourier transform, has been presented in [11]. This transform is targeted for compression of depth images and its underlying graph contains negative edges that describe negative correlations between pixel pairs.…”

Section: B Graph-based Image Codingmentioning

confidence: 99%

“…Given an image signal, we first solve the optimization problem in (11) obtaining the optimal solution w * . To transmit w * to the decoder, we first compute its GFT coefficients ŵ * and the reduced vector ŵ * r , then we quantize ŵ * r and code it using the entropy coder described above.…”

Section: Graph-based Image Compressionmentioning

confidence: 99%

“…The computational cost of this operation is approximately O(N 3 ), where we recall that N is the number of pixels in a block. Moreover, at the encoder it is also necessary to solve the optimization problem in (11), whose complexity is at most O(M 3 ), where M is the number of edges and, since we use a grid graph, M is lower than 2N . For this reason, the overall complexity of the proposed image compression method is higher at the encoder than at the decoder.…”

Section: A Computational Complexitymentioning

confidence: 99%

“…In all our experiments on natural images, we use Q = 8 possible quantization step sizes ∆ i for ŵr and we set M = 64, which is the length of the reduced coefficient vector ŵr . In order to set the value of the parameter α in (11), we first have to perform a block classification. In fact, we recall that the parameter α in ( 11) is related to the l 1norm of ŵ, where ŵ are the GFT coefficients of the signal w that lies on the dual graph.…”

Section: A Experimental Setupmentioning

confidence: 99%

“…In the first case, in addition to the bitrate of û, we count the bitrate due to the transmission of ŵ * i and log Q additional bits per block to transmit the chosen quantization step size ∆ i for ŵr . We point out that we do not need to send any information about the block class, because this classification is only needed at the encoder in order to define the parameters of the optimization problem (11). For both methods, we vary the quantization step size q of the transform coefficients to vary the encoding rates.…”

Section: A Experimental Setupmentioning

confidence: 99%

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Graph Transform Optimization With Application to Image Compression

Fracastoro

Thanou

Frossard

2020

IEEE Trans. on Image Process.

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In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an effective graph-based transform. We introduce a novel graph estimation algorithm, which uncovers the connectivities between the graph signal values by taking into consideration the coding of both the signal and the graph topology in rate-distortion terms. In particular, we introduce a novel coding solution for the graph by treating the edge weights as another graph signal that lies on the dual graph. Then, the cost of the graph description is introduced in the optimization problem by minimizing the sparsity of the coefficients of its graph Fourier transform (GFT) on the dual graph. In this way, we obtain a convex optimization problem whose solution defines an efficient transform coding strategy. The proposed technique is a general framework that can be applied to different types of signals, and we show two possible application fields, namely natural image coding and piecewise smooth image coding. The experimental results show that the proposed graph-based transform outperforms classical fixed transforms such as DCT for both natural and piecewise smooth images. In the case of depth map coding, the obtained results are even comparable to the state-of-the-art graph-based coding method, that are specifically designed for depth map images.

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Section: B Graph-based Image Codingmentioning

confidence: 99%

Section: Graph-based Image Compressionmentioning

confidence: 99%

Section: A Computational Complexitymentioning

confidence: 99%

Section: A Experimental Setupmentioning

confidence: 99%

Section: A Experimental Setupmentioning

confidence: 99%

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