Event-3DGS: Event-based 3D Reconstruction Using 3D Gaussian Splatting
Authors: Haiqian Han
Jianing Li
Henglu Wei
Xiangyang Ji
Venue: NeurIPS 2024 poster (2024)
Keywords: Event Camera
Event-based vision
3D reconstruction
3D gaussian spallating
Primary area: machine_vision
TL;DR: We introduce a novel reconstruction algorithm achieving high-quality scene reconstruction from Event data under low-light, high-speed conditions.

Abstract: Event cameras, offering high temporal resolution and high dynamic range, have brought a new perspective to addressing 3D reconstruction challenges in fast-motion and low-light scenarios. Most methods use the Neural Radiance Field (NeRF) for event-based photorealistic 3D reconstruction. However, these NeRF methods suffer from time-consuming training and inference, as well as limited scene-editing capabilities of implicit representations. To address these problems, we propose Event-3DGS, the first event-based reconstruction using 3D Gaussian splatting (3DGS) for synthesizing novel views freely from event streams. Technically, we first propose an event-based 3DGS framework that directly processes event data and reconstructs 3D scenes by simultaneously optimizing scenario and sensor parameters. Then, we present a high-pass filter-based photovoltage estimation module, which effectively reduces noise in event data to improve the robustness of our method in real-world scenarios. Finally, we design an event-based 3D reconstruction loss to optimize the parameters of our method for better reconstruction quality. The results show that our method outperforms state-of-the-art methods in terms of reconstruction quality on both simulated and real-world datasets. We also verify that our method can perform robust 3D reconstruction even in real-world scenarios with extreme noise, fast motion, and low-light conditions. Our code is available in https://github.com/lanpokn/Event-3DGS.

Event-3DGS: Event-based 3D Reconstruction Using 3D Gaussian Splatting
Hanqian Han
Jianing Li
Henglu Wei
Xiangyang Ji"
Tsinghua University
Abstract
Event cameras, offering high temporal resolution and high dynamic range, have brought a new perspective to addressing 3D reconstruction challenges in fast- motion and low-light scenarios. Most methods use the Neural Radiance Field (NeRF) for event-based photorealistic 3D reconstruction. However, these NeRF methods suffer from time-consuming training and inference, as well as limited scene-editing capabilities of implicit representations. To address these problems, we propose Event-3DGS, the first event-based reconstruction using 3D Gaussian splatting (3DGS) for synthesizing novel views freely from event streams. Tech- nically, first propose event data and reconstructs 3D scenes by simultancously optimizing scenario and sensor parameters. Then, present high-pass literrbased photovoltage estima- tion module, which effectively reduces noise in event data to improve the robustness of our method in real-world scenarios. Finally, design event-based 3D recon- struction loss to optimize the parameters of our method for better reconstruction quality. The results show that our method outperforms state-of-the-art methods in terms of reconstruction quality on both simulated and real-world datasets. We also verify that method can perform robust 3D reconstruction even in real-world scenarios with extreme noise, fast motion, and low-light conditions. Our code is available https:::s.. //tptgggtttttttt/// com
based 3DGS framework that directly processes
Introduction
3D reconstruction g plays a crucial role in various cutting-edge fields, such as robot vision, virtual reality, and augmented reality systems. It usually enables the creation of accurate 3D models from ideal frame sequences. Nevertheless, with conventional cameras, 3D reconstruction performance has suffered from significant drop some challenging conditions 1 36) (e.g., fast motion blur and low light). Thus, how to use new visual sensing paradigm for 3D reconstruction to overcome the shortcomings of conventional cameras remains partially unsolved issue.
Event cameras 9 21 30), namely bio-inspired dynamic vision sensors, fundamentally differ from conventional cameras that capture frames at fixed intervals. Event cameras operate asynchronously, recording light changes with dynamic events at the microsecond level. This unique property endows event cameras with high temporal resolution, high dynamic range, low power consumption, and low latency. These advantages have driven their application in various challenging vision tasks [12 20
23 41 43 50), including recent efforts in 3D reconstruction [32
Despite efforts 3 42 5T to use event cameras for 3D reconstruction, real-world performance in terms of quality, robustness, and real-time capabilities still needs improvement. Traditional
non-learning optimization based methods [ 17 32 51) serve as the foundation for event-based 3D reconstruction, but they often struggle with robustness and rendering quality. Recently, Neural
Corresponding author: xyji@tsiiiga tsinghua.cdu.co
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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have gained popularity for scene representation and novel view synthesis from event data, utilizing a Multi-Layer Perceptron (MLP) and differentiable rendering. Although these NeRF-based methods [ 2 results photorealistic 3D reconstruction from neuromorphic cameras, they suffer from time- consuming training and inference processes. Additionally, their implicit representations limit scene editing capabilities. Moreover, NeRF have primarily been investigated using simulated data and high-quality real-world images captured under ideal conditions (c.g., optimal lighting and minimal noise), posing limitations on real-world 3D reconstruction. In contrast, the emergence of 3D Gaussian Splatting (3DGS) [I] 15 46, 477 presents compelling alternative, boasting high reconstruction accuracy and swift inference speed. However, 3DGS has predominantly been utilized with image or video data for 3D reconstruction, with limited exploration in event streams.
Radiance Fields (NeRF) [10 28 40
6
14
18
24
25
26
27
31
35
52 achieve impressive
To address this gap, we propose Event-3DGS, the first event-based reconstruction framework utilizing 3DGS for synthesizing novel views from event streams. More specifically, we introduce an event- based 3DGS framework, enabling direct processing of event data and reconstruction of 3D scenes while simultaneously optimizing scenario and sensor parameters. Then, we present a high-pass filter-based photovoltage estimation module, effectively reducing noise in event data to enhance the robustness of our method in real-world scenarios. Finally, we propose an event-based 3D reconstruction loss to optimize the parameters of our method for better reconstruction quality. Extensive experiments show that method outperforms state-of-the state-of-the-art the-art methods in reconstruction quality on simulated and real-world datasets. This pioneering work in event- 3D reconstruction with 3DGS sets new benchmark, opening avenues for high-quality, efficient, and robust 3D reconstruction in challenging real-world scenarios, such as extreme noise, fast motion, and low light. Our contributions can be summarized as follows:
We introduce Event-3DGS, the first framework that combines event cameras with 3DGS technol- ogy, enabling 3D reconstruction in challenging real-world scenarios.
We present high-pass filter-based photovoltage contrast estimation module, which effectively estimates photovoltage contrast by reducing noise in event streams for robust 3D reconstruction.
We design a novel event-based 3D reconstruction loss to optimize the parameters of our method for better reconstruction quality.
2 Related Works
using event cameras for 3D reconstruction typically relied on geometric models and handcrafted features. However, these non-learning, optimization-based methods often struggle to achieve robust and high reconstruction quality. A growing trend is the use of neural radiance fields (NeRF) for scene representation and novel view synthesis. For instance, Ev-NeRF [4] and E-NeRF [18] are some of the carliest works to apply NeRF for event- based 3D reconstruction. These methods render images at different times, generate events through differencing, and compare them with actual events. Further advancements include DeNeRF [25] and EvDNeRF[]. which introduce Deformable NeRF for dynamic scene reconstruction. EventNeRF 35 extends this by enabling colored rendering through the incorporation of three-channel events into NeRF. Some methods like E2NeRF [31 and Ev-DeblurNeRF 2 perform hybrid reconstruction to mitigate motion blur by combining blurred images with events. However, these NeRF-based approaches face significant challenges. including the time-consuming generation of novel views and limited scene editing capabilities due to implicit representations. Additionally, NeRF have primarily been explored using simulated data and high-quality images captured under ideal conditions, leaving a considerable gap between the models and real-world scenarios. Therefore, our goal is to design novel event-based 3D reconstruction framework that ensures nigh-quality, efficient, and robust performance in real-world scenarios.
Event-based 3D Reconstruction. Early attempts B 16 32 51
3D Gaussian Splatting for 3D Reconstruction. 3D Gaussian Splatting (3DGS) 15 has significantly advanced in 3D scene representation, offering notable advantages over NeRF by capturing complex geometries and lighting effects more accurately and efficiently. These advantages make 3DGS highly suitable for real-time and real-world applications. Extended works like 4DGS [46] 47 and D-3DGS 48 further enhance dynamic scene rendering. Besides, some works integrate with Simultaneous Localization and Mapping (SLAMM) [39] and text-to-3I models 4 to expand 3DGS capabilities. However, these methods have primarily been applied to image and video data, leaving

