TensoRF: Tensorial Radiance Fields

A

19

TensoRF Representation Details.

We illustrate the feature grid of our tensorial radiance field and the tensor factors
in TensoRF with both CP and VM decompositions in Fig. 5.
Number of components. The total number of tensor components (#Comp) is(Rσ + Rc ) for TensoRF-CP and 3(Rσ + Rc ) for TensoRF-VM (because VM has
three types of components). Therefore, the R we use for TensoRF-CP is threetimes as large as the R used for TensoRF-VM to achieve the same number ofcomponents shown in Tab. 2. We also find that using Rσ < Rc is usually better
than Rσ = Rc when Rσ is large enough (> 8). In particular, for TensoRF-VM,
we use Rσ = Rc = 8 for #Comp = 48; Rσ = 8, Rc = 24 for #Comp = 96;
Rσ = 16, Rc = 48 for #Comp = 192; Rσ = 32, Rc = 96 for #Comp = 384. Note
that, as discussed in Eqn. 3,4, here we apply the same number of components for
AX , AY , AZ with R1 = R2 = R2 = R for both density and appearance (where
R is Rσ and Rc respectively), assuming the three spatial dimensions are equallycomplex.
Forward-facing settings. We use the above settings with R1 = R2 = R2 , forall 360◦ object datasets in Tab. 1. On the other hand, Forward-facing scenes
apparently appear differently in the three dimensions; especially, in NDC space,
the X and Y spatial modes (corresponding to the image plane) contains more
appearance information that is visible to rendering viewpoints. We therefore use
more components for the X − Y plane, corresponding to AZ = vZ ◦ MX,Y . In
this case, these AZ components can also be seen as special compressed versionsof neural MPIs. In particular, the detailed numbers of components we use forgenerating the results in Tab. 4 are: for #Comp=48 Rσ,1 = Rσ,2 = 4,Rσ,2 =16,Rc,1 = Rc,2 = 4,Rc,2 = 16; for #Comp=96, Rσ,1 = Rσ,2 = 4,Rσ,2 = 16,Rc,1 =Rc,2 = 16,Rc,48 = 16.
Number of parameters. We briefly discuss the number of parameters in ourmodel. With the same #Comp, when I = J = K and Rσ + Rc = R, the total
number of parameters used for TensoRF-CP is 3KR + P Rc ; for Tensor-VM, thenumber is K 2 R + KR + P Rc (here considering Rσ /3, Rc /3 are used to makethe #Comp the same as TensoRF-CP ). For example, for a 300 × 300 × 300
feature grid with P = 27 channels (plus one density channel), the total numberof parameters in a dense grid is 756 M; the number of parameters used for
TensoRF-CP (when R = 192) is 360 K; the number of parameters used for
TensoRF-VM (when R = 192) is 17 M. Our CP and VM model can achieve
0.048% and 2.25% compression rates respectively.

B

More Implementation Details.

Loss functions. As described in sec. 4.4, we apply a L2 rendering loss andadditional regularization terms to optimize our tensor factors for radiance fieldreconstruction. In general, this loss function is expressed by

20

A. Chen, Z. Xu et al.

Feature Grid

TensoRF-CP

Features Per Voxel

TensoRF-VM
Volume density

Appearance
feature vector

Fig. 5: Feature grids and factorized tensors in TensoRF. We leverage a regularvoxel grid G, covering a 3D scene, to model a radiance field of the scene. Each voxelof G contains multi-channel features, where one channel represents the volume
density (σ) and the remaining P channels lead to an appearance feature vector(fc ) for computing view-dependent colors. We split the density and appearance
features into two feature grids Gσ and Gc , consider them as 3D and 4D tensors,and factorize them into compact factors with outer products. TensoRF with CP
decomposition factorize the tensors into only vectors and TensoRF with VM
decomposition factorize the tensor into vector and matrix factors (Eqn. 7, 8).
Note that, each voxel of the original grid is only related to one value from each
XYZ-mode vector/matrix factor in both decompositions, which are marked in
the figure.

