Learning Accurate Entropy Model with Global Reference for Image Compression
Authors: Yichen Qian
Zhiyu Tan
Xiuyu Sun
Ming Lin
Dongyang Li
Zhenhong Sun
Li Hao
Rong Jin
Venue: ICLR 2021 Poster (2021)
Keywords: Image compression
Entropy Model
Global Reference

Abstract: In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation function. This greatly limits their performance due to the absence of a global vision. In this work, we propose a novel Global Reference Model for image compression to effectively leverage both the local and the global context information, leading to an enhanced compression rate. The proposed method scans decoded latents and then finds the most relevant latent to assist the distribution estimating of the current latent. A by-product of this work is the innovation of a mean-shifting GDN module that further improves the performance. Experimental results demonstrate that the proposed model outperforms the rate-distortion performance of most of the state-of-the-art methods in the industry.

Published as a conference paper at ICLR 2021
LEARNING ACCURATE ENTROPY MODEL GLOBAL REFERENCE FOR IMAGE COMPRESSION
WITH
Yichen Qian
Zhiyu Tan
Xiuyu Sun
Alibaha Group Hangzhou, China
Alibaha Group Hangzhou, China
Alihaha Group Hangzhou, China
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Ming Lin
Dongyang Li Alibaba Group Hangzhou, China
Zhenhong Sun
Alibaba Group
Alibaba Group
Bellevue, WA, 98004, USA
Hangzhou, China
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Hao Li
Rong Jin
Alibaba Group
Alibaba Group
Hangzhou, China
Bellevue, WA, 98004, USA
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ABSTRACT
In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation function. This greatly limits their performance due to the absence of global vision. In this work, we propose novel Global Reference Model for image compression to effectively leverage both the local and the global context information, leading enhanced compression rate. The proposed method scans decoded latents and then finds the most relevant latent to assist the distribution estimating of the current latent. A by-product of this work is the innovation of mean-shifting GDN module that further improves the performance. Experimental results demonstrate that the proposed model outperforms the rate-distortion performance of most of the state-of-the-arr methods in the industry.
INTRODUCTION
Image compression is fundamental research topic in computer vision. The goal of image com- pression is to preserve the critical visual information of the image while reducing the bit-rate for storage or transmission. The satte-of-thh-att image compression standards, such as JPEG (Wallace, (992), (Rabbani & Joshi 2002), HEVC/H.266 (Sullivan et al. 2012) and Versatile Video Coding (VVC) (Ohm & Sullivan 2018), are carefully engineered and highly tuned achieve better performance.
Albeit widely deployed, the conventional human-designed codecs take decades of development to achieve impressive compression rate today. Any further improvement is expected to be even more difficult. Inspired by the successful stories of deep learning in many vision tasks, several pioneer works (Toderici et al. 20166] Agustsson et al.] [2017; Theis et al. [011]] Ballé et al.) 2017; Ballé et al. M008|MMettar et al. 2018 Lee al. 2019 Minnen et al. (2018a) demonstrate that the image compression task can be effectively solved by deep learning too. This breakthrough allows us to use data-driven learning system to design novel compression algorithms automatically. As a result, majority of deep image compression (DIC) models are based on autoencoder framework. In this framework, an encoder transforms pixels into quantized latent representation suitable for com- pression, while decoder is jointly optimized to transform the latent representation back into pixels.
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Figure 1: Global spatial redundancy in the image, For standard codees and previous learned codecs, non-local relevant patches (marked by yellow and blue) would consume equal bit rates.
The latent representation can be losslessly compressed to create a bitstream by using entropy coding method (Rissanen & Langdon 1981).
In the entropy coding, the compression quality is controlled by the entropy estimation of latent features generated by the encoder. It is therefore important learn an accurate entropy model. To this end, several solutions have been considered. With additional bits, some methods propose entropy model conditioned on a hyperprior, using side information of local histograms over the latent representation (Minnen et al. (0018) or hierarchical learned prior (Ballé et al. 2018). Context- adaptive models (Minnen al. 20188 Lee al. 2019) incorporate predictions from neighboring symbols to avoid storing the additional bits. While these methods improve the accuracy of the entropy models, they are unable to use global context information during the compression, leading to suboptimal performance.
In this work, we observe that global spatial redundancy remains in the latents, as shown in Figure T Motivated by this, we propose to build up global relevance throughout the latents. Inspired by the recent reference-based Super-Resoluse empower the entropy model with global vision by incorporating reference component. Unlike the super-resolution scenario, incorporating global reference information is non-trivial in deep image compression. The image during decoding is often incomplete which means that the information is badly missing. Besides, our target is to reduce the bit rates and recover the image from the bitstream faithfully, rather than inpainting low-resolution image with vivid generated details.
