ACRF: Compressing Explicit Neural Radiance Fields via Attribute Compression
Authors: Guangchi Fang
Qingyong Hu
Longguang Wang
Yulan Guo
Venue: ICLR 2024 poster (2024)
Keywords: NeRF; NeRF Compression; 3D Data Compression
Primary area: general machine learning (i.e., none of the above)

Abstract: In this work, we study the problem of explicit NeRF compression. Through analyzing recent explicit NeRF models, we reformulate the task of explicit NeRF compression as 3D data compression. We further introduce our NeRF compression framework, Attributed Compression of Radiance Field (ACRF), which focuses on the compression of the explicit neural 3D representation. The neural 3D structure is pruned and converted to points with features, which are further encoded using importance-guided feature encoding. Furthermore, we employ an importance-prioritized entropy model to estimate the probability distribution of transform coefficients, which are then entropy coded with an arithmetic coder using the predicted distribution. Within this framework, we present two models, ACRF and ACRF-F, to strike a balance between compression performance and encoding time budget. Our experiments, which include both synthetic and real-world datasets such as Synthetic-NeRF and Tanks&Temples, demonstrate the superior performance of our proposed algorithm.

Published as a conference paper at ICLR 2024
ACRF: COMPRESSING EXPLICIT NEURAL RADIANCE FIELDS VIA ATTRIBUTE COMPRESSION
Guangehi Fang', Qingyong Hu², Longguang Wang', Yulan Guo
Sun Yat-sen University, University of Oxford, 3 AAviation University of Air Force,
National University of Defense Technology
ABSTRACT
In this work, study the problem of explicit NeRF compression. Through an- alyzing recent explicit NeRF models, we reformulate the task of explicit NeRF compression 3D data compression. We further introduce our NeRF compres- sion framework, Attributed Compression of Radiance Field (ACRF), which fo- cuses on the compression of the explicit neural 3D representation. The neural 3D structure is pruned and converted to points with features, which are further encoded using importance-guided feature encoding. Furthermore, we employ an anportaacc-priooriiiee entropy model to estimate the probability distribution of transform coefficients, which are then entropy coded with an arithmetic coder using the predicted distribution. Within this framework, we present two models, ACRF and ACRF-F, to strike a balance between compression performance and en- coding time budget. Our experiments, which include both synthetic and real-world datasets such as Synthetic-NeRR NeRF and & Temples, demonstrate the superior performance of our proposed algorithm.
INTRODUCTION
In recent years, neural radiance fields (NeRFs) (Mildenhall et al. 2020) have emerged as a popular research topic due to its wide application and expressive performance in novel view synthesis, 3D reconstruction, and 3D perception. To improve the performance of NeRFs quality and training/infereen sentations such as voxel grids (Sun et al., 2022, Chen et al. 2022a: Yu al. 2022. 202T). point clouds (Xu et al.) 2022] Ost et al. 2022). and meshes (Chen et al. 2023). These representations provide a stronger capacity for NeRFs learn and represent 3D scenes by explicitly encoding the geometry and topology of the scene into structured data format. However, the use of explicit 3D representations comes with a significant drawback, which is the substantial increase model size, leading to challenges in transmitting and storing NeRF models. In this regard, study the criti- cal problem of explicit NeRF compression, which aims to reduce the size of a NeRF model while maintaining its rendering quality and other performance metrics.
terms of rendering efficiency, recent research has explored the use of explicit 3D repre-
Several previous works (Deng & Tartaglione 2023 et al.
2023 Rho et al.] 2023 Xie al. (023) have explored vol-
umetric NeRF compression techniques. Re:NeRF (Deng & Tartaglione 2023) and HollowNeRF (Xie al. 2023) focuses
on voxel pruning, while VQRF (Li et al. 2023) introduces a pruning strategy and compresses voxel features using vector quantization. Rho et al. (Rho et al. (023) employ wavelet transform to learn a more compact representation. These algo- rithms utilize techniques in both model compression (i.e,, prun- ing and weight quantization) and data compression (i.e., vector quantization and wavelet transform), and demonstrate promising compression performance. However, these algorithms primarily focus on the voxel representation and overlook the redundancy inherent in the 3D geometry structure and textured latent features. As depicted in Fig. [ it is clear that latent features follow a certain dis- tribution closely associated with the original color, revealing spatial redundancy between features. This observation suggests the potential for explicit NeRF model compression. Moreover, existing
Figure 1: Latent features of explicit neural 3D representation.

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methods have primarily emphasized compression performance and have not adequately considered the compression time budget, which is crucial for real-world applications.
In this paper, first conduct comprehensive analysis of the task of explicit NeRF compression and reformulate as 3D data compression problem. Next, we propose a novel NeRF compression framework, named ACRF, which utilizes 3D data compression techniques. The proposed framework focuses on compressing the explicit neural representation, by first pruning the neural 3D structure points with features, followed by importance-guided feature encoding of latent features. Finally, we apply entropy coding to further compress the encoded results with an importance-priorittzee entropy model. To balance both compression performance and encoding time budget, we present two pipelines, ACRF and ACRF-F. By simply combining the rendering and bitrate loss, our compression pipeline, ACRF, can achieve superior compression performance. By directly distribution fitting, our ACRF-F can achieve fast NeRF compression. Our main contributions can be listed as follows:
Based on an in-depth analysis of explicit NeRF models, we reformulate the task of NeRF compression, shifting the focus of previous works from model compression to 3D data compression. In light of this reformulation, we present an innovative NeRF compression framework that incorporates advanced 3D data compression techniques.
We introduce time-efficient pruning strategy with only view-independent information, and propose two importance-bant importance-priorte prioritized entropy modeling leveraging importance as auxiliary information. Our framework is compatible with typical explicit representations (voxel grid and point cloud), and strikes a well balance between rate-distortion and encoding time. Experimental results on several datasets show the great potential and promising scalability of our method.
components: importance-guiie feature encoding and
RELATED WORK
2.1 NEURAL RADIANCE FIELDS
Neural radiance field (NeRF) Mildenhall et al.) 20220) has seen significant improvements in the last three years for novel view synthesis. Follow-up algorithms (Liu et al. [2020] Hedman et (021 Yu
al.,
2021 2022 Sun et al. 2022, Chen et al. 2022a) have introduced volumetric representations
to improve inference speed and rendering quality. For instance, NSVF (Liu et al. 2020)) develops sparse voxel octree to represent the 3D scene, while DVGO (Sun et al., 2022) separately models two voxel grids for density and color, and TensorRF (Chen et al. 2022a) decomposes its feature voxel into low-rank tensor components. Apart from the aforementioned voxel-based representations, MobileNeRF (Chen al.