  \begin {aligned} \loss = \|\Color - \tilde {\Color } \|^2_2 + \omega \cdot \loss _{reg} \label {eq:loss} \end {aligned} 

(17)

Where C̃ is the groundtruth color, ω is weight of the regularization term.
To encourage the sparsity in the parameters of our tensor factors, we apply
the standard L1 regularization, which we find is effective in improving the quality
in extrapolating views and removing floaters/outerliers in final renderings. Note
that, unlike previous methods [20,55] that penalize predicted per-point densitywith a Cauchy loss or entropy loss, our L1 regularizer is much simpler and directly
applied on the parameters of tensor factors. We find that it is sufficient to apply
the L1 sparsity loss only on the density parameters, expressed by
  \begin {aligned} \loss _{L1} = \frac {1}{N}\sum _{r=1}^{R_\Dens } (\|\Matrix _{\Dens ,r}\| + \|\Vector _{\Dens , r}\|), \label {eq:loss_reg} \end {aligned} (18)where ∥Mσ,r ∥ and ∥vσ,r ∥) are simply the sum of absolute values of all elements,
and N = Rσ · (I · J + I · K + J · K + I + J + K) is the total number of parameters.
We use this L1 sparsity loss with a ω = 0.0004 for the Synthetic NeRF andTensoRF: Tensorial Radiance Fields

21

Synthetic NSVF datasets. An ablation study on this L1 loss on the Synthetic
NeRF dataset is shown in Tab. .
For real datasets that have very few input images (like LLFF[36]) or imperfectcapture conditions (like Tanks and Temples [26] that has varying exposure andinconsistent masks), we find a TV loss is more efficient than the L1 sparsity loss,
expressed by
  \begin {aligned} \loss _{TV} = \frac {1}{N} \sum (\sqrt {\triangle ^2 \Comp ^m_{\Dens ,r}} + 0.1 \cdot \sqrt {\triangle ^2 \Comp ^m_{\Color ,r}}), \label {eq:loss_reg} \end {aligned} 

(19)Here △2 is the squared difference between the neighboring values in thematrix/vector factors; we apply a smaller weight (weighted by 0.1 additionally)on appearance parameters in the TV loss. We use ω = 1 when using this TV loss.
Binary occupancy volume. To facilitate reconstruction, we compute a binary
occupancy mask grid at steps 2000 and 4000 using the volume density prediction
from the intermediate TensoRF model to avoid computation in empty space. For
datasets that do not provide bounding boxes, we start from a conservatively
large box and leverage the occupancy mask computed at step 2000 to re-computea more compact bounding box, with which we shrink and resample our tensor
factors, leading to more precise modeling. For forward-facing scenes in the LLFF
dataset [36], we apply NDC transformation that bounds the scene in a perspective
frustum.
More details. As described in Sec. 5, we use a small two-layer MLP with 128
channels in hidden layers as our neural decoding function. In particular, the input
to this MLP contains the viewing direction and the features recovered by our
tensor factors (no xyz positions are used). Similar to NeRF and NSVF [37,31],
we also apply frequency encodings (with Sin and Cos functions) on both theviewing direction and features. Unlike NeRF that uses ten different frequencies,
we use only two.
During optimization, we also apply an exponential learning rate decay tomake the optimization more stable when the reconstruction is being finished.
Specifically, we decay our initial learning rates at every training step, until
decayed by a factor of 0.1 in the end of the optimization.

C

More Evaluation.

We perform an ablation study to evaluate our L1 regularization. Tab. 5 shows
how our framework performs by removing the L1 regularization on the SyntheticNeRF dataset, our models exceed NeRF fidelity (31.01 in average) even without
regularization. We observe the performance gap between w/ and w/o L1 regularization is mostly caused by the floaters in the empty space. We also provide more
results on our model with different numbers of training steps in Tab. 6, which isbasically a detailed version of Tab. 3 with more settings. These results showcasethat our models consistently improve when training with more iterations.