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3D suene
Intendtt
Render Inbmsiit
Event Image (20 vinw)
Toy
Camera Trajectryy
Tugbt)
D.0%
Photovoltage Contrad
1-
Photovoltago Controst Rendering
Maptre
High-past filtacnn
Photovollage Contraat
Milh grad
Initfal value
Intensity
High-pass Filler- Photovollage Contrast Estimation
Reconstraction siono ooe
Negalive
Sy mbolls
Figure I; The pipeline of Event-based 3D Reconstruction using 3D Gaussian Splatting (Event- 3DGS). The proposed wrent-based 3DGS framework enables direct processing of event data and reconstructs 3D scenes while simultaneously optimizing scenario and sensor parameters. A high-past filter- photovoltage contrast estimation module is presented to reduce noise in event data, enhancing the robustness of our method in real-world scenes. An event-based 3D reconstruction loss designed to optimize the parameters of method for better reconstruction quality.
their potential with cameras largely unexplored. Thus, designing novel 3DGS model to directly process asynchronous events for 3D reconstruction remains an open challenge.
3 Method
3.1 Event-3DGS Architecture
To achieve high-quality, efficient, and robust 3D reconstruction in challenging real-world scenarios, propose novel event-based 3D reconstruction framework using 3D Gaussian Splatting (Event- 3DGS). As shown in Fig. [ our framework mainly consists of three modules: high-pass filter- based photovoltage contrast estimation, photovoltage contrast rendering, and event-based 3D reconstruction loss. More precisely, we first present high-pass filter-based photovoltage contrast estimation module that reduces noise in event data enhance the robustness of method in real-world scenes (see Sec. 3.2). Then, we design a photovoltage contrast rendering module that obtains the photovoltage contrast image by calculating the difference in light intensity in 3DGS. After obtaining two contrast estimations, we propose a novel event- bastd 3D reconstruction loss to measure the differences (see See B.3). Finally, our method optimizes the 3D scene and camera parameters by propagating gradients through backpropagation.
3DGS [15] demonstrates superior 3D reconstruction capabilities by rapidly converting input images into highly detailed 3D point clouds, accurately representing the scene. For specific 3D scene represented by 3D Gaussian functions, the forward process of 3DGS can be regarded mapping function G(T), which gets the rendered image by alpha blending in the corresponding camera pose T in time For single pixel single channel, alpha blending can be described follows:
N
a1-a;,
where L denotes the pixel value result, which can be intensity or one of the three channels. 4 and ag the color and opacity of each point mapped to this pixel, respectively.
Event cameras operate on fundamentally distinct imaging principle, generating event data in the form of sparse points (see Sec. 3.2) This disparity prevents the direct integration of asynchronous events into the original 3DGS formulation. with the output of 3DGS by leveraging photovoltage contrast (i.e., intensity changes). Considering two close-in-time instances I and 12, the camera poses corresponding to these two moments are T, and T2. We can obtain its photovoltage contrast between two moments using the proposed high-pass
bridge this gap, we integrate event data seamlessly