(SR) methods (Zheng et al. 2018 Yang et al., 2020 we
To address the above challenges, in our proposed method, a global reference module searches over the decoded latents find the relevant latents the target latent. The feature map of the relevant latent is then combined with local context and hyperprior to generate a more accurate entropy es- timation. A key ingredient in the global reference ensemble step is that we consider not only the similarity between the relevant and the target but also a confidence score to measure the high-order staticties in the latent feature distribution. The introduction of the confidence score enhances the robustness of the entropy model, especially for images with noisy backgrounds. Also, we found that the widely used Generalized Divisive Normalization (GDN) in image compression suffers from mean-shifting problem. Since the GDN densities are zero-mean by definition, mean removal is nec- essary to fit the density (Ballé et al. 2016b). Therefore we propose an improved version of GDN, named GSDN (Generalized Subtractive and Divisive Normalization) to overcome this difficulty.
We summarize our main contributions as follows:
To the best of our knowledge, are the first to introduce global reference into the entropy model for deep image compression. We develop a robust reference algorithm to ensemble local context, global reference and hyperprior in novel architecture. When estimating the latent feature entropy, both similarity score and confidence score of the reference area are considered to battle with the noisy background signals.
We propose a novel GSDN module that corrects the mean-shifting problem.
Experiments show that our method outperforms the most advanced codes available today both PSNR and MS-SSIM quality metrics. Our method saves by 6.1% compared to the context-adaptive deep models (Minnen et al. 2018b Lee et al.] 2019) and as much as 21.0% relative to BPG (Bellard. 2014).
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The remainder of this work is organized as follows. In Section we introduce the backbone of the end-to-end deep image compression network as well as the reference-based component for the entropy model. Section demonstrates the structure of our combined entropy model. The GSDN with mnean-shifting correction is given in Section 4 We present experimental comparison and visu- alization Scction[5] Finally, we enclose this work with an open discussion in Section 6
LEARNED IMAGE COMPRESSION
Learned image compression using deep neural networks has attracted considerable attention cently. The work of Toderici et al. (2016) first explored a recurrent architecture using an LSTM- based entropy model. A wide range of models (Ballé et al. 2017 Ballé et al. 2018 Mentzer al., 2018 Minnen et al. 201 Sa Lee et al.) 2019 Hu et al.] 2020 Cheng et al. 2020 used a CNN-based autoencoder with constrained entropy.
General learned image compression consists of an encoder, quantizer, decoder, and an entropy model. An image x is transformed into latent representation y via the encoder (1)), which is discretized by the quantizer Qzy to form ÿ. Given the entropy model Pg. the discretized value 1 can be compressed into a bitstream using entropy coding techniques such as arithmetic coding (Rissanen & Langdon 1981). The decoder (ū) then forms the reconstructed image à from the quantized latent representation ÿ, which is decompressed from the bitstream. The training goal for leamed image compression is to optimize the trade-off between the estimated coding length of the bitstream and the quality the reconstruction, which is a rate-distortion optimization problem:
-= R + XD = Ez-pp [- log2 Py (g((g) + ABz~p= [d(x, (e)),,,
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where À is the coefficient which controls the rate-distortion trade-off, pa the unknown distribution of natural images. The first term represents the estimated compression rate of the latent represen- tation. The second term d(x, à) represents the distortion value under given metric, such as mean squared error (MSE) or MS-SSIM (Wang et al. (2003)).
Entropy coding relies on an entropy model to estimate the prior probability of the latent representa- tion. Ballé al. (2017) propose fully factorized prior for entropy estimation as shown in Figure 2(a). while the prior probability of discrete latent representations is not adaptive for different im- ages. As shown in Figure b)) [Ballé al. (2018) model the latent representation
zero-mean Gaussian distribution based on a spatial dependency with additional bits. In Lee et al.) (0019) and Minnen al. (2018a), they introduce an autoregressive component into the entropy model. Taking advantage of high correlation of local dependency, context-adaptive models contribute to more ac- curate entropy estimation. However, since their context-adaptive entropy models only capture the spatial information of neighboring latents, there is redundant spatial information across the whole image. To further remove such redundancy, our method incorporates reference-based model to capture global spatial dependency.
Specially for learned image compression, a generalized divisive normalization (GDN) (Ballé al., 2016a) transform with optimized parameters has proven effective in Gaussianizing the local joint statistics of natural images. Unlike many other normalization methods whose parameters are typi- cally fixed after training, GDN is spatially adaptive therefore is highly nonlinear. As the reference- based model calculates relevance over the latents, it is crucial to align the distribution of the latents. To better align the latents, the proposed GSDN incorporates subtracting factor with GDN. We also present an effective method of inverting when decompressing the latent representation back to image.