2023) represents the scene
triangle mesh textured by deep features. merge measured LiDAR point clouds directly into their framework, and
Ost et al. (Ost et al. 2022
PointNeRF (Xu al.] 2022) generates neural points using multi-view stereo and their point growing and pruning strategy. Further, SPIDR (Liang et al. 2022) extends points to SDF.
Recently, handful of works (Deng & Tartaglione 2023 Li et al. 2023 Rho al. 2023 Xie
et al. 2023 Shin & Park 2023 Wang et al. (202)) have been proposed for volumetric NeRF com- pression. For example, Re:NeRF (Deng & Tartaglione 2023) and HollowNeRF (Xie et al. 2023) presents a voxel pruning algorithm that iteratively removes voxels. VQRF (Li et al. 2023) pro- poses a volumetric NeRF compression framework that includes voxel pruning, vector quantization, and post- post-processing. Rho et al. (Rho et al., 2023) propose to learn a compact representation using wavelet coefficients with a voxel mask.
2.2
3D DATA COMPRESSION
Existing algorithms (Meagher 1982, Schwarz et al., 2018) usually adopt octree structures to en- code 3D positions of point clouds voxel occupancy. For instance, G-PCC (the MPEG point cloud compression standard) (Schwarz et al. 2018), employs an octree-based method for position compression. Learning- based methods (Huang et al. 2020 Biswas et al. 2020 Que et al.) 2021 Fu et al.] 2022 Chen et al., 2022b) have also leveraged the octree representation and introduced octree-based based entropy models for entropy coding.
To achieve attribute compression (i.e., compression of point attributes such as color and reflectance), several techniques have been proposed to extend image compression methods (Wallace) 1992
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Goyal 2001 Skodras et al., 2001 Sullivan al. 2012 Bellard 2015) to point clouds. Generally, this process involves three steps: transform coding, quantization, and entropy coding. Transform coding involves carefully designing transformation of attributes into the frequency domain duce signal redundancy. For example, Zhang et al. (Zhang et al. 2014) construct graph by dividing point cloud into blocks and applying the graph Fourier transform point attributes. Queiroz al. (De Queiroz & Chou 2016) propose a region adaptive hierarchical transform (RAHT) by in- troducing wavelet transforms to point clouds. Quantization is used to quantize coefficients from transform coding into transmitted symbols. Entropy coding aims to encode these symbols into bitstream through an entropy coder, such as Huffman (Huffman, 1952), arithmetic (Witten et al,) 1987), or Golomb-Rics coders (Weinberger et al. 2000) RRchardsoon 2004). To achieve attribute compression, 3DAC (Fang et al. [2022) introduces an attribute-oriented deep entropy model based on the RAHT tree structure. Rho et al. (Rho et al. (023) and ReRF (Wang et al., 2023) also use
run-length coding and Huffman coding in their NeRF compression pipeline.
REVISIT NERF COMPRESSION
Neural Radiance Fields (NeRFs) (Mildenhall al. 2020 leverage implicit neural representation to model a 3D scene through volume rendering. Specifically, first employs multi-layer perceptrons (MLPs) map spatial position and view direction the point density and color
(c, MLPs(x d).
(I)
Then, volume rendering (Kajiya & Von Herzen 1984) is further adopted to accumulate the point densities and colors e into an expected color C ) of ray r following Max (Max 1995):
N ((r) = Σ Ti .l.a: a. Ci, where T; = =xxp
i-1
- o50
a, = - exp(-o,6.).
N the number of sampled points and 8 is the distance between two nearby points. Finally, the ray colors are merged into an image with rendering loss as the optimization objective.
Explicit 3D representations, such as voxel grids (Sun et al., 2022), point clouds (Xu et al. 2022).
and meshes (Chen et al. 2023), can be incorporated into the NeRF pipeline to improve rendering quality and training/mferrnce speed (e.g., use spatial interpolation to obtain latent features instead of using MLPs in Eq. (.. However, these 3D representations also result in significant increase in model size, which poses a challenge for transmitting and storing these NeRF models.
3.1 COMPRESS EXPLICIT NERF AS 3D DATA
The task of NeRF compression is still in its early stages, and there is currently no general and universal framework for this task. Several recent works have investigated this problem from different aspects. A handful of recent studies designed to learn compact neural representation (Rho al.) 2023 Wang et al. 2023) Shin & Park 2023), while others focus on model or data compression Techniques such pruning and quantization (Deng & Tartaglione 2023 Li al. 2023] Xie al.) 2023). In this section. we first analyze the components of explicit NeRF models and then present our formulation of this task.
First, we identify that explicit NeRF algorithm with additional 3D data structures such as voxel grids, neural points, or meshes in addition to MLPs, re- quire more storage than the original MaPed NeRF model (5 MB). For example, DVGO (Sun) al. 2022) constructs their model using two voxel grids [100 MB) and shallow MLP (0.1 MB), while PointNeRF (Xu et al.) 2022) combines neural points
(515))
Fentures
Density Gird
Point Positions
(a)
(b)
Figure 2: Percentage of disk storage of each part for (a) DVGO (Sun et al. 2022) and (b) Point- NeRF (Xu et al. 2022).
(over 100 MB) and MLPs (1.4 MB). As shown in Fig. explicit 3D representations take up a significant amount of storage compared to other net-
work parameters (i.e., MLPs).
Considering the spatial redundancy illustrated in Fig. D we point out that the neural 3D representa- tion constitutes novel category of 3D data. Thus, we propose to reformulate the problem of explicit
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Pruning (Sec. 4.1)
Deep Entropy Model
Probshility Fatimation
Confficients Feature Encoding (Sec. 4.2)
Arritmetic Coding
Explici NeRF
Points
Volume Resdering
Entropy Minimization (Sec. 4.3)
(a) ACRF
Joint Learning:
Eyd Ma
(b) ACRE-F
Distribution Fitting:
L -
tee
Figure 3: The frameworks of our NeRF compression method, (a) ACRF and (b) ACRE-E.