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filter-based photovoltage contrast estimation module, and it can be formulated as:
Da(()) (2) -2(,,))
(2)
where ((p, t) refers the photovoltage in pixel p and time t.
Correspondingly, we need use 3DGS to render the photovoltage contrast and light intensity, and then compare these with the ground truth obtained from the event data for subsequent reconstruction. The photovoltage contrast image can be obtained by the proposed photovoltage contrast rendering module. The rendering process can be mathematically described as follows:
D,(-) l2 = (log(G(Tz) + - log((((T)) + +)),
(3)
where G(T) denotes the intensity result in 3DGS. (p(p) is the normalized contrast value in the pixel and is small number that avoids log(0). 0 is learnable parameter, which is an estimate of the threshold the event sensor. For the sake of convenience writing, we do not strictly distinguish between time t and the corresponding pose T.
Given the intrinsic characteristics of event data, it's essential to highlight that intensity estimation methods [37 445 are unlikely to outperform photovoltage contrast estimation techniques. Even models 7 34 may only yield visually appealing results without ensuring physical accuracy and generality. To address this challenge, we proposed a dynamic adjustment strategy for intensity to use high-quality photovoltage while ensuring robustness and stability.
data-driven learning-basee
3.2 High-pass Filter-based Photovoltage Contrast Estimation
To gain deeper understanding of the high-pass filter-based photovoltage contrast estimation module, it's essential to begin with a fundamental understanding of the Dynamic Vision Sensor (DVS) (9]. The DVS designed capture changes in light intensity pixel-wise and asynchronously. accomplishes this by converting the light spectrum into photocurrent as follows:
T(p, t) = / A QE(A) 1(,,, -d)
where L(p, 1, A) denotes the spectrum, is time, p refers to the pixel coordinate {or, y. and À the wavelength of light. T(p, t) is the photocurrent intensity in pixel p and time QF is quantum efficiency, which represents the weighting of different wavelength light converted into photocurrent.
Subsequently, the photocurrent will be converted into photovoltage through a logarithmic function. When the voltage change surpasses a predefined threshold 0, an event will be triggered (30 as:
Vi,, /2) V(p, 41) = of0,
(5)
where V(p. t) refers to the logarithmic operation of the photocurrent [(p, t). of is either +1 or -1 by comparing Vpp, 12) and V (p,11) l1).
In general, the threshold is an inherent attribute of the DVS. can be defined as follows:
Caifs Ven
(6)
A,
where Caifs is determined by the capacitance in the Vv. is fixed constant, Up is thermal voltage, and A, is voltage gain factor. This formula illustrates that 0 often varies with sensor settings and environmental changes, making it generally difficult to obtain its true value. In this work, will optimize the threshold 0 together with the 3D scene.
Intuitively, asynchronous events appear as sparse points 19 in the spatiotemporal domain:
N
E(p,t)
Σ
oB t!),
where 8 (-) refers to the Dirac delta function, with fō (t) dt 1 and (t) 0, Vt + 0.

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In this work, we implement the reverse process of dynamic event generation by extracting photovolt- age contrast and intensity from the event stream Epp, The photovoltage is given as:
tp V(p, (2) = E(r,t)) + w((, 1),
(8)
where i, and i are the times corresponding to two adjacent events around w(p, t) denotes an uncertainty term, which is determined by the mathematical principles of the event camera and is unrelated to noise. This formula indicates that the event camera cannot accurately reconstruct the intensity of light outside the triggering event's timing. Moreover, since ((p,4) is unknown, it is also impossible to accurately obtain the intensity light at each event's 's timing. In short, only the intensity difference between each event's triggering times can be accurately obtained.
For the photovoltage between two events, we can simply assume:
w(p,t) E(p. t,),t < tz.
(9)
The above assumption will not interfere with the voltage the time of event triggering. E(p, is ideal, V can be directly obtained from F. through pure integration, that is:
Vd(p.t) (pp, t) - (p, to) - E(p, t)dt,
(10)
where Va(p, is the photocurrent contrast be estimate. Ideally, this method can accurately provide the photovoltage contrast between the triggering moments of each event.
However, when event cameras are applied in real-world 3D reconstruction, they often encounter various types of noise, making challenging to accurately estimate the photovoltage contrast through
pure integration [37]. To address this issue, use high-pass filtering process the event data. The high-pass filtering can be depicted as follows:
V Voue(s)
(11)
Vin (8)
ST
where (s) and (s) are the onput- signals after the Laplace transformation. 7 is the time constant related the cutoff frequency. We treat J Elp, t)dt noisy input V., and Va(p, t) the output Vour. When substituted into Eq. II and transformed back into the time domain, we obtain that:
= 1 Va(p,t),
(12)
where (p, t) is the differential with respect to the timestamp.
By simultaneously solving with Eq. we can estimate the photovoltage contrast between any two corresponding moments. Once the photovoltage is obtained, the intensity be computed as:
[(p, t) = e (e(p.t)+&.(p..))
(13)
V(p, (o) does not affect photovoltage contrast estimation. Therefore, high-pass filter-based method typically provides more accurate results than restoring pure photovoltage or intensity.
3.3 Event-based 3D Reconstruction Loss
For better reconstruction quality, we loss function with two key components: intensity estimation and photovoltage estimation. The light intensity is evaluated as follows:
4 (I(, t1), G(T)))
(14)
where 4 is a loss function that computes the average of the absolute values between each pixel.
For the evaluation of photovoltage contrast, it's important to consider that 3DGS uses a rasterization method generate the entire image at once. This means the rendering sampling time often does not match the event triggering time for most pixels. According to Eq. [ the ground truth of the photovoltage contrast inherently contains some errors. Additionally, despite applying filtering methods, event data still has significant noise that cannot be entirely eliminated. Consequently, if we directly use the L, loss to compare the rendered photovoltage contrast with the photovoltage contrast calculated from event data, these errors will be strictly considered during the reconstruction process,
5