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Our compression model with combined local, global, and hyperprior entropy model. Tan items represent data tensors, blue represents learned modules (e.g. convolutional layer), green is for quantization, and red represents entropy coding. The left side shows autoencoder with quantizer, the right side corresponds to the entropy model. The entropy model progressively incorporates local context, global context and hyperprior. Each parameter network predicts the Gaussian parameters conditioned on both the previous features and predictions. Using the Gaussian parameters (/1,, d3), the quantized latents are compressed into stream by an arithmetic encoder (AE) and decompressed by an arithmetic decoder (AD).
Figure 3:
COMBINED LOCAL, GLOBAL AND HYPERPRIOR ENTROPY MODEL
The models analyze in this paper build on the architecture introduced in Minnen al. 201 8a), which combined an autoregressive model with the hyperprior. Figure S provides a high-level overview our approach. The compression model contains main sub-networks. The first the core autoencoder, which learns the transform and the inverse transform between image and latent representation. Q represents the quantization function. The gradient-based optimization in learned methods is hindered by quantization. Here, we make use of mixed approach that has proven ef- ficient in Minnen & Singh (220)). The second sub-network is the combined entropy model, which responsible for estimating probabilistic model over the latents for entropy coding. The com- bined entropy model consists of a context model, a reference model, and a hyper-network (hyper encoder and hyper decoder). The three components combined progressively. Then three pa- rameter networks generate the mean and scale parameters for conditional Gaussian entropy model respectively.
Following the work of Minnen et al. (a). we model each latent, ÿi. as a Gaussian with mean 14: and deviation d; convolved with unit uniform distribution:
Po II (W of) * u( (.0,(-000000 0.5))) (0.)
where i and a are the predicted parameters of entropy model, is the quantized hyper-latents, is the entropy model parameters. The entropy model for the hyperprior is the same in Ballé et al. (2018), which non-paran non-parametric, fully factorized density model. As the hyperprior is part of the compressed bitstream, we extend the rate of Equation]] aas follows:
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The compressed latents and the compressed hyper-latents are part of the bitstream.
The reference-based SR methods (Zheng et 2018 Yang search for proper reference information. However, in the serial processing of image compression, the latent representation during decoding is often incomplete. We extend this search method by using illustrates how the relevance embedding module estimates similarity and fetches the relevant latents. When decoding the target latent, we use neighboring latents (left and top) as basis to compute the similarities between the target latent and its previous latents. Particularly, the latents are unfolded into patches and then masked, denoted as q E [H x W, k k x C] (where H, W. k. C' correspond to height, width, unfold kernel size and channels, respectively). We calculate the similarity matrix r E [ x W, H x W] throughout the masked patches by using cosine similarity,
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Note that we can only see the decoded latents, so the lower triangular of the similarity matrix is set zero. We get the most relevant position for each latent as well as the similarity score. According to the position, we fetch the neighboring latents (left and top) as well as the center latent, which named as "relevant latents". We use masked convolution as in Van den Oord et (2016) to transfer the relevant latents.
To measure how likely reference patch perfectly matches the target patch, Yang al. (2020) pro- pose a soft-attention module to transfer features by using the similarity map S. However, we found that a similarity score is not sufficient to reflect the quality of reference latent image compression. For this reason, confidence score is introduced to measure the texture complexity of the relevant latent. We use the context model to predict the Gaussian parameters (i.e., Pl. σ1) of latents solely. The latents are now modeled Gaussian with mean Yl and standard deviation 0 The probabil- ities of the latents are then calculated according to (11,, 01) as in Equation 2 As reference model is designed in spatial dimension, the confidence map U is obtained by averaging the probabilities across channel. With the above two parameters, the more relevant latent combination would be en- hanced while the less relevant one would be relived. The similarity S and the confidence U are both 2D feature maps.
Figure 5 provides the structure our combined entropy model. For the context model, we transfer the latents (i.e., Ø) with a masked convolution. For the reference model, we transfer the unfolded relevant latents with masked convolution. We use Local, global and hyperprior features are ensembled stage by stage, as well as the predicted Gaussian parameters. The mean parameters are estimated by the context model first, and then updated by the global model and the hyperprior model. We use the Log-Sum-Expp trick for resolving the under or overflow issue of deviation parameters. The output of global reference is further multiplied by the similarity S and the confidence U. The context model is based on the neighboring latents of the target latent to reduce the local redundancy. From the perspective of the global context, the reference model makes further efforts to capture spatial dependency. As the first decoded latents, there exists uncertainty that can not be eliminated solely. The hyperprior model leams to store information needed reduce the uncertainty. This progressive mechanism allows incremental accuracy for distribution estimation.