NeRF compression the task of 3D data compression. In other words, aim to compress the neural 3D representations (including the geometry structure and the textured deep features) to re- duce the model size. Given that deep features contribute significantly more information to the NeRF model and consequently require greater storage, we focus on the feature compression stage, also known as attribute compression in the data compression community.
4 METHODOLOGGY
In this study, we introduce novel NeRF compression framework, with a particular focus on com- pressing explicit neural 3D representations. Given pre-trained NeRF model with an explicit 3D representation, the objective of our framework is to reduce the model size while maintaining high- quality rendering. particular, we present two compression pipelines, ACRF (a full model) and ACRF-F (a light model), balancing compression performance and encoding time complexity.
Compression Pipeline ACRE Figure 3 illustrates the compression framework of ACRE Given NeRF model with explicit neural representation, our framework begins by converting the explicit representation into points with features through view-dependent pruning (VD pruning, Section 4. We then perform importance-guidee feature encoding for point features (Section 4.2). Furthermore, we minimize the information entropy within the 3D model through jointly training an importance- prioritized entropy model and updating the point features with both cross-entropy (i.e., loss for probability estimation) and rendering loss (Section 4.3) Finally, we convert transform coefficients bitstream using arithmetic coding.
Compression Pipeline of ACRF-F. The overall pipeline of ACRF-F, as depicted in Fig. (b), is closely similar the ACRF process. The primary difference lies in the utilization of proposed view-independent pruning (VI pruning) for the fast removal of less important voxels (Section 4.1) Additionally, we learn the entropy model fit the coefficient distribution while keeping the point features and other NeRF parameters fixed (Section 4.3)
4.1 PRUNING
Voxel pruning Li et al. 2023 Deng & Tartaglione 2023 Xie et al. 2023 is a key step in volumetric NeRF compression
voxels with low information. Most existing algorithms (Deng & Tartaglione 2023 Xie et al. 2023) integrate pruning strategies into their training pipeline, which is time-consuming and impractical for compression. In contrast, VQRF (Li et al.) (023) achieves voxel pruning by constructing importance for each voxel and then removing voxels with low cumulative importance.
Here, we refer to the pruning strategy proposed by VQRF as view-dependent pruning as it relies on training camera poses to generate importance (Details can found in appendix Sec. B.). This approach proves effective because it directly considers blending weights in the rendering func- tion. However, this approach necessitates the availability of trained camera poses for generating the transmittance T; and weights w. Additionally, the time required for pruning increases with the number training views and sampled ray points, making it impractical for several real-world scans (e.g., e, the T Temples dataset), where pruning times
comparable to fine-tuning times

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as shown in Table 1 Here, we introduce our view-independent pruning strategy leveraging voxel features and sampled points in voxel space.
Pruning with Voxel Features. Our approach leverages the insight that the feature tensor f, of voxel grid Vi encodes essential information for recovering the color and density of the 3D scan. Therefore, statistical measures, such as the maximum absolute value, the amount of information contained in a feature tensor. Specifically, we can compute the importance I, directly from the voxel et as the maximum absolute value of the feature fa:
be employed quantify
I M MAX((E
The rationale for utilizing the maximum absolute value of features is grounded in the observation that this value is indicative of the corresponding feature's s information content. During initialization, the NeRF model is information-devoid, and most works (e.g.. DVGO (Sun et al. (022) and PointNeRF (Xu et al. 2022 initialize features with zeros or small random values. During optimization, these features become informational they encode color and density. As shown in Fig. [T_ the feature distribution aligns with the scene over time. More explicitly, the feature values elevate from their origin (typically zeros during initialization) form a distribution reflecting the scene. Consequently, features with small values approximating zero often contain less information, indicating minimal updates during optimization. In contrast, features with larger values are usually more informative. More statistical analyses about the maximum absolute value are provided in appendix Sec. G.
Our goal for compression is eliminate features with low informational content and retain those with higher value. This process justifies the use of the distance from the origin as an importance met- ric for the features. Similar some model pruning algorithms (Li et al. 2016) which use statistical measures to estimate the importance of convolution kernels, several values, such as the maximum absolute value, the sum of absolute value, and the mean square value, were considered. However, given that features are further fed into NeRF MLPs to generate colors, and networks are usually more sensitive to larger inputs, we opted for the maximum absolute value as the importance indica- tor. This approach, for instance, would favor preserving feature of (16, O...... 0) over (1.1.... 1), despite them having the same mean square distance to the origin.
Pruning with Sampled Points. In addition to voxel features f., the interpolated feature tensor f. at the sampled position x; and the corresponding probability of termination as can also provide important information for neural rendering. Similar to Eq. ( the sampled point importance Iz can be calculated as I = AX (f.)) aq In practice, we adopt a uniform sampling strategy in the 3D space with a sampling step set as half of the grid size. Similar to VQRF (appendix Eq. (I)), this enables us to obtain the importance I, of the voxel v; by evaluating the contributions of sampled points to the voxel's feature tensor. We can finally get our new-independent importance = Lo Ip. then use it to prune voxels through the quantile function in VQRF (appendix Eq. (2)).
4.2 FEATURE ENCODING
Following the pruning process, we obtain a concise point representation that includes both point positions (approximately 10%) and point features (about 90%), shown in Fig. 2 (b). Inspired by previous work (Schnabel & Klein 2006) which organizes point cloud as octree to skip empty space, we employ octree coding to encode point positions, and then conduct feature encoding.
To reduce point feature redundancy, we employ a point-based wavelet transform, region adaptive hierarchical transform (RAHT) (De Queiroz & Chou 2016) as the basis for our baseline algorithm. This involves taking quantized points p from octree coding and converting their features f into trans- form coefficients e as e = RAHT fp.). Notably, RAHT primarily relies on matrix multiplication, allowing us to create a fully differentiable pipeline for feature encoding and subsequent entropy minimization. Details about position encoding and RAHT can be found in appendix Sec. C and D.