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Table 1: Performance comparison on the DeepVoxels synthetic dataset 38 outperforms two state-of-the-art methods and our baseline using pure integration without filtering.
our Event-3DGS
Sequence
F2VID
F2VID
34
+DGS
[3
PI-MDGS
Event-3DGS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
mic
0.938
0.048
0.946
19.955
21.979
0.060
0.952
21.127
0.063
ship
0.808
16.556
0.108
0.825
16.681
0.122
0.792
16.750
0.177
0.818
17,815
0.147
materials
0.872
0.084
18.325
0.925
20.053
0.933
0.060
lego
0.883
19.744
0.075
0.899
20,002
0.084
0.928
23.853
0.056
0.925
23,046
0.058
ficus
0.932
19.795
0.043
0.935
19.626
0.056
0.939
19,880
0.050
0.940
19.939
0.049
drums
0.908
18.312
0.071
0.915
18.288
0.085
0.953
22.643
0.041
0.951
22.568
0.042
chair
0.939
23.842
0.040
0.949
23.866
0.050
0.954
27.024
0.042
0.953
27.336
0.050
Average
0.897
19,502
0.067
0,908
19.535
0,080
0.921
21.740
0.070
0.925
21.762
0,067
which can actually degrade the reconstruction quality. Thus, if new loss can be designed that allows for a certain tolerance in the estimation of photovoltage contrast, it would enable better completion of the reconstruction task. For simplification, we denote L (pc( L.P Dr(p),, The loss function of photovoltage contrast can be formulated as:
R 14 - 3 - if 1 RRIL 31
12.4 (LG L.)
(15)
if <
where R(x) (0. and 9 is measure of the tolerance in the estimated photovoltage contrast obtained from rendering. When /3 is infinitely large, the loss becomes a trivial constant zero, imposing no constraints. Conversely, if 3 is zero, the loss degenerates into very strict L1 loss. Theoretical analysis shows that setting 3 to 0.5 yields excellent results in the real-world dataset. When 3 is set to 0.5, it best aligns with the characteristics described in Eq.
Finally, the total loss function for event-based 3D reconstruction can be described as follows:
f2 LP)
(t1 12) = a Σ
= (1 (1-a)( a)
(16)
W *
PER
where W and H are the width and height of the image, respectively. a is parameter that controls the weight of the intensity. For the first 8000 epoch, is set to 0 to give initialization of the reconstruction. Then, a is generally set near I to improve the quality of 3D reconstruction.
4 Experiments
4.1 Experimental Setting
Datasets. To evaluate the effectiveness of our Event-3DGS, we conduct experiments on the Deep els synthetic dataset (38) and the real-world use seven sequences with continuous 180-degree image rotations on a gray background as the ground truth for reconstruction. These sequences are processed by the VOLT simulator [22 to generate event data, offering a more realistic simulation than ESIM (3 with higher noise levels. For real-world dataset, we select five typical sequences that provide aligned image and event data under fast motion and low-light conditions. For longer sequences, we typically utilize the initial 100 images for training and evaluate performance on separate data not employed during reconstruction.
[ataset[29]. For the synthetic dataset, we
Implementation Details. We set to 0.05 for the high-pass filter-based photovoltage contrast estimation module. In the loss function, we set a to 0.9. For synthetic experiments with low noise, is set to O, while for real data with higher noise, 3 is set to 0.5. We utilize E2VID [4]] for initial intensity estimation. We use E2VID+3DGS as a baseline for event-based 3D reconstruction, comparing with our full method to validate its efficacy. All experiments are conducted on an AMD Ryzen Threadripper 3970X 32-Core CPU and an NVIDIA GeForce RTX 3080 Ti GPU. The evaluation metrics use the Peak Signal Noise Ratio (PSNR), the Structural Similarity (SSIM) 4B and the Learned Perceptual Image Patch Similarity (LPIPS) 49].