22

A. Chen, Z. Xu et al.

CP-384
VM-48
VM-192-SH
VM-192

PSNR
31.56/31.23
32.39/31.71
32.00/31.14
33.14/32.43

SSIM
0.949/0.947
0.957/0.953
0.955/0.949
0.963/0.960

LPIPSV GG
0.076/0.078
0.057/0.062
0.058/0.068
0.047/0.052

LPIPSAlex
0.041/0.043
0.032/0.036
0.058/0.044
0.027/0.030

Table 5: We compare the averaged scores against w/o L1 regularization on theSynthetic-NeRF dataset.

CP-192
VM-48
VM-96
VM-192
VM-384

5k

8k

10k

12k

15k

20k

30k

40k

60k

100k

28.38
29.28
29.65
29.86
29.95

29.13
30.39
30.72
30.93
30.88

29.93
31.11
31.52
31.74
31.75

30.38
31.47
31.93
32.17
32.20

30.80
31.80
32.26
32.52
32.62

31.18
32.08
32.56
32.85
32.94

31.56
32.39
32.86
33.14
33.21

31.75
32.55
33.00
33.27
33.35

32.03
32.68
33.17
33.44
33.52

32.18
32.84
33.29
33.54
33.64

Table 6: PSNRs on the Synthetic NeRF datasets with different numbers of
training steps. This is more detailed version than Tab. 3.

D

Discussion

In fact, the reconstruction problem with dense feature grid representation isrelatively over-parameterized/under-determined; e.g., a 3003 grid with 27 channels
has >700M parameters, while one hundred 800 × 800 images provide only 64M
pixels for supervision. Therefore, many design choices – including pruning empty
voxels, coarse-to-fine reconstruction, and adding additional losses, which havebeen similarly used in TensoRF and concurrent works (DVGO, Plenoxels) – are all
essentially trying to reduce/constrain the parameter space and avoid over-fitting.
In general, low-rank regularization is crucial in addressing many reconstruction
problems, like matrix completion [6], compressive sensing [15], denoising [21];tensor decomposition has also been widely used in tensor completion [30,16],
which is similar to our task. Tensor decomposition naturally provides low-rank
constraints and reduces parameters; this similarly benefits the radiance fieldreconstruction as demonstrated by our work.
Moreover, TensoRF represents a 5D radiance field function that expresses both
scene geometry and appearance; hence, we believe our 4D tensor is generally lowrank, because a 3D scene typically contains a lot of similar geometry structuresand material properties across different locations. Note that, in various appearance
acquisition tasks, similar low-rank constraints have been successfully applied
for reconstructing other functions, including the 4D light transport function inrelighting [60] and the 6D SVBRDF function in material reconstruction [72,39](where a common idea is to model a sparse set of basis BRDFs; this is similar to
our modeling of vector components in the feature dimension in the matrix B). We
combine low-rank constraints and neural networks from a novel perspective, in
tensor-based radiance field reconstruction. TensoRF essentially models the scene
with global basis components, discovering the scene geometry and appearance
commonalities across the spatial and feature dimensions.

TensoRF: Tensorial Radiance Fields

E

23

Limitations and Future Work.

Our approach achieves high-quality radiance field reconstruction for 360◦ objects
and forward-facing scenes; however, our method currently only supports boundedscenes with a single bounding box and cannot handle unbounded scenes withboth foreground and background content. Combining our method with techniques
like NeRF++ [70] to separately model a foreground field inside a regular box anda background field inside another box defined in a spherical coordinate space canpotentially extend our method to address unbounded scenes. Despite the successin per-scene optimization shown in this paper, an interesting future direction is
to discover and learn general basis factors across scenes on a large-scale dataset,leveraging data priors to further improve the quality or enable other applications
like GANs (as done in GRAF [51], GIRRAF [40] and EG3D [8]).

F

Acknowledgements

We would like to thank Yannick Hold-Geoffroy for his useful tips in video
animation, Qiangeng Xu for providing some baseline results, and, Katja Schwarz
and Michael Niemeyer for providing helpful video materials. This project was
supported by NSF grant IIS-1764078 and gift money from Kingstar. We would
also like to thank all anonymous reviewers for their encouraging comments.