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4 GENERALIZED SUBTRACTIVE AND DIVISIVE NORMALIZATION
Virtually the traditional image and video compression codec consists of several basic modules, i.e. transform, quantization, entropy coding and inverse transform. An effective transform for image compression maps from the image to compact and decorrelated latent representation. As part of a Gaussianizing transformation, generalized divisive normalization (GDN) joint nonlinearity has proven effective removing statistical dependencies in image data (Ballé et al. 2016b). shows an impressive capacity for learned image compression.
We define generalized subtractive and divisive normalization (GSDN) transform that incorporates a subtractive operation. Inspired by the zero-mean definition Gaussian density, an adaptive sub- tractive operation is applied before the divisive operation. Particularly, we apply subtractive-divise normalization after convolution and subsampling operation in the encoder 9a (except the last convo- lution layer). We represent the ith channel at spatial location u,- The normalization operation
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Figure 6: Rate-distortion curves aggregated over the Kodak dataset. The left plot shows peak signal-to-noise ratios as function of bit rate (101og10 d with d representing mean squared error), the right plot shows MS-SSIM values converted decibels (-10logıu) d). where is the MS-SSIM value in the range between zero and one). In both terms, our full model consistently outperforms standard codecs and the state-of-the-ard learned models.
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We invert the normalization operation in the decoder ys based on the inversion of GDN introduced in Ballé et al. (a). We apply inverse GSDN (IGSDN) after deconvolution and upsampling opera- tion (except the last deconvolution layer) correspond the encoder. In the decoder, represent the ith channel at a spatial location as vi; For the inverse solution, subtraction is replaced by addition while division replaced by multiplication:
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5 EXPERIMENTS
5.1 IMPLEMENTATION DETAILS
Architecture For the results in this paper, we did not make efforts reduce the capacity (i.e. number of channels, layers) of the artificial neural networks to optimize computational complexity. The architecture of our approach extends on the work of Minnen et al. (2018a) in two ways. First, the main autoencoder is extended by replacing the GDN with the proposed GSDN (IGDN with IGSDN in decoder). Second, the entropy model extended by incorporating a reference model. Three modules are combined in progressively.
Training The models were trained on color PNG images from CVPR workshop CLIC training dataset (http: htpp://challlee wewale.eee....mm wwwpressscsc.ccoco on cc/). The models were optimized using Adam Kingma & Ba 2014) with batch size of and a patch size of 512 x 512 randomly extracted from the training dataset. Note that large patch size is necessary for the training of the reference model. As our combined entropy model have three predictive Gaussian parameters, we first trained the three modules with weight of 0.3 0.3 0.4 as warm-up with 1000 epochs. After that,

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Figure 7: Each curve shows the rate savings at Figure Examples of target region (indicated different PSNR quality levels relative to BPG. by purple) and its relevant region (indicated by Our full model outperforms BPG by 21% at low yellow). bit rates.
trained three modules with weight of 0.1 0.1 0.8 because the third output is used for entropy coding in practice. In the experiments, we trained different models with different À to evaluate the rate-distortion performance for various ranges of bit-rate.
Distortion measure We optimized the networks using two different types of distortion terms, one with MSE and the other with MS-SSIM (Wang et al. (003). For each distortion type, the average bits per pixel (BPP) and the distortion, PSNR and MS-SSIM, over the test set are measured for each model configurations.
Other codecs For the standard codecs, we used BPG (Bellard., 2014) and JPEG (Wallace) 1992).
For the learning-based codees, we compared ofte-of-theearr methods that combine spatial context with hyperprior (Minnen et al. (2018a): Lee et al. (2019)), which also shares similar structure of our method.
5.2 RATE DISTORTION PERFORMANCE
We evaluate the effects of global reference and GSDN in learned image compression. Figure shows RD curves over the publicly available Kodak dataset (Kodak 1993) by using peak signal-to- noise ratio (PSNR) and MS-SSIM as the image quality metric. The RD graphs compare our full model (Entropy Model with Reference GSDN) existing image codecs. In terms of PSNR and MS-SSIM, our model shows better performance over state-of-the-an learning- based methods as well standard codecs.
Figure 7 shows the results that compares different versions of our models. Particularly, it plots the rate savings for each model relative the curve for BPG. This visualization provides more readable way than a standard RD graph. It shows that the four components (i.e. local context, global reference, hyperprior) yield progressive improvement. Especially, the combination of global reference provides a rate saving of 5.3% over the context-only model at the low bit rates. As we introduce the confidence U. the performance of the reference model further improved. Our full model, which replaces GDN with GSDN, provides a rate savings about 2.0% over the proposed entropy model.