Importance-Guided Feature Encoding. As illustrated in Sec. 4. points with higher importance typically carry more information, and are thus more essential for the accurate recovery of the 3D scan. However, regarding that RAHT is originally designed to process point cloud attributes, pri- marily focusing on the spatial relationships between point features while neglecting the concept of point importance I/. One straightforward implementation for this limitation is enhance features based on their importance as e = RAHT(p. f. It). More details are provided in appendix Sec. H. Although this approach preserves high-importance features, it introduces additional high-frequency
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noise to the original features and necessitates the transmission of importance values for decoding. Consequently, this augmentation significantly increases the final storage requirements.
To deal with these issues, employ the importance metric 4 as selective masks to split points to several independent point sets, and derive coefficients e following this formulation:
(1) Q1
()))(6,82))
elE((n-1.80. 1m.)
Q2
On
(4)
(00 = RAHT(PLEEO
Here, I E (0; - -, 0.) is the selective mask, and E (0.1..... n). We can tune the masks through Two of hyperparameters, the importance threshold 0, and the quantization factor Qi, to encode features with their importance. In practice, 0; can be tuned by the quantile function similar to VQRF (appendix Eq. (2)), and Q: can be set based on the chosen 6g. Furthermore, the masks can be merged and transmitted using standard zip compression techniques, incurring negligible storage overhead.
4.3 ENTROPY MINIMIZATION
According to information theory (Shannon 1948). the information entropy (e) of coefficients indicates the average level of 'information' as H(e) = E - logz p (e)]. where p((e) is the probability distribution of coefficients e. The objective of this section is to minimize the information entropy H (e) inherent to the NeRF model through imposing constraints reducing the model size of NeRF. Inspired by deep image compression (Ballé et al. 2017), we learn an estimated distribution q(e) to constrain p(e). It is also worth noting that there exists strong interrelation between the distribution of point features and their corresponding importance I,. Thus, further introduce I as a prior information component.
the distribution p(e). thereby
Formulation. Given coefficients e and importance 4, we aim to minimize the KL Divergence D between the coefficient distribution p(e) and the estimated distribution q(e), incorporating I, as prior knowledge: = Ee-p [- logg g (e [i)]- Inspired by deep image compression (Ballé et al,) 2017). we learn a deep entropy model to generate the estimated distribution g(e). Moreover, we can further factorize q(e) into product of conditional probabilities: q(e) I11 q (e(() I1, w),, where w is the weights of our entropy model.
Importance-Prioritizee Entropy Modelling. In the context of our task, the challenge is how to leverage importance I as prior information. This is because there is straightforward one-to- one correspondence between coefficients and importance (The RAHT algorithm has converted the spatial-domain features into the frequency-domain coefficients, and the importance is still in the spatial domain. More details are provided in appendix Sec. D.). One simple yet effective ap- proach to model multiple independent distributions based on importance 4, Specifically, we reuse the definitions of selective masks and coefficients in Eq. 4 e = fer...., h. where -1.00) For each set of coefficients e,, we introduce independent learnable parameters w; to generate the corresponding distribution q(e,). Consequently, we can further factorize q(e) as q(e) II, (e; w.) = =II,, 9 (e(²) w.) for each coefficient el and optimize all parameters with a cross-entropy loss toe --E EE. log (c.") w:). This approach allows us implicitly incorporate importance information and thus benefiting entropy modelling.
e,
Q,
Joint Learning. In our full model ACRF, we simultaneously update the weights of the entropy model and fine-tune the NeRF model. As result, the cross-entropy loss Lee can further reduce the spatial redundancy by updating the transform coefficients. The final optimization loss is a combination of the rendering loss Erd and the cross-entropy loss lex: L = Era + Xlees where À can be tuned to control the model size. Since the cross-entropy loss updates large number of features, we add toe every 100 iterations to accelcrate learning. For the fast mode ACRF, simply fix the NeRF model and only enable the cross-entropy loss: L lee-
Monte Carlo Sampling for Distribution Fitting. Directly predicting probabilities for all coeffi- cients can be tome-consuming, particularly when the number of coefficients is large. For example, PointNeRF (Xu et al.] 2022) generates millions of points for scans in the Tanks& Tanks&Temples dataset, and processing coefficients from these points directly can be challenging. To tackle this issue, we perform random sampling obtain n% of coefficients, and estimate the probabilities of only these

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coefficients as tce = - EndeN log q (c:)) w.). where N is the set of sampled indices in cach iteration. We set the number of iterations to 100 and the sampling percentage to 1% empirically.
Finally, we have transform coefficients from Sec. 4.2 and predicted distributions of coefficients from our deep entropy model. Thus, the coefficients be losslessly encoded into final bitstream through the arithmetic coder. We transmit several components, including a position bitstream, a fea- ture bitstream, the importance masks, the learned entropy model, NeRF MLPs and other metadata. After decoding, we can reconstruct our explicit NeRF model on the decoder side.
5 EXPERIMENTS
(1) Datasets. We conduct experiments on two datasets:
SyntheticNNeRF (Mildenhall et al., 2020). This is view synthesis dataset consisting of 8 syn- thetic scans, with 100 views used for training and 200 views for testing.
Tanks& Temples (Knapitsch et al., 2017). This is a real-world dataset with scenes (Bamn Caterpillar, Family, Ignatius, and Truck). We used the default settings of DVGO (Sun et al. 2022) and PointNeRF (Xu al. 2022) for the voxel and point-based methods, respectively.
(2) Baselines. We compare our ACRF and ACRF-F with the following baselines, Additional imple- mentation details and hyperparameter settings are provided in appendix Sec. F.
DVGO (Sun et al. 2022). This is explicit NeRF algorithm that uses voxel grids the neural representation. We train a DVGO model from scratch following the default setting, and use the same model for all voxel-based compression methods ensure fair comparison.
PointNeRF (Xu al. 2022). This is an explicit NeRF algorithm that uses point representation. We use the PointNeRI model trained with 200K iterations for compression and adopt the official pre-trained model for all point-based methods.
VQRF (Li et al. 2023). This is a recent volumetric NeRF compression method. We re-implement the algorithm on the pretrained DVGO model following the official implementation to ensure fair comparison with our method.
VQRF-F. We directly disable the joint finetune step of VQRF for fast NeRF compression.