G

Per-scene Breakdown.

Tab. 8-11 provide a per-scene break down for quantity metrics in Synthesis-nerf[34], Synthe-nsvf [31], Tanks&Templates [26] and forward-facing [36] dataset.

24

A. Chen, Z. Xu et al.

Methods

Avg. Chair Drums Ficus Hotdog Lego Materials Mic

PSNR↑
SRN [54]22.26 26.96 17.18 20.73 26.81 20.85
NeRF [37]31.01 33.00 25.01 30.13 36.18 32.54
NSVF [31]31.75 33.19 25.18 31.23 37.14 32.29
30.38 33.24 24.57 29.32 34.33 33.82
SNeRG [20]PlenOctrees [68] 31.71 34.66 25.31 30.79 36.79 32.95
31.71 33.98 25.35 31.83 36.43 34.10
Plenoxels [50]
DVGO [55]31.95 34.09 25.44 32.78 36.74 34.64
Ours-CP-384
31.56 33.60 25.17 30.72 36.24 34.05
Ours-VM-192-SH 32.00 34.68 25.37 32.30 36.30 35.42
Ours-VM-48
32.39 34.68 25.58 33.37 36.81 35.51
Ours-VM-192-15k 32.52 34.95 25.63 33.46 36.85 35.78
Ours-VM-192-30k 33.14 35.76 26.01 33.99 37.41 36.46

18.09
29.62
32.68
27.21
29.76
29.14
29.57
30.10
29.30
29.45
29.78
30.12

Ship

26.85 20.60
32.91 28.65
34.27 27.93
32.60 27.97
33.97 29.42
33.26 29.62
33.20 29.13
33.77 28.84
33.21 29.46
33.59 30.12
33.69 30.04
34.61 30.77

Table 7: PSNR results on each scene from the Synthetic-NeRF [37] dataset.

TensoRF: Tensorial Radiance Fields

25

Methods

Avg. Chair Drums Ficus Hotdog Lego Materials Mic

Ship

SSIM↑
SRN [54]
NeRF [37]NSVF [31]SNeRG [20]PlenOctrees [68]Plenoxels [50]
DVGO [55]Ours-CP-384
Ours-VM-192-SH
Ours-VM-48
Ours-VM-192-15k
Ours-VM-192-30k

0.846 0.910 0.766 0.849 0.923 0.809
0.947 0.967 0.925 0.964 0.974 0.961
0.953 0.968 0.931 0.973 0.980 0.960
0.950 0.975 0.929 0.967 0.971 0.973
0.958 0.981 0.933 0.970 0.982 0.971
0.958 0.977 0.933 0.976 0.980 0.976
0.957 0.977 0.930 0.978 0.980 0.976
0.949 0.973 0.921 0.965 0.975 0.971
0.955 0.979 0.928 0.976 0.977 0.978
0.957 0.980 0.929 0.979 0.979 0.979
0.959 0.982 0.933 0.981 0.980 0.981
0.963 0.985 0.937 0.982 0.982 0.983

0.808
0.949
0.973
0.938
0.955
0.949
0.951
0.950
0.941
0.942
0.949
0.952

0.947 0.757
0.980 0.856
0.987 0.854
0.982 0.865
0.987 0.884
0.985 0.890
0.983 0.879
0.983 0.857
0.983 0.875
0.984 0.883
0.985 0.886
0.988 0.895

LPIPSV GG ↓SRN [54]0.170 0.106 0.267 0.149 0.100 0.200
NeRF [37]0.081 0.046 0.091 0.044 0.121 0.050
PlenOctrees [68] 0.053 0.022 0.076 0.038 0.032 0.034
Plenoxels [50]0.049 0.031 0.067 0.026 0.037 0.028
DVGO [55]0.053 0.027 0.077 0.024 0.034 0.028
Ours-CP-384
0.076 0.044 0.114 0.058 0.052 0.038
Ours-VM-192-SH 0.058 0.031 0.082 0.028 0.048 0.024
Ours-VM-48
0.057 0.030 0.087 0.028 0.039 0.024
Ours-VM-192-15k 0.053 0.026 0.078 0.025 0.038 0.021
Ours-VM-192-30k 0.047 0.022 0.073 0.022 0.032 0.018

0.174
0.063
0.059
0.057
0.058
0.068
0.069
0.072
0.063
0.058

0.063 0.299
0.028 0.206
0.017 0.144
0.015 0.134
0.017 0.161
0.035 0.196
0.022 0.160
0.021 0.155
0.020 0.153
0.015 0.138

LPIPSAlex ↓0.047 0.043 0.069 0.017 0.025 0.029
NSVF [31]
DVGO [55]0.035 0.016 0.061 0.015 0.017 0.014
Ours-CP-384
0.041 0.022 0.069 0.024 0.024 0.014
Ours-VM-192-SH 0.058 0.031 0.082 0.028 0.048 0.024
Ours-VM-48
0.032 0.014 0.059 0.015 0.017 0.009
Ours-VM-192-15k 0.032 0.013 0.056 0.014 0.017 0.009
Ours-VM-192-30k 0.027 0.010 0.051 0.012 0.013 0.007

0.021
0.026
0.031
0.069
0.036
0.029
0.026

0.010 0.162
0.014 0.118
0.018 0.130
0.022 0.160
0.012 0.098
0.013 0.101
0.009 0.085

Table 8: Quantitative results on each scene from the Synthetic-NeRF [37]dataset.

26

A. Chen, Z. Xu et al.

Our-CP-384

Our-VM-192-SH

Our-VM-48

Our-VM-192

GT

Fig. 6: Our rendering results on Synthetic-NeRF dataset. From top to bottom:
Ship, Hotdog, Lego, Mic, Chair, Drums, Materials, Ficus.

TensoRF: Tensorial Radiance Fields

Methods

Avg. Wineholder Steamtrain

Toad

Robot

Bike

Palace27

Spaceship Lifestyle

PSNR↑
SRN [54]24.33 20.74
NeRF [37]30.81 28.23
NSVF [31]35.13 32.04
DVGO [55]35.08 30.26
Ours-CP-384
34.48 29.92
Ours-VM-192-SH 35.30 29.72
Ours-VM-48
35.34 30.46
Ours-VM-192-15k 35.59 30.31
Ours-VM-192-30k 36.52 31.32

25.49 25.36 22.27 23.76 24.45 27.99 24.58
30.84 29.42 28.69 31.77 31.76 34.66 31.08
35.13 33.25 35.24 37.75 34.05 39.00 34.60
36.56 33.10 36.36 38.33 34.49 37.71 33.79
36.07 31.37 35.92 36.74 36.26 37.01 32.54
37.33 34.03 37.59 38.61 36.09 35.82 33.21
37.06 33.13 36.92 37.98 36.32 37.19 33.68
37.20 33.63 37.29 38.33 36.57 37.77 33.62
37.87 34.85 38.26 39.23 37.56 38.60 34.51

SSIM↑
SRN [54]0.882 0.850
NeRF [37]0.952 0.920
NSVF [31]0.979 0.965
DVGO [55]0.975 0.949
Ours-CP-384
0.971 0.947
Ours-VM-192-SH 0.977 0.953
Ours-VM-48
0.976 0.952
Ours-VM-192-15k 0.978 0.953
Ours-VM-192-30k 0.982 0.961

0.923 0.822 0.904 0.926 0.792 0.945 0.892
0.966 0.920 0.960 0.970 0.950 0.980 0.946
0.986 0.968 0.988 0.991 0.969 0.991 0.971
0.989 0.966 0.992 0.991 0.962 0.988 0.965
0.986 0.950 0.990 0.987 0.971 0.984 0.951
0.988 0.974 0.993 0.991 0.972 0.982 0.964
0.988 0.968 0.992 0.990 0.973 0.985 0.962
0.989 0.972 0.993 0.991 0.975 0.987 0.964
0.991 0.978 0.994 0.993 0.979 0.989 0.968