5.3 VISUAL. RESULTS OF REFERENCE-BASEE ENTROPY MODEL AND GSDN
Figure shows the results of the relevance embedding module. The target region (indicated by purple) and its relevant region (indicated by yellow) are marked by the same numbers. As the relevance calculated on the latents, we map the position back to the RGB image. The region box just indicates position of target latent (relevant latent) and does not represent receptive field. The relevance results explain the bit savings caused by the combining global reference.
Figure g visualizes the internal mechanisms of different entropy model variants. Three variants are showed: local context only (first row), combined global reference with local context (second row), full entropy model(third row). Intuitively,
how these components complemen-

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Figure 9: Each row corresponds to different entropy model variant and shows information for the channel with the highest entropy. The predicted mean corresponds to the Gaussian parameters (i.e. M1,, M2. (3). The last column shows progressive entropy difference (red is better while blue is worse). The visualizations show that the combined model reduces the prediction error. The ensemble of local context, global reference and hyperprior allows more accurate estimation and thus lower entropy.
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Example of confidence U map and similarity S map. The S map is tend represent shape while the map is tend to represent texture, e.g., the wood pile on the right of the boat.
tary. The Kodak image 19 (first column) is encoded, and then the latents for the channel with the highest entropy (second column) are extracted. The predicted mean (third column) corresponds to the Gaussian parameters (i.e. Pr, P2, (a) estimated by the three entropy model variants. Since the context model is based on the prediction from casual context, it has limited accuracy when dealing with irregular texture. The reference model can search throughout latents that have been decoded and benefit from similar texture. The combining of global reference over local context leads to lower prediction error. Finally, the last two columns show how the entropy is distributed across the image for the latents. The global reference leads to rate savings over the latents which have similar reference latents, especially those with irregular texture. From the perspective of hyperprior, it uses bit-consuming side information by which the uncertainty could be reduced over all the latents.
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Figure 11: Histograms of latent representation by GDN-based model and GSDN-based model. Each plot corresponds to one channel of the latents over 24 Kodak images. Four channels with highest entropy are visualized.
As shown in Figure 10 the S map tend represent shape while the U map tend represent texture, e.g., the wood pile on the right of the boat. The multiplication by the confidence U would influence the similarity S. The U map represents the texture score of the reference latent, which measures the complexity of the reference feature. It agrees with what we have assumed that U would compensate for the weakness of S.
We also visualized the distributions of the latents on the GDN-based model as well as the GSDN- based model. We constructed two-stage model. A GDN-based model is trained first, which is then used construct GSDN-based model by adding parameters of subtraction. Histograms of the latent representation are shown Figure IT Compared to GDN, GSDN relieves the mean-shifting problem of the latents. The latents of GSDN- model comes closer to zero-mean.
DISCUSSION
Based on previous context-adaptive methods (Minnen et al., 2018a Lee et al. 2019). we have in- troduced new entropy model for learned image compression. By combining global reference, we have developed more accurate distribution estimating for the latent representation. Ideally, our combined entropy model effectively leverages both the local and global context information, which yields enhanced compression performance. The positive results from global reference somewhat surprising. We showed in Figure 7 that the combined entropy model provides a progres- sive improvement in terms of rate-distortion performance without increasing the complexity of the model.
Global reference model scans decoded latents and then finds the most relevant latent to assist the distribution estimating of target latent. Our reference model is inspired by recent works of reference- based super-resolution (Zhang al. 2019 Yang et al. 2020). We extend this reference-based mod- ule in three ways to adapt it to image compression. First, we extend it to single-imas reference module. The second extension that we incorporate the reference module into entropy model. The idea is that avoid influencing the highly compacted latent representation. Moreover, confidence variable introduced to enable adaptive reference. Intuitively, we can see how the local context and global reference are complementary as shown in Figure
The improvement by the reference model also implies that current learned image compression is not ideal to model the spatial redundancy. The proposed reference model develops relevance across the latents of a single image. Reference within a single image limits its benefit. The upper part of latents has fewer decoded latents reference. An alternative direction for future research may be to extend the reference model to multi-image compression. We also plan to investigate combining video compression with reference model to see if the two approaches complementary.

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George Toderici, Sean M O'Malley, Sung Jin Hwang, Damien Vincent, David Minnen, Shumeet Baluja, Michele Covell, and Rahul Sukthankar. Variable rate image compression with recurrent neural networks. 2016.