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Evenllmg
E2VID EZVID+33GG PI-3DGS
Event-3DGS
GroundTruth
Logo
Material
Deun
Figure 2: Representative visualization results the Deep Voxels synthetic dataset 38 Obviously, our Event-3DGS produces visually pleasing images with fine details and fewer artifacts.
Table 2: Performance comparison on the real-world Event-Camera dataset 29 3DGS surpasses three comparative methods three metrics.
Note that, our Event-
Sequence
EZVID
34
E2VID
14 +DGGS (LS
PI PI-DDGS
Event-3DGS 3DGS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIP'
boxos
0.356
8.705
0.320
0.408
8.841
0,228
0.224
8.364
0,749
0,575
17.696
0.260
ollie_zigzag
0.326
7.550
0.287
0.346
7,649
0,233
0.310
10.009
0.424
0.430
14.043
0.183
slider_deptt
0.353
7.634
0.317
0.356
7.620
0.309
0.477
13,509
0.276
0.497
12.448
0.261
outdoors_ walking
0.136
3.657
0.508
0.179
3.499
0.361
0.138
3.429
0.738
0.271
10.583
0.300
calibration
0.293
0.276
5.742
Averago
0.286
6.643
0.345
0.313
6.670
0.290
0.284
9.402
0.580
0.417
13:167
0.245
4.2 Effective Test
Evaluation on Synthetic Data. To verify the effectiveness of method, select two state-of-the- art methods (i.e., E2VID (34] and reconstructed images for 3DGS (15)) and our baseline using Pure Integration without filtering for 3DGS (PI-3DGS) as three comparison methods. As shown in Table T our method and our baseline outperform the representative reconstruction method (i.e., E2VID [
on the DeepVoxels synthetic dataset (38] More precisely, our method has improved by 0.017 and 2.227 respectively compared to the competitor (i.e., E2VID 34 +3DGS (15) in SSIM and PSNR, while decreasing by 0.013 in LPIPS. Furthermore, we present some representative visualization results on the Vexelsxels synthetic dataset (38) in Fig. 2 Note that, our method produces visually pleasing images with fine details and fewer artifacts. For clarification, the visualization for comparative analysis, our method is capable of synthesizing novel views.
Evaluation on Real-world Data. To evaluate the performance of our method in real-world scenarios, we present the comparative results of the real-world Event-Camen dataset [2 in Table [ We select three representative comparison methods to highlight the performance of Event-3DGS. Our baseline (i.e., P1-3DGS) performs worse because the pure integration method for estimating light intensity sensitive to noise. Our method, with its high-pass filter-based photovoltage contrast estimation module, effectively filters out noise in real scenes and improves reconstruction quality (see Fig.B) To demonstrate its robustness in extreme scenarios such as high-speed motion or low lighting, we selected two typical scenarios in Fig. We can find that conventional cameras struggle in low-light conditions and produce significant motion blur in high-speed scenarios. These examples show that our method can reconstruct 3D scenes from the event stream to overcome the limitations of conventional cameras in challenging conditions.
4.3 Ablation Test
7

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Eventing
EDVID
EZV ID -DDS
PI-3DGS
Event- 3DGB
Frame camera
oftice Haglogg
Slickr drget
Figure 3: Representative visualization results the real-world Event- Event-Camera dataset (29]. Note that, our Event-3DGS achieves better reconstruction quality than the three comparative methods.
Contribution of Each Component. To ex- plore the impact of each component on the final reconstruction performance, we chose the pure integration image without the adap- tive threshold and event loss as the base- line. As illustrated in Table We use three different strategies (e.g., adaptive threshold- ing, high-pass filtering, and loss function) to enhance our baseline. As result, our method achieves the best performance among all competitors. In other words, our method employs these effective components pro- cess event streams for 3D reconstruction.
RGB
Eventling
E2vid+3DGS
Event-3DGS
light
Hllgh spood
Figure 4: Representative visualization examples low-light and high-speed motion blur scenarios.
Influence of the Parameter To analyze the hyperparameter the loss function, we set the hyperparameter with various values (e.g., 0.05, 0.2, 0.4, 0.6, 0.8, 0.9, and 1). As shown in Table large values of pose risk of the training deviating to suboptimal points. Small values render the main phase ineffective, resulting in degraded outcomes similar to the initial phase.
Table 3: The contribution of each component.
Threshold Filtering
Loss
SSIM
0219
0.317 0.376
0.221
0.410
0.310
0.393
0.430
PSNR
6.13 11.197
9.594
6.878
11.715
10.009
9,840
14,04
0.424
Influence of the Parameter 3. We report the
Table 4: The influence of the Parameter
impact of varying in Table 5) The results indicate that the reconstruction performs op-
0.99
0.9
0.8
0.6
0.4
0.2
0.05
timally when 3 is set to 0.5. Deviations from
SSIM 0.945
0.953
0.956
0.955
0.954
0.953
0.952
0.952
PSNR
25.688
27.302
25.974
25.066
24.540
24.300
24.146
24.148
this value to a decline in performance, consistent with theoretical predictions.
LPIPS
0.063 0.051
0.039
0.040
0.038
0.038
0.039
0.039
4.4 Scalability Test
Event-3DGS for Motion Deblurring. Our Event-3DGS can be further expanded motion deblur- ring. By integrating event data with RGB frames, our method can achieve deblurring effects using the hybrid reconstruction manner. As shown Fig. 6 We test the hybrid framework on some simulated sequences [15] using VOLT 22) Note that, blurred image is generated through integration to serve as the RGB input. Our Event- 3DGS leverages event data achieve deblurred color reconstruction.

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EVDD
EDIS
ENeri-JDSS
E-Deblur $765
Figure 6: Representative visualization examples of motion deblurring. Note that, Event-3DGS can be extended for high-quality hybrid reconstruction using events and frames with motion blur.
Event-3DGS for Color Reconstruction. In general, adding color information to 3D reconstructed im- ages is crucial for visual appeal and downstream ap- plications. achieve this, we extend Event-3DGS from single channel to three channels enable color reconstruction. As illustrated in Fig 5 we se- lected video sequence [15] and utilized the VOLT simulator [22] to convert the RGB channels into events. Using method framework, we jointly reconstructed these three channels. The results in Fig. degmonstmttttete that our method can achieve high- quality color reconstruction.
Event
EXVDAEDGS
C-EvarL3DGS
Limitation. method rendering module's adap- tive threshold learns a threshold for each scene but doesn't 't account for variations within the same scene over time. Additionally, our current 3DGS lacks support for dynamic scenarios, where 4DGS may be solution. Future research will address these limitations to enhance Event-3DGS practicality.
Figure 5: Representative examples of colorful ovent-based 3D reconstruction.
Conclusion
This paper introduces Event-3DGS, pioneering event-based 3D reconstruction framework that uti- lizes 3D Gaussian Splatting (3DGS) to directly pro- cess event streams for synthesizing novel views. We present high-pass filter-based photovoltage esti- mation module to effectively reduce noise in event data, enhancing the robustness of our method in real- world scenarios. Additionally, we design an event- based 3D reconstruction loss to optimize the parameters of our method. Our results demonstrate that our method surpasses state-of-the-ar methods in both reconstruction quality and computational speed on simulated and real-world datasets. We also verify that our method can perform robust reconstruction even in real-world cases with extreme noise, fast motion, and low-light conditions. We believe that our method establishes a new benchmark for using 3DGS with event data, paving the way for high-quality, efficient, and robust 3D reconstruction in challenging real-world scenarios.
Table 5: The influence of the Parameter 3.
8
0.1
0.15
0.2
0.25
0.5
0.75
SSIM 0.405 0.418 0.416
0.459
0.459
0.497
0.430
0.477
PSNR 8.523 8,874 8.904
10.754
10.688
12.448
9,508
11.44
LPIPS