LPIPSV GG ↓DVGO [55]0.033 0.055
0.045 0.082
Ours-CP-384
Ours-VM-192-SH 0.031 0.057
Ours-VM-48
0.034 0.061
Ours-VM-192-15k 0.031 0.060
Ours-VM-192-30k 0.026 0.051

0.019 0.047 0.013 0.011 0.043 0.019 0.054
0.031 0.067 0.016 0.023 0.031 0.028 0.084
0.024 0.035 0.011 0.013 0.030 0.026 0.051
0.023 0.047 0.013 0.014 0.029 0.025 0.059
0.020 0.040 0.011 0.012 0.028 0.022 0.055
0.017 0.031 0.010 0.010 0.022 0.020 0.048

LPIPSAlex ↓SRN [54]0.141 0.224
NeRF [37]0.043 0.096
NSVF [31]0.015 0.020
0.019 0.038
DVGO [55]Ours-CP-384
0.021 0.040
Ours-VM-192-SH 0.015 0.030
Ours-VM-48
0.016 0.031
Ours-VM-192-15k 0.015 0.033
Ours-VM-192-30k 0.012 0.024

0.082 0.204 0.120 0.075 0.240 0.061 0.120
0.031 0.069 0.038 0.019 0.031 0.016 0.047
0.010 0.032 0.007 0.004 0.018 0.006 0.020
0.010 0.030 0.005 0.004 0.027 0.009 0.027
0.010 0.039 0.006 0.007 0.014 0.015 0.042
0.008 0.021 0.003 0.003 0.016 0.016 0.025
0.008 0.025 0.004 0.004 0.015 0.013 0.026
0.008 0.022 0.004 0.004 0.015 0.011 0.026
0.006 0.016 0.003 0.003 0.011 0.009 0.021

Table 9: Quantitative results on each scene from the Synthetic-NSVF [31]dataset.

28

A. Chen, Z. Xu et al.

Our-CP-384

Our-VM-192-SH

Our-VM-48

Our-VM-192

GT

Fig. 7: Our rendering results on NSVF [31] dataset. From top to bottom: Spaceship, Robot, Toad, Lifestyle, Palace, Wineholder, Steamtrain.

TensoRF: Tensorial Radiance Fields
Methods

Avg.

Ignatius

Truck

Barn

Caterpillar

FamilyPSNR↑
SRN [54]
NeRF [37]NSVF [31]PlenOctrees [68]Plenoxels [50]
DVG [55]
Ours-CP-384
Ours-VM-192-SH
Ours-VM-48
Ours-VM-192-15k
Ours-VM-192-30k

24.10
25.78
28.48
27.99
27.43
28.41
27.59
27.81
28.06
28.07
28.56

26.70
25.43
27.91
28.19
27.51
28.16
27.86
27.78
28.22
28.27
28.34

22.62
25.36
26.92
26.83
26.59
27.15
26.25
26.73
26.81
26.57
27.14

22.44
24.05
27.16
26.80
26.07
27.01
26.74
26.03
26.70
26.93
27.22

21.14
23.75
26.44
25.29
24.64
26.00
24.73
25.37
25.43
25.35
26.19

27.57
30.29
33.58
32.85
32.33
33.75
32.39
33.12
33.12
33.22
33.92

SSIM↑
SRN [54]
NeRF [37]NSVF [31]PlenOctrees [68]Plenoxels [50]
DVGO [55]Ours-CP-384
Ours-VM-192-SH
Ours-VM-48
Ours-VM-192-15k
Ours-VM-192-30k

0.847
0.864
0.901
0.917
0.906
0.911
0.897
0.907
0.909
0.913
0.920

0.920
0.920
0.930
0.948
0.943
0.944
0.934
0.942
0.943
0.944
0.948

0.832
0.860
0.895
0.914
0.901
0.906
0.885
0.900
0.902
0.905
0.914

0.741
0.750
0.823
0.856
0.829
0.838
0.839
0.834
0.845
0.855
0.864

0.834
0.860
0.900
0.907
0.902
0.906
0.879
0.897
0.899
0.902
0.912

0.908
0.932
0.954
0.962
0.956
0.962
0.948
0.960
0.957
0.960
0.965

LPIPV GG ↓PlenOctrees [68]Plenoxels [50]
DVGO [55]Ours-CP-384
Ours-VM-192-SH
Ours-VM-48
Ours-VM-192-15k
Ours-VM-192-30k