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Published as a conference paper at ICLR 2021
A
APPENDIX
A.1 RESULTS ON THE CLIC VALIDATION DATASET
PSNR (MGB)
30
32
JPLG (4:2:0)
JPE2200 (Open)PEG)
BPG (4:4:4]
Reproduced Minnen (2018) mix quantization
Full
3.0
62
per (BPP)
28
MS SSIM (0B)
1.2
JPEG (4:2:0)
JPEG2000 (OpenjPEG)
BPG (4:434)
Repradluted Minnnn (2018) mix quantization Our Full Model topt. for MS-55504)
3.6
62
3.6
1.0
Bits per pixel (BPP)
Performance Evaluation on CLIC Validation dataset. Our method performs very well when optimized for MSE or MS-SSIM. Each point on the RD curves is calculated by averaging over the PSNR (or MS-SSIM) and bit rate for the 102 images from CLIC Validation dataset (http: 7/challenee cct.esssssssscccoo...o.....
Figure 12:
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Published as a conference paper at ICLR 2021
Encoder
Decoder
Hyper Encoder
Hyper Decader
Consext Model
Referance Midel
Parameter Netwock
Conc: 13:19222
Decouv: 15c19222
Coav: k3c191s1
Decomw: 1S219242
Masked: 15C38451
Masted: k323865]
Cosy: kicl
GSDN
IGSDN
Lesky
Lesky ReLU
ReLU
Conv: k5c192x2
Decom: k3c19222
Coev: k52192s2
Deconv: k3c19262
Coay: kitel 152s1
GSDN
IGSDN
Lesky ReLU
Lesky ReLU
Lesky ReLU
Cunc: 15:19222
Decum: k5c19222
Conv: k5e192x2
Deconv: k3c768s1
Conv: klc768s1
Cone: k5c384s2
Decomw: 35c322
Table I: Each row corresponds to a layer of our generalized model. Convolutional layers are spec- ified with the "Conv" prefix followed by the kernel size, number of output channels and downsam- pling stride (e.g. the first layer of the encoder uses 5x5 kernels with 192 output channels and a stride 2). The "Deconv" prefix corresponds to upsampled convolutions, while "Masked" corresponds to masked convolution as in Van den Oord et al. (2016). GSDN stands for generalized subtractive and divisive normalization, and IGSDN is inverse GSDN. The three parameter networks share a similar architecture.
Hyper Encoder
Hyper Decoder
Context Model
Reference Model
Parameter
Method
Encoder
Decoder
Network
Minnen et al. 2018a
74.63
269.98
2.92
7.62
11.32
NA
8.15
Ours
84.12
279.47
2.92
7.62
11.32
7.70
24.46
Table 2: GFLOPs of each module for the proposed method and reproducing method (Minnen et al.
8a.. The size of the test image is 512x768.
240p
360p
480p
512x768
720p
1080p
GFLOPs Proportion of Reference
9,98
22,85 10.90%
41.59
54.03
138.04
366.57
3296.99 66.28%
9.36%
12.98%
14.25%
21.34%
33.36%
Table 3: GFLOPs of entropy model and proportion of reference model with various image size.
A.2 ARCHITECTURE DETAILS
Details about the individual network layers in each component of our models are outlined in Table The output of the last layer encoder corresponds the latents, and the output of the last layer in hyper-encoder corresponds to the hyper-latents. The output of the last layer in decoder corresponds to the generated RGB image. The three parameter networks share a similar architecture. The only difference is the number of the first layer's input channels in parameter network. The output of the parameter network must have exactly twice as many channels as the latents. This constraint arises because the entropy model predicts two values, the mean and deviation of Gaussian distribution, for each latent.
A.3 COMPUTATIONAL COMPLEXITY
Our main goal was to optimize for compression performance. To make a fair comparison with pre- vious methods, have taken
match model capacities between Hontext+ method MMnnenn et al. 2018b) and Context-Adaptive method (Lee et al. 2019). We did not to choose number filters that would limit the capacities of encoder, decoder and entropy model.
method (Minnen et al. 2018b). the increased computation by GSDN and global reference about 10% when processing the 5T2x Kodak images. The com- plexity of search module is O(N about the size of latents, while the complexities of other modules are (NN.. Although not the main goal our paper, the computational complexity crucial for the application of deep learning method in industry field. We add two tables in appendix to describe computational complexity and FLOPs our method. As you concerned, the complexity of refer- ence model increases with image size more fast than other modules. The reason is that the search module computes similarity matrix throughout the latents. And we just use a naive way for the search module. So, there is room improve the global reference model and are interested in researching this further.
Compared to Context+Hy
We have not yet optimized our compression method for computational complexity. Rather, chose the number of filters high enough to rule out the Reference model. We just set the model larger than necessary, and let the model determine the number of channels that yield the best performance.