---

Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant 61827804, 62131011.
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A Appendix Efficiency Advantages over NeRF-based Method
To demonstrate the efficiency of our approach over existing NeRF-based event-based 3D reconstruc- tion methods, we focus on three key aspects: the speed of rasterization compared to ray tracing, the superior parallel support for rasterization in current GPU hardware, and the efficiency of manually derived gradients over neural network backpropagation.
Firstly, the core algorithm of Event-3DGS relies on rendering the 3D Gaussian point cloud using rasterization. Rasterization is inherently faster than ray tracing, which is the method used in NeRF This speed advantage is crucial for achieving efficient 3D reconstruction.
Secondly, modern GPU hardware is optimized for parallel processing in rasterization. This means that rasterization can be executed with greater efficiency and speed compared to ray tracing, which requires more computational resources and time to process each ray individually. The ability to leverage the parallel processing capabilities of GPUs allows Event-3DGS to perform
efficiently.
Lastly, Event-3DGS utilizes manually derived gradients for optimization, bypassing the complex and time-consuning process of neural network backpropagation used in NeRF. This not only reduces computational overhead but also speeds up the overall process, enabling faster and more efficient 3D reconstruction.
In summary, due the faster nature of rasterization, better parallel support on GPUs, and the efficiency of manual gradient derivation, Event-3DGS is significantly more efficient than existing NeRF-based methods. This allows for high-quality reconstruction results be achieved in less time.
B Appendix / The Principle of
Deblurring based on Event-3DGS
To achieve Event-Based Deblurring using Event-3DGS (E-Deblur-3DGS) the key is to associate blurred frames with event data. For a blurry frame camera, its imaging principle can be described as:
(), - - Attt (A.QEC(A) Lp, 44, dAdli,
(17)
where C' represents additional color channel, typically red, green, and blue. QEc denotes the response magnitude of this channel to different wavelengths of light, while te stands for the camera's 's exposure time, which is the primary cause of motion blur.
Comparing Equation 17 with Equation 4 we see that RGB cameras, while prone to blurring due to their exposure time, offer rich color information. Conversely, event cameras, with their extremely fast response times, capture almost no motion blur but only single-channel spectral information. By combining these strengths through loss function, motion deblurring can be achieved.
For the event data, directly apply the loss described in the main text. For the blurry camera, neglecting unit influence, we can sample the output of 3DGS, perform numerical integration, and compare with the blurry camera's result, expressed as:
( 12, (D G(T(t))dt)
(18)
blur
W * H
where W and H are the image's width and height, T(t) is the camera pose at time t, and G(T(t)) is the 3DGS render result. If the exposure time is not too long and the motion speed is not too fast, the integral can be approximated using numerical integration with single sample.
Finally, combining the above formulas, the resulting loss is:
1 UE- (t1, 12) (1- astar) (uu 12) + Oldiu Isturs
(19)
where Olter is hyperparameter controlling the weight of latur By calculating the gradient with this loss and jointly optimizing the scene and sensor parameters, a clear color image can successfully reconstructed.
13

---

EventImq
E2VID
E2VID +3DGS
PI-3DGS
Event-3DGS
Frame camera
Figure 7: Representative visualization results series the real-wor world Event-Camera dataset 29
Our
Event-3DGS method produces clearer results compared other methods.
C Appendix The Principle of Event-3DGS for Color Reconstruction
Since conventional DVS cameras lack color information capture capability, new sensor type capable of acquiring three-channel events is imperative. Its operational principle is defined as:
Te(p, -,,, (FC(())))) QFc(A) Lp,,, dd,
(20)
where C' signifies additional color channel, typically denoted red, green, and blue. QEc denotes the magnitude of this channel's 's response to various light frequencies.
Expanding our method algorithm to C-Event-3DGS merely requires extending the loss function. The approach involves computing the loss for each channel's event using the Event-3DGS method and then aggregating these losses to derive the final loss:
(c-au(11,1)) OR lan(t1, 12) + ag (2) aa (2),
(21)
where lau(ti, (2) lau(tz, t2 and (t1, (itt,,tt)) t2) represent the loss calculated for each channel's event data using the original Event-3DGS algorithm. The parameters 0'g ag, and ag are hyper- parameters adjusting the weights of each channel. With this loss formulation, C-Event-3DGG reconstruct color scene solely based on three-channel event data input. Note that in actual color event cameras, the Bayer pattern is often used to achieve the color effect. Therefore, additional post-processing is required during use, specifically interpolation to obtain the three-channel intensity differences
can
14