5.1 EXPERIMENTAL RESULTS
The quantitative compression results of different methods are presented in Fig. 4 The first row presents a comparison of all voxel-based methods. To obtain the rate- distortion curve for ACRF, we fixed the quantization factors of RAHT and tuned the loss factor X, while for ACRF-F, we tuned the quantization factors. All compression algorithms exhibit high com- pression ratios, highlighting the substantial redundancy in voxel-based representations. Moreover, our proposed methods, ACRF and ACRF-F, outperform VQRF and VQRF-F, respectively. This can
Quantitative Evaluation.
Model Slao vs PSNR (Satherk)
Modal Siza va STM (Syebution
Model va ITNAI
Medil Size vu (STM.
6912
1880
Voor Arki DVCO
VIKE MEAP
31.
Model Sox (MB)
Model Stx
Modei Siz (MBB)
Modi Sox (MB)
Medd
30.3
0.5C
2000
90
12
66
35
55
340
244
Sox (MB)
Model Ster
Saar (MB9)
(M0
Figure 4: Quantitative results of our ACRF and other NeRF compression approaches on Synthetic- NeRF (Synthetic) and Tanks&Temple (T&T).
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(4225,342)
(1.07.344)
(3.39
(7.019,3500)
(9.05, 34.4)
(129934.77)
(3.0333555)
GT
DVGD
VQRF
ACRF (DVGO)
ACRF-F (DVGO)
PointNoRF
ACRF (PointNeRF)
ACRF-F (PointNeKF)
Figure 5: Qualitative results (lego and Family) of our ACRF and other basclines. ACRF/ACRE-F (DVGO/PointNeRRF) means DVGO/PoimNeeR-- basee ACRF/ACRF-F, Model size MB and PSNR displayed below the figure (model size, PSNR).
Methods
Syuthetic-NeRR
Tanks&
VD Pruning
VQ
Finetune 3min 22s
Total
VD Pruning
VQ
Finetune 4min 38
Total
VQRF al. 2023
26s
40s
4min 28s
4min 31s
39s
9min
VQRF-F
26s
40s
Imin 6s
4min 31s
39%
Smin 10s
VD Pruning
RAHT
EM
Total
VD Pruning 4min 31s
RAII
EM
Total 8min 56s
ACRF
26s
0.5s
3min 28s
3min 55s
0.4s
4min 25s
VI Pruning
RAHT 0.4s
EM
Total 3.9s
VI Pruning
RAITT 0.4s
EM
Total 3.9s
ACRE-F
2.2s
1.3s
2.3s
1.2s
Table I: Encoding time of VQRF and our ACRE. "VQ" and "EM" denotes vector quantization and entropy minimization, respecitvely. "VD" and "VI" denotes view-dependent and view-independent pruning. respectively.
be primarily attributed to the proposed feature and entropy encoding algorithms. The second row presents the results of all point-based methods. For ACRF, our method can achieve a 10 x compres- sion ratio with negligible performance degradation. Compared to the voxel representation, neural points are more compact, making it more challenging to achieve 100 x compression ratio.
Qualitative Comparison. The qualitative results depicted in Fig. are consistent with the quan- titative results. Despite a minor reduction in performance, it is difficult to discern any noticeable differences between the rendering outputs of the various algorithms.
Encoding Time Comparison. We also compare the encoding time of DVGO-based approaches in Table | For consistency and fairness across all experiments, we utilize a workstation equipped with Intel Xeon Silver 4210 CPU @2.20 GHz and NVIDIA TITAN RTX GPU. For VQRF and ACRF, we set the same iteration (10K) for finetuning and joint learning (the main part EM). Our ACRF takes shorter to complete the joint learning phase and achieves better compression performance than VQRF, because it adopts our feature encoding strategy and learns an auxiliary cross-entropy loss for entropy minimization. Moreover, with pruning, feature encoding, and entropy coding modules, our ACRF-F can encode a NeRF model within seconds while delivering competitive compression results. During decoding, our methods require additional time for the inverse RAHT transform and entropy decoding, which takes less than Is.
5.2 ABLATION STUDY
We conduct several ablation studies on chair of the Synthetic-NeRF dataset.
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View-Independent Pruning. We investigate the impact of wew-independent pruning on our DVGO-based ACRF algorithm. Our experiments, reported in Table show that progressively incor- porating the probability of termination (A), fea- tures (F) of sampled points, and features (F) of the voxel grid leads to steady improvements PSNR and reductions in model size. We observe that fur- ther incorporating the probability of termination (A) of the voxel grid can result in unacceptable distortion. This because the density and feature grid of DVGO are separated, and voxel with low a may also contain valuable features.
Sampled Points
Voxel Grid
PSNR
SIZE
F
A
F
(dB)t
(MB)
33,97
2,46
33,99
2.34
33,99
2.18
31.08
1.16
Table 2: Ablation study on the view-
independent voxel pruning (Sec. [41]] "A" and "F" denote the probability termination a and features, respectively.
importance-basel Feature Encoding and Entropy Modelling. We further study the effect of ieportaace-guided feature encoding and importance-priorttzeed entropy modelling on our ACRF and ACRF-F. As depicted in Fig. 6 (a), we start with two baseline models without our importance- based strategies, denoted as 'baseline A' and 'baseline B' for ACRF-F and ACRF, respectively. Subsequently, introduce importance-guided feature encoding (Imp FE) these baseline models. is worth noting that directly applying feature encoding with importance masks might ini- tially lead a performance decrease. This is primarily because transforms in different regions yield coefficients that follow distinct distributions. We further include the modelling develop our ACRF and ACRF-F. The results clearly demonstrate that the combination of importance-basee feature encoding and entropy modeling significantly improves the compression performance of both ACRF and ACRF-F, which underscores the effectiveness of our importance- based strategies in enhancing the overall performance of our methods.
entropy
Effectiveness of Components. As shown in Fig. 6 (b), we evaluate the effectiveness of each com- ponent of our framework. We start with the original DVGO method and progressively incorporate our see-inndependent pruning, deep entropy model, RAHT, joint learning, and importance-bast modules (importance-guider feature encoding and prrootance-piortiiized entropy modelling). Fi- nally, we can obtain our full model, ACRF. The results show that the performance is consistently improved with the addition of each module, which proves the effectiveness of each component.