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Cortot reforescel *ygsgpet
Reproduced Miree (2018) mi
Reprodueed (21101 mis Q prograale
20.0 31.2
115
32.5
33.5
25.0
994R mange
Figure 13: Each curve shows the rate savings at different PSNR quality levels relative to BPG. We reproduced similar models of (Minnen et al. 201 8a) Context+ Hyperprior with two variants of mixed quantization and progressive entropy model. The training procedures (e.g. training data, environment, hyper parameters, etc) are same with the other experiments.
Similar to reported in previous work, found that small channels is enough and does not harm the compression performance when training model to low bit rates.
A.4 VISUAL COMPARISON ON THE KODAK DATASET
(a) Ours 1.pp-0.1444 PSNR 91.90
(b) BPG (bpp 0.10-7 PSNR-31.
(c) JPEG 1658, PSNR-21.82)
(d) Original
Figure 14: At similar bit rates, our combined method provides the highest visual quality on the Kodak 15 image. BPG introduces few geometric artifacts around the girl's mouth and nose. JPEG shows severe blocking artifacts at this bit rate.
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Published as a conference paper at ICLR 2021
(a) Ours 0opp-0.3033, PSNR-30.68)
(b) BPG (bpp-0.3036 PSNR-29.91)
(c) JPEG (bpp-0.3145, 25.762
(d) Original
Figure 15: At similar bit rates, our combined method provides the highest visual quality on the Kodak 21 image. BPG shows more "classical" compression artifacts, egg,, ringing around the edge of the lighthouse.
(a) Ours (bpp-0.1144 1147 PSNR-33.94)
(b) BPG (bpp- 1289, PSNR-33.35)
(c) JPEG 05p9-0.1591, PSNR-22.53)
(d) Original
Figure 16: At similar bit rates, our combined method provides the highest visual quality on the Kodak 23 image. Note that the BPG reconstruction has some ringing and geometric artifacts (e.g., at the top of the red parrot's 's head).
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Published as a conference paper at ICLR 2021
A.5 VISUAL COMPARISON THE CLIC VALID DATASET
Ours 1bpp-0.1512, PSNR-31.8)
BPG (bpp-0.1678, PSNR-31.62)
Original
Figure 17: similar bit rates, our method provides the better visual quality on the high resolution image on CLIC valid dataset.
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Published as a conference paper at ICLR 2021
A.6
ARCHITECTURE COMPARISON
Factorized Eatroyy Modal
Model
Model
AE
PN
PN
AD
My. 45g
Hyperprior
Global Reference
Local Context
Figure 18: Context-only Entropy Model. This model relies only on an autoregressive process with local context to predict the Gaussian parameters. The benefit of this approach is that no additional bits are added to the bitstream. The downside of this model is that it conditions predictions only on neighboring latents.
Fanortaed Enerpy Model
Context Model
AE
PN
PN
PN
8
9
AD
Oz.
Mgg 0g
Hyperprior
Reference
Local Context
Figure 19:
Context + Reference Entropy Model. This model combines global reference with local context. The benefit of this model is that can access all previous latents.
Factorized Eatroy Model
AD
Referenee Model
Content Model
8
Ê
PN
PN
PN
AD
Ry.03
02.0z
My. 02
Hyperprior
Global Reference
Locul Context
Figure 20: Context + Reference Hyperprior Entropy Model. This model uses hyper-networt to learn (hyper-)laten) representation to transmit side information. The benefit of hyperprior in this model is that it leams to represent information useful for correcting the context-basee based predictions.
17


Reviews:
[{"review_id": "zCuTR69TEHt", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "**Summary of paper**\nThe paper presents a learning-based approach for image compression. To reduce the compression rate, it describes two novel extensions, one to take the global context into account and an improved version of the commonly used GDN layer. Their advantage has been shown in a thorough ablation study. Overall, the method achieves superior performance compared to standard codecs as well as other state-of-the art learning-based method on the evaluated dataset (from Kodak).\n\n**Strengths**\n\n(S1) The approach is clearly described, and the figures help to follow the paper.\n\n(S2) The proposed approach of using a reference model to consider the global context is novel for the application of image \ncompression. \n\n(S3) Suggestion to improve GDN layer to address the mean shift problem of the existing formulation.\n\n(S4) The ablation study shows the effect of the different modules.\n\n(S5) The method achieves superior results on the tested dataset (Kodak), standard in image compression, and both PSNR/SSIM have been reported.\n\n**Weaknesses**\n\n(W1) Runtime for encoding and decoding not listed. In case, that the global reference model leads to some overhead in runtime, especially for decoding time, that would be worth mentioning. Also are there any limits in terms of image size the method can handle?\n\n**Justification**\nInteresting approach with superior results.\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "3HMNfq5Mye9", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper propose two methods for improve deep image compression performance: (i) Global Reference Module and (ii) Mean-shifting GDN Module (GSDN). (i) Global Reference Module searches over the decoded latents to find the relevant latents to the target latent for improve accuracy of entropy estimate. Authors extended Yang et al. 2020 method to using masked patch. (ii) GSDN extends GDN to use subtractive operation.\n\nPros: \n- Proposal seems better Rate-Distortion results than Lee 2019 and Minnen 2018 (Figure 6 and 7).\n\nCons: \n- The method for generating U (2D feature maps) is not clearly described; it is unclear how the output channel of the parameter network (768) is calculated in the form of 2D feature maps.\n- In Table 1, the output channel of the Encoder is 384, while the corresponding input channel of the decoder is 192. I couldn't understand why the number of channels are not the same.\n- In Figure 5, the meaning of σ's log is unclear and seems not appear to have been mentioned in the text.\n- The proposed method uses the mix quantization approach (Minnen & Singh 2020), but the evaluation of figure 7 is compared to Minnen 2018 as Context + Hyperprior so it is not fair comparison. For example, to put the results of the Minnen 2018 approach + mix quantization on it and compare it will make the claim of the proposal effect credible.\n- According to Figure 7, GSDN appears to be effective. It is an interesting, but I thought the effects were less explained. It would be more convincing if direct data on the mean-shifting problem were presented.", "extra_scores": {}, "extra_text": {}}, {"review_id": "33y33CMjzl5", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "1\tThe explanation of the proposed “confidence U” is significantly deficient. Further statements to the calculation process, theory and function are expected. Please provide more details.\n2\tWhat the point of the operation that the output of global reference is multiplied by similarity S and confidence U directly as shown in Figure 5?  Will the direct multiplication by the confidence U impair the function of the attention S? A more reasonable and efficient method is expected for applying the confidence map.\n3\tDifferent from conventional entropy models, this paper proposed to progressively use the prior from context model, reference model and hyperprior model instead of obtaining priors respectively and then combining them to obtain estimation results. But the paper lacks the explanation and experiments to the rationality of the design of the progressive process. The comparison results of whether progressive or not are missing.\n4\tGenerally, the performance gain is very limited as shown in the RD curves in Figure 6. In particular, why the performance gain appears to be so minor in the low bitrate range? \n5\tIn Figure 10, why the comparison results with any learned compression methods are missing? The comparisons with various methods only on Kodak dataset in Fig. 6 are not convincing. \n6\tThe visual comparison results on the CLIC dataset of high resolution are missing. And some key references for deep-network based image compression are also missing.", "extra_scores": {}, "extra_text": {}}, {"review_id": "-Zno45rCp4G", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The authors introduce global reference into the entropy model for deep image compression. \nThey also develop a reference algorithm to ensemble local context, global reference and hyperprior. \nThis causes the algorithm to be robust to background noise.\nAlso, the authors develop GSDN module to handle mean-shifting issue.\nThe proposed method demonstrates good quality and memory usage gain. \n\nThis paper propose to take into account the global information as well as the local information to perform better image compression. \nThe authors also demonstrate comparison to popular image compression standards and recent deep learning approaches. \nI think this work is a nice work, however I have two main concerns. \nThe dataset used for evaluation is rather outdated. Have the authors tried evaluating on recent image compression datasets, or custom data and compare with the state of the art?\nHave the authors compared computational complexity? The main reasons why industry standards are not enthusiastic about deep learning approaches to compression is due to the computational complexity, not so much memory. Have the authors compared FLOPS? Moreover, since this work is dealing with global image information, it seems the complexity would increase rapidly with image size, while standard jpeg will relatively be not as severe. Have the authors experimented computational time with UHD, QHD, or 4k?\n\nI am leaning towards accept but not by a lot.\nI would like the authors to discuss upon \n- Empirical results on more recent datasets\n- Computational complexity and in terms of image size\n- FLOPS\n- Computational complexity and time with high resolution like UHD to 4k\n\nAfter these comments, I would like to adjust the rating", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper received moderately good reviews, 3 positives (6, 6, 7) and 1 negative (5). The reviewers are generally positive about the main idea but identified several limitations; performance improvement is marginal compared to existing approaches, the proposed method incurs higher computational complexity, and the presentation is not clear enough. Some of these issues are addressed in the rebuttal, though. Overall, the merits of this work outweigh the drawbacks and I recommend accepting this paper.
Decision: Accept (Poster)