---

D Appendix Additional Experiment Result
Visualization Results on Real Data. To further showcase the reconstruction prowess of Event-3DGS, we present the reconstruction outcomes from various camera poses within the same scene, denoted as "slider "slider_depth".. In Fig. [ the results illustrate the real Event data reconstruction capabilities of Event-3DGS. Each row in the figure corresponds to the camera positioned in the same pose. As we progress from top to bottom, the camera gradually moves from left to right. Remarkably, Event-3DGS consistently upholds high-quality image reconstruction across spectrum of poses, underscoring its robust 3D reconstruction capabilities.
Comparison with Ev-NeRF[14) To highlight the accuracy superiority of our method over existing approaches, we conducted a comparative analysis with the Ev-NeRF method using real dataset. Table presents the performance evaluation of our method and Ev-NeRF in three typical real-world scenarios. Observing the results, it's evident that our method consistently outperforms Ev-NeRF across all metrics in the real dataset. This substantial improvement across various scenarios strongly attests the superiority our approach.
Table 6: Experiment results on real dataset between Ev-NeRF and our Event-3DGS. Our Event-3DGS outperforms Ev-NeRF in all metrics.
Ex-NeRF
Event-3DGS
SSIM
PSNR
LPIPS
SSIM
PSNR
LPIPS
office_zignan
0.415
14.589
0.275
0.430
14,043
0.183
boxes
0.470
13.979
0.320
0.575
17.696
0.259
Dynamic_6on 6doo
0.260
7.100
0.420
0,212
11.404
0.307
Average
14.381
Impact of Training Iterations on Performance and Time. To empirically demonstrate the time complexity of our proposed Event-3DGS, we investigate the impact of training iterations on its performance and time requirements. Table presents the performance and time metrics of Event- T
3DGS using synthetic data. The "initial" stage in the table indicates the phase when the parameter is set to zero. Following this stage, is adjusted to 0.99, and training proceeds consistently until 7999 iterations. The table illustrates that Event-3DGS achieves high-quality reconstruction results in approximately five minutes. This indicates its potential for real-time applications.
Table 7: Experiment results performance and time of different training iterations
iterations
initial
999
1999
2999
3999
4999
5999
6999
7999
SSIM
0.9493
0.9528
0.9544
0.9549
0.9546
0.9545
0.9539
0.9530
0.9534
PSNR
23 866666
26.5129
27.0038
27.1565
27.2864
27.2990
27.3594
27.1334
27.0929
LPIPS
0.0500
0,0448
0,0422
0,0414
0.0428
0,0450
0.0486
0.0509
0.0500
Running time(s)
123
141
220
267
361
407
453
500
15