0.131
0.162
0.155
0.181
0.156
0.155
0.152
0.140

0.080
0.102
0.083
0.106
0.089
0.085
0.084
0.078

0.130
0.163
0.160
0.202
0.161
0.161
0.162
0.145

0.226
0.303
0.294
0.283
0.286
0.278
0.269
0.252

0.148
0.166
0.167
0.227
0.175
0.177
0.173
0.159

0.069
0.078
0.070
0.088
0.069
0.074
0.071
0.064

LPIPSAlex ↓SRN [54]
NeRF [37]NSVF [31]
DVGO [55]Ours-CP-384
Ours-VM-192-SH
Ours-VM-48
Ours-VM-192-15k
Ours-VM-192-30k

0.251
0.198
0.155
0.148
0.144
0.164
0.145
0.140
0.125

0.128
0.111
0.106
0.090
0.089
0.098
0.089
0.087
0.081

0.266
0.192
0.148
0.145
0.154
0.168
0.145
0.150
0.129

0.448
0.395
0.307
0.290
0.237
0.309
0.266
0.240
0.217

0.278
0.196
0.141
0.152
0.176
0.175
0.161
0.157
0.139

0.134
0.098
0.063
0.064
0.063
0.072
0.066
0.066
0.057

29

Table 10: Quantitative results on each scene from the Tanks&Temples [26]dataset.

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Our-CP-384

Our-VM-192-SH

Our-VM-48

Our-VM-192

GT

Fig. 8: Our rendering results on Tanks&Temples[26] dataset. From top tobottom: Family, Ignatius, Truck, Caterpillar, Barn.

TensoRF: Tensorial Radiance Fields

Methods

31

Avg. Room Fern Leaves Fortress Orchids Flower T-Rex Horns

PSNR↑
NeRF [37]26.50 32.70 25.17 20.92 31.16
Plenoxels [50] 26.29 30.22 25.46 21.41 31.09
Ours-VM-48 26.51 31.80 25.31 21.34 31.14
Our-VM-96 26.73 32.35 25.27 21.30 31.36

20.36 27.40 26.80 27.45
20.24 27.83 26.48 27.58
20.02 28.22 26.61 27.64
19.87 28.60 26.97 28.14

SSIM↑
NeRF [37]0.811 0.948 0.792 0.690 0.881
Plenoxels [50] 0.839 0.937 0.832 0.760 0.885
Ours-VM-48 0.832 0.946 0.816 0.746 0.889
Ours-VM-96 0.839 0.952 0.814 0.752 0.897

0.641 0.827 0.880 0.828
0.687 0.862 0.890 0.857
0.655 0.859 0.890 0.859
0.649 0.871 0.900 0.877

LPIPSV GG ↓NeRF [37]0.250 0.178 0.280 0.316 0.171
Plenoxels [50] 0.210 0.192 0.224 0.198 0.180
Ours-VM-48 0.217 0.181 0.237 0.230 0.159
Ours-VM-96 0.204 0.167 0.237 0.217 0.148

0.321 0.219 0.249 0.268
0.242 0.179 0.238 0.231
0.283 0.187 0.236 0.221
0.278 0.169 0.221 0.196

LPIPSAlex ↓Ours-VM-48 0.135 0.093 0.161 0.167
Ours-VM-96 0.124 0.082 0.155 0.153

0.204
0.201

0.084
0.075

0.121 0.108 0.146
0.106 0.099 0.123

Table 11: Quantitative results on each scene from the forward-facing [31]dataset.

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Our-VM-192

Our-VM-48

Our-VM-192

GT

Fig. 9: Our rendering results on forward-facing [31] dataset. From top to bottom:
Flower, Fern, Fortress, Horn, Leaves, Orchids, T-Rex, Room.