PSNR Model Size
PSNR Model Size
34.3
34.3
34
pSNc (UB)
PSNC
Hanciie A A lop FE ACtti-
Add Vi Pruring
PVGO
33.7
33.7
Add Entroge Madel
Leorning
ACRF
Add Imsootaace
1.5 Model Sizo (MB)
0.7
1.5
2.3
15.7 106.6
Model
(h)
Figure 6: Ablation studies. (a): Ablation study the importance- based feature and entropy encod- ing. (b): Ablation study on each component of our framework.
CONCLUSION
In this paper, we propose explicit NeRF compression algorithm. Our method includes several key components, including a view-independent pruning strategy, importance guided feature encoding, and importance prrioriicee entropy modeling. Extensive experimental results validate the effective- ness of our 3D-data-oriented NeRF compression methodology, showcasing a remarkable improve- ment in compression performance while achieving reduction in encoding time complexity. It is feasible to further extend our algorithm for dynamic and real-tmme NeRF compression.
Acknowledgements. This work was partially supported by the National Natural Science Foundation of China (No. U20A20185).

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Published as a conference paper at ICLR 2024
REFERENCES
Johannes Ballé, Valero Laparra, and Ecro P Simoncelli. End-to-end optimized image compression. In ICLR, 2017.
Fabrice Bellard. BPG image format. https::/beellrrd.orr//bg.. 2015.
Sourav Biswas, Jerry Liu, Kelvin Wong, Shenlong Wang. and Raquel Urtasun. MuSCLE: Multi sweep compression of LiDAR using deep entropy models. NeurIPS, 33, 2020.
Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. TensoRF: Tensorial radiance fields. In ECCV, 2022a.
Zhili Chen, Zian Qian, Sukai Wang, and Qifeng Chen. Point cloud compression with sibling context and surface priors. In ECCV, pp. 744-759. Springer, 2022b.
Zhiqin Chen, Thomas Funkhouser, Peter Hedman, and Andrea Tagliasacchi. MobileNeRI: Exploit- ing the polygon rasterization pipeline for efficient neural field rendering mobile architectures. In CVPR, pp. (6569-16578, 2023.
Ricardo L De Queiroz and Philip A Chou. Compression of 3D point clouds using a region-adaptive hierarchical transform. IEEE TIP, 2598):3947-3956, 2016.
Chenxi Lola Deng and Enzo Tartaglione. Compressing explicit voxel grid representations: fast NeRFs become also small. In WACV, pp. 1236-1245, 2023.
Guangehi Fang, Qingyong Hu, Hanyun Wang. Yiling Xu, and Yulan Guo. 3DAC: Learning attribute compression for point clouds. In CVPR, pp.
2022.
Chunyang Fu, Ge Li, Rui Song, Wei Gao, and Shan Liu. Octattention: Octree-based large-scale contexts model for point cloud compression. In AAAI, volume 36, pp. 625-633, 2022.
Vivek K Goyal. Theoretical foundations of transform coding. IEEE Signal Processing Magazine, 18(5):9-21, 2001.
Peter Hedman, Pratul P Srinivasan, Ben Mildenhall, Jonathan T Barron, and Paul Debevec. Baking neural radiance fields for real-time view synthesis. In ICCV, pp. 5875-5884, 2021.
Lila Huang, Shenlong Wang, Kelvin Wong, Jerry Liu, and Raquel Urtasun. Octsqueeze: Octree- structured entropy model for LiDAR compression. In CVPR, pp. 1313-1323, 2020.
David A Huffman. A method for the construction of minimum-reduudancc codes. Proceedings of the IRE, 40(9): 11009881101 1952.
James T Kajiya and Brian P Von Herzen. Ray tracing volume densities. ACM SIGGRAPH computer graphics, (8(3):155-177 1984.
Arno Knapitseh, Jaesik Park, Qian Yi Zhou, and Vladlen Koltun. Tanks and temples: Benchmarking large-scale scene reconsiruction. ACM TOG, 36(4), 2017.
Hao Li, Asim Kadav, Igor Durdanovic, Hanan Samet, and Hans Peter Graf. Pruning filters for efficient convnets. In ICLR, 2016.
Lingzhi Li, Zhen Shen, Zhongshu Wang, Li Shen, and Liefeng Bo. Compressing volumetric radi- ance fields to MB. In CVPR, pp. 4222 4231, 2023.
Ruofan Liang, Jiahao Zhang, Haoda Li, Chen Yang, Yushi Guan, and Nandita Vijaykumar. SPIDR: SDF-based neural point fields for illumination and deformation. arXiv preprint TrXiv:2210.0839: 2022.
Lingjie Liu, Jiatao Gu, Kyaw Zaw Lin, Tat- Tat-Seng Chua, and Christian Theobalt. Neural sparse voxel fields. NeurIPS, 33:15651-15663. 2020.
Nelson Max. Optical models for direct volume rendering. IEEE TVCG, 1(2):99-108, 1995.
10

---

Published as a conference paper at ICLR 2024
Donald Meagher. Geometric modeling using octree encoding. Computer graphics and image pro- cessing, (9(2):19-147)) 1982.
Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing scenes as neural radiance fields for view synthesis. In ECCV, 2020.
Julian Ost, Issam Laradji, Alejandro Newell, Yuval Bahat, and Felix Heide. Neural point light fields. In CVPR, pp. 18419-18888 18429, 2022.
Zizheng Que, Guo Lu, and Dong Xu. VoxelContext- An octree based framework for point cloud compression. In CVPR, pp. 6042-6051, 2021.
Daniel Rho, Byeonghyeon Lee, Seungtae Nam, Joo Chan Lee, Jong Hwan Ko, and Eunbyung Park. Masked wavelet representation for compact neural radiance fields. In CVPR, pp. 20680 -0680- 2023.
lain Richardson. 264 and MPEG-4 video compression: video coding for next-generation multimedia. John Wiley & Sons, 2004.
Ruwen Schnabel and Reinhard Klein. Octree-based point-cloud compression. In SIGGRAPH,, pp. 111-120, 2006.
Sebastian Schwarz, Marius Preda, Vittorio Baroncini, Madhukar Budagavi, Pablo Cesar, Philip A Chou, Robert A Cohen, Maja Krivokuća, Sébastien Lasserre, Zhu Li, et al. Emerging MPEG standards for point cloud compression. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 9():1133-448, 2018.
Claude Elwood Shannon. A mathematical theory of communication. The Bell system technical journal, 27(3):379-427 423, 1948.
Seungjoo Shin and Jaesik Park. Binary radiance fields. arXiv preprint arXiv:3306.0758/, 2023.
Athanassios Skodras, Charilaos Christopoulos, and Touradj Ebrahimi. The JPEG 2000 still image compression standard. IEEE Signal processing magazine, 18(5):36 58, 2001.
Gary Sullivan, Jens-Rainer Ohm, Woo-Jin Han, and Thomas Wiegand. Overview of the high efficiency video coding (HEVC) standard. IEEE TCSV7, (2(12))1149-1666 2012.
Cheng Sun, Min Sun, and Hwann- Tzong Chen. Direct Voxel Grid Optimization: Super- fast conver- gence for radiance fields reconstruction. In CVPR, pp. $459-5469, 2022.
Gregory K Wallace. The JPEG still picture compression standard. IEEE transactions consumer electronics, 38V)::xvii-xxxix 1992.
Liao Wang, Qiang Hu, Qihan He, Ziyu Wang, Jingyi Yu, Tinne Tuytelaars, Lan Xu, and Minye Wu. Neural residual radiance fields for streamably free-viewpoint videos. In CVPR, pp. 76-87, 2023.
Marcelo J Weinberger, Gadiel Seroussi, and Guillermo Sapiro. The LOCO-I lossless image com- pression algorithm: Principles and standardization into JPEG-LS. IEEE TIP, 90):1309-1324, 2000.
lan H Witten Radford M Neal, and John G Cleary. Arithmetic coding for data compression. Com- munications of the ACM, 3006):50,,540, 1987.
Xiufeng Xie, Riccardo Gherardi, Zhihong Pan, and Stephen Huang. HollowNeRF: Pruning hashgrid-basee NeRFs with trainable collision mitigation. In ICCV, pp. 3480-3490, 2023.
Qiangeng Xu, Zexiang Xu, Julien Philip, Sai Bi, Zhixin Shu, Kalyan Sunkavalli, and Ulrich Neu- mann. Point-NeRF: Point-based neural radiance fields. In CVPR, pp. 5438-5448, 2022.
Alex Yu, Ruilong Li, Matthew Tancik, Hao Li. Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In ICCV, pp. 5752-5761, 2021.
Alex Yu, Sara Fridovich-Keil. Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In CVPR, 2022.
Cha Zhang, Dinei Florencio, and Charles Loop. Point cloud attribute compression with graph trans- form. In ICIP, pp. 2066-2070 IEFE, 2014.


Reviews:
[{"review_id": "lnjfswkWcS", "reviewer": "Reviewer_MUJE", "summary": "This work addresses the problem of compressing explicit Neural Radiance Fields (NeRFs) for 3D data representation. The authors introduce a framework called Attributed Compression of Radiance Field (ACRF) to achieve this. ACRF prunes the neural 3D structure and encodes it as points with features using importance-guided encoding. It also employs an importance-based entropy model to optimize the encoding process. The authors present two models, ACRF and ACRF-F, balancing compression performance and encoding time. Experiments on synthetic and real-world datasets, including Synthetic-NeRF and Tanks&Temples, showcase the superior performance of their approach.", "questions": "Major:\n- Could you provide more elaboration about why RAHT with point importance introduces additional high-frequency noise to the original features and necessitates the transmission of importance values for decoding?\n- Could the author provide more explanations for the motivation for adopting entropy minimization?\n- How can the \\labmda be tuned to control the model size?\n\nMinor:\n- Why do the authors only conduct the ablation study on the chair of the Synthetic-NeRF dataset? Could the authors provide experimental results of the ablation study on different datasets?\n\n------------------------------------------------\n### Post rebuttal:\n\nMost of my concerns are addressed after reviewing the authors' responses and discussion between authors and reviewers. I am willing to raise my evaluation from 5 to 6.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The idea is simple yet effective.\n- The experimental results are convincing and the ablation study shows the necessity of each component.", "weaknesses": "Major\n- The proposed method is based on voxel-grid compression of NeRF with limited change so the novelty of it is limited.\n- The paper writing can be further improved. For instance:\n  - In section 3, the concrete definitions of r and N are not shown.\n  - The motivation for adopting entropy minimization mentioned in section 4.3 is unclear.\nMinor:\n- I recommend the authors mention which section in the supplementary describes the details in the main paper.", "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": "", "extra_scores": {}}, {"review_id": "8SpCtKFwx7", "reviewer": "Reviewer_HSPa", "summary": "This manuscript proposed a novel framework of Radiance Field attribute compression, which treated the compression task of explicit neural 3D representation as 3D data compression. Specifically, the neural 3D structure is pruned and converted to points with features, which are further encoded using importance-guided feature encoding. An importance-prioritized entropy model is proposed to estimate the probability distribution of transform coefficients, which are then entropy coded with an arithmetic coder using the predicted distribution. Experimental results demonstrate that the proposed method achieves superior performance on both synthetic and real-world datasets such as Synthetic-NeRF and Tanks&Temples.", "questions": "Please refer to the Weaknesses section.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The whole manuscript is well structured and the technique details are easy to follow. Experimental results demonstrate that the proposed method achieves superior performance on both synthetic and real-world datasets, in terms of RD performance and encoding/decoding time,.\n\nThe method proposed in this manuscript follows the standard point cloud attribute compression process, and has been optimized based on the characteristics of the explicit neural 3D representation in multiple stages such as data pruning, feature encoding and entropy minimization. The idea is reasonable and interesting.", "weaknesses": "1）Some technique details are not clear enough. For example, only encoding time data are provided in Table 1, it is suggested to provide decoding time data to highlight the practicality of the proposed algorithm. The model size and quality info are missing in Fig. 5.\n\n2)  Other type of compression methods such as Rho et al. (Rho et al., 2023) are not evaluated in this manuscript.\n\n3) Typos. ``As depicted in 6,``=>``As depicted in Fig. 6,``", "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": "", "extra_scores": {}}, {"review_id": "kNHA3rGIPc", "reviewer": "Reviewer_GWvi", "summary": "This paper proposes a novel approach for explicit NeRF compression, focusing on compressing the latent features of the NeRF model. More specifically, the authors first conduct a comprehensive analysis of NeRF compression and reformulate the task as 3D data compression. Then, they propose their ACRF framework, comprising pruning, feature encoding, and entropy minimization. Experiments were conducted to demonstrate the effectiveness of the proposed method, both for the compression performance and coding speed.", "questions": "1. Include discussion and future direction for recent NeRF algorithms. The gaussian-splatting algorithm represents the radiance field in a point-cloud-like structure, showcasing notable achievements in training and rendering performance. One limitation of this approach is the significant storage budget. For example, the output model takes over 1GB for unbounded scenes, like bicycle in mipnerf360. It will be interesting to integrate these techniques with the proposed algorithm.\n2. See weakness 3, 4, 5 and 6.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Originality: The analysis and reformulation of NeRF compression seems reasonable, and the utilization of attribute compression is practical.\n2. Quality: The experimental results validate the effectiveness of the proposed algorithm, which integrates the conventional image compression pipeline with several NeRF-oriented modules.\n3. Clarity: The paper is well-written and easy to read.\n4. Significance: Given the rising popularity of NeRF models, the investigation of NeRF compression is of great significance.", "weaknesses": "1. From the perspective of conventional image compression, additional computation and time budget is required for encoding and decoding, which might be a problem for real NeRF applications. \n2. In the related works (Sec. 2.2), it would be better to illustrate the main difference between the proposed method and prior research, such as the mentioned 3DAC, Rho et al. and ReRF.\n3. Experiments: In Table 2, it seems that there is a performance drop with additional information (Voxel Grid, A). Please check the result and give some explanations. Similarly, in Figure 6, Baseline A outperforms A+Imp FE. Please justify.\n4. Experiments: In Figure 5, the qualitative results of two relatively simple scans are provided. It would be beneficial to extend the analysis to include more complex scans (e.g., object with high reflectance).\n5. In the appendix (Sec. D), it seems that the proposed modules do not perform well on PointNeRF. It would be beneficial to extend the analysis in the appendix, and add some discussions in the main paper.", "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": "", "extra_scores": {}}, {"review_id": "Fw09PJjxR7", "reviewer": "Reviewer_sVJV", "summary": "Given a pre-trained NeRF model with an explicit 3D representation, this paper aims to reduce the model size while maintaining good performance. It proposes reformulating the task as 3D data compression with three steps.\nFirstly, it proposes view-dependent pruning, which eliminates features with low absolute values.\nThen, it performs a point-based wavelet transform with octree coding to convert features with importance to coefficients.\nLastly, it minimizes the information entropy for the coefficients.\nDepending on whether there is a rendering loss, two versions are introduced.\nExperiments are conducted on the Synthetic-NeRF and Tank&Temples datasets to show their significant compression rates.", "questions": "See weakness", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "[Results] The quantitive results in Fig. 4 and encoding time comparison Tab. 1 show the proposed method achieves a modestly larger compression ratio in comparison with voxel-based methods and a remarkably higher compression ratio in comparison with point-based methods.\n\n[Novelty] The proposed three-step method is reasonable, achieves remarkable improvements in compression performance, and simultaneously reduces the encoding time.", "weaknesses": "[Clarity]\n\n- In Sec.4.1, the paper uses a half page and two formulations to introduce view-dependent pruning. I think this part seems redundant. Because the following view-independent pruning is not based on the view-dependent pruning.\n\n- In Sec.4.2, the paper introduces $e = RAHT(p,f \\cdot I_l)$ as a straightforward implementation. I am not sure how to introduce the importance and then recover $f$. Actually, I think $f \\cdot I_l $ destroy $f$ and it is hard to recover $f$. It is not a noise issue. Instead, I think the proposed mask strategy is more intuitive. Also, if $e = RAHT(p,f \\cdot I_l)$ is important, it would be better to use it as a baseline. I think this part introduces more confusion.\n\n- I could not follow the first formula in Section 4.3, the independent variables are distributions p and q, but in the right of the equation, there is only q. I am not sure how to eliminate the distribution of p. Are any assumptions or references missing?\n\n- Fig.1 is too small, and it does not provide enough explanation. I cannot follow the meaning of the color or the connection between local patterns and latent features.\n\n- Fig.5 is hard to distinguish. All the results of different methods seem the same. It would be better to highlight their difference.\n\n[Fig.4] In Fig.4, the compressed model achieves a 100 $\\times$ compression ratio while obtaining a higher SSIM (top right). Would you please provide more discussion on it?\n\n[Speed & Practicality] In Sec.5.1 Encoding Time Comparison part, the paper claims that the proposed method only requires additional 1s for decoding. This part is vague. I am not sure whether this time has a huge impact or is insignificant during testing. The overall compression seems complex. I suggest the decoding time and the overall inference time should be discussed in detail. More specific settings, including batch size, image size, and overall inference time, are needed.\n\n[$|f_v|$] Eq.5 is not so convicting. For me, I think it is easy to understand that the minimum absolute value means low information. But I am not sure the maximum absolute value can be employed to quantify the amount of information. The paper claims this is based on''statistical measures''. It would be better to provide statistical evidence or some references to support this claim.\n\n[Task specific] The feature encoding and the entropy minimization seem like standard strategies for data compression and are not specifically designed for Nerf. It would be better to highlight the main contribution of those two parts regarding Nerf.\n\n\n[Experiments]\n\n- This paper claims that integrating pruning strategies into training pipeline is time-consuming and impractical for compression(Section 4.1). But it is still important to compare those existing methods(Deng & Tartaglione, 2023; Xie et al., 2023), even the proposed method is a post-optimization method.\n\n- The comparison experiments are insufficient. I suggest to compare previous works like (Li et al.,2023; Rho et al., 2023;)\n\n[Typo]\n- Section 1, propsoe -> propose\n- Appendix Section C, subscript error\n-The description of baselines should be more specific (Fig. 5), like the definitions of \"ACRF(DVGO)\" and \"ACRF-F(DVGO)\".", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)