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Reviews:
[{"review_id": "BWZ5BVG1HO", "reviewer": "Reviewer_kCE4", "summary": "This paper proposes a new method for novel view synthesis of intensity images using Event-Camera data via 3d Gaussian Splatting. Event-cameras are a type of camera that captures log intensity changes on the image plane. While 3D Gaussian splatting is a method for novel view synthesis that has been originally developed for images from traditional cameras. Thus, the overall achievement of this work is to make 3D Gaussian splatting work for asynchronous event data.\n\nTo achieve this, the authors introduce a high-pass filter for noise reduction in the photovoltage contrast estimation, a technique for integrating event data in the rasterization process, and a two component loss term including a proposed schedule for the loss terms parameters. The work is evaluated on a synthetic and a real-world dataset and compared against an event-based video generation and its integration with the image-based Gaussian splatting.", "questions": "* In l. 112, what is meant by \"point mapped to this pixel\"? The Gaussian function, its center, or a point on its surface?\n* In l.200 it is said that \"theoretical analysis shows that setting $\\beta$ to 0.5 yields excellent results\". I am not sure I have seen any theoretical analysis. Did I overlook? If not, could the authors elaborate on this?\n* What is the intuition for setting $\\alpha$ to 0 in the beginning of the optimization? Does it speed up training time? Which other training schedules have been tried? What happens if it has a non-zero value already from the beginning of the process?\n* How were the datasets used? Do the scenes already contain a test validation split or was it created by the authors? What was the length of event-sequences that were sampled during training? I.e. what is the value of $N$ from eq. 7 during training.\n* What is the impact of different values for $\\tau$? Is there a reason why it is set to 0.05?\n* What is meant by \"$E(p,t)$ is ideal\" in l. 164?\n* What is the intuition of high pass filtering. Is the noise assumed to be low frequency?\n* What is the purpose of the subscript $i$ in eq. 14. It seems to not appear on the right hand side.\n* l. 253: in what sense is the threshholding adaptive?\n* Looking at Table 7 in the appendinx, to the authors have an intuition on why the performance goes down as training progresses?\n* Sec. 4.4. seems to introduce a new method that combines events and images rather than be a \"Scaling test\". Could you provide some information on how the combined method works?\n* Also, how are the visualizations created? Using purely events does not yield a baseline color and the intensity might be off by a constant offset. How is this resolved in the work?", "limitations": "Overall, the work mentions most limitations. One that is currently omitted is that the way it incorporates colors is not realistic in practice. If understood correctly, the work assumes color information to be equal in each pixel. However, in practice color event cameras use a Bayer RGB pattern and require some sort of remosaicing during the splatting process.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "Integrating event-camera data with Gaussian Splatting is an interesting research direction. The work makes a meaningful technical contribution that are of interest for both, the event-vision and novel view synthesis sub-communities. I also want to applaud the authors for committing to releasing the source code making the reproduction of this work easy. From the work itself, I liked the idea of introducing a filter and the loss design to the extent that I understood it.", "weaknesses": "The work is currently written in a way that is more amenable to the vision community and might need some rewriting to be understandable by the broader NeurIPS audience, which e.g. cannot be assumed to be familiar with Gaussian Splatting. Even if space does not permit to add a full background section (which would be desirable), it would be useful to at least introduce $G(\\mathbf{T})$ in a way that gives a high-level undstanding of what Gaussian Splatting does. The current writing merely says \"For a specific 3D scene represented by 3D gaussian points, the forward process of 3DGS can be regarded as a mapping function G(T)\" which is probably not enough for a reader unfamiliar with 3DGS. There are more examples like these where average NeurIPS readers might need more background or better explanations than those at vision venues.\n\nSome terminology in the paper is used wrongly or made up which makes it hard to understand. E.g. the authors speak of 3D Gaussian points which is not a common term and in this context wrong as 3DGS uses 3d Gaussian functions (or simply 3D Gaussians) rather than points. A more nuanced point is that 3DGS is referred to as a reconstruction method. And although its explicit representation is much closer linked to reconstruction than the neural network-based radiance fields, I would carefully argue that Novel View Synthesis (NVS) would be the more correct term. The evaluation of the work also does not focus on reconstruction but on NVS.\n\nThe work seems not to compare against any Event-based NeRF techniques which one would expect due to the conceptual similarity. Moreover I wonder whether the proposed methodology could also be used for some of the recent NeRF techniques. Unless, I overlooked something, it seems like the work does not make any use of the fact that the underlying representation is Gaussian. So, it would be interesting to see how much of the performance is due to the authors ideas and how much is due to the use of 3DGS as underlying representation.\n\nMinor points:\n* The authors often speak of \"our Event-3DGS\" in reference to their method. I am not sure this is grammatically correct. Shouldn't this be rather \"our method\" or \"our approach\"?\n* The research gap mentioned in l.25/26 is not a fully open reseach problem in the generality stated there. It's rather that specific aspects of it are unsolved.\n* l.34/35 \"Traditional non-learning optimized-based methods\" -> \"Traditional non-learning optimization-based methods\"\n* l. 39-42 slightly too long sentence should maybe be split. Also \"achieves\" -> \"achieve\"\n* The structure of the contribution list is confusing. Since the first bullet point encompasses the other two. I would suggest to focus on the technical contributions and maybe leave out the first point. The content of the first point could still be acommodated in the previous paragraph.\n* l.69 / 70 \"often struggle to achieve robustness and high-quality reconstruction\" -> \"often struggle to achieve robust and high reconstruction quality\" maybe?\n* l.78/79 I am not sure whether some of the statements about NeRFs are true. Modern NeRFs have shown significant improvement in training time. Isn't the main advantage of splatting the fast view generation?\n* In Fig 1., is there a reason why $\\frac{1}{\\theta}$ is also dark red in the \"Photovoltage Contrast Rendering\" pane? Also, shouldn't  \"Symbol\" be replaced by \"Symbols\" or \"Legend\"?\n* In l.109, should the second \"T\" be bold? Also, the authors do not spell out how poses are parametrized. I assume it is the same as in 3DGS?\n* The work speaks of \"forward process of 3DGS\"\n* The letter $\\alpha$ is used in two different contexts (l.110 and eq 16) and, thus, overloaded which may create confusion.\n* l. 114/115 \"integration of asynchronous events into raw 3DGS\" -> \"integration of asynchronous events into the original 3DGS formulation\" \n* In eq. 2, is it work including $p$ instead of writing $\\cdot$ as a placeholder for the pixel location?\n* Can an explanation of photovoltage be added to the paper? At least, maybe the explanation of the image formation in event cameras at the beginning of Sec. 3.5 should come earlier in the paper.\n* Some subscripts are broken in l. 147 and eq. 7\n* In eq 8. does $w(p,t)$ also encode the quantization error?\n* l. 162 \"we can simply assume as\" -> \"we can simply assume\"\n* Also the typesetting of $\\log$ is not consistent. It is italic in eq. 3 and upright in l. 127. I recommend using the latter to e consistent with the $\\max$ in l.197\n* Is it woth renaming Sec. 4.2. to \"Results\" and Sec. 4.3 to \"Ablation Studies\"?\n* Some of the advertising (to the extent that it even should be in the paper) in l. 292-296 seems to be more suited for the conclusion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for you insightful suggestions and affirmation. The tables and figures mentioned below can be found in the attached PDF.\n\nW1: Rewriting should be clear for the NeurIPS audience.\n\nR1: We will add a high-level introduction to Gaussian Splatting in the main manuscript and provide clearer explanations in the appendix of the revised version.\n\nW2: Some terminology may be hard to understand. Not focus on reconstruction but on NVS.\n\nR2: Thanks. We will clarify the terminology in the revised version.\n\nBesides, existing 3DGS methods mainly evaluate NVS to align with common image reconstruction quality metrics. Therefore, we also use NVS to assess our Event-3DGS. However, our method is not restricted to NVS and can be extended to obtain depth and reconstruct 3D meshes.\n\nW3: The work seems not to compare against any NeRF techniques. Please explain the performance contributions.\n\nR3: First, we compare our Event-3DGS with a typical method (i.e., Ev-NeRF) on both synthetic datasets (see Table R1 and Fig. R1) and real datasets (see Table R2 and Fig. R2). Note that, our Event-3DGS significantly outperforms Ev-NeRF in terms of SSIM, PSNR, and LPIPS.\n\nSecond, our Event-3DGS benefits from both 3DGS itself and our proposed modules (see the ablation test in Table 3). Unlike NeRF’s ray tracing, 3DGS uses raster-based rendering to generate the entire image at once, which can introduce errors if many pixels are not sampled when events occur. Our loss design and filtering techniques address these errors, improving performance.\n\nW4: Some writing minor points.\n\nR4: Thanks. We will address these writing minors one by one.\n\nQ1: In Line 112, what is meant by \"point mapped to this pixel\"?\n\nA1: The transparency of the 3D Gaussian function is first mapped to screen space. Next, pixel transparency is determined based on each pixel's position within the 3D Gaussian function. The color is determined from the spherical harmonics lighting coefficients. We will clarify this description in the revised version.\n\nQ2: In Line 200, elaborate on the theoretical analysis.\n\nA2: An event camera cannot capture intensity information between events, and the intensity can vary within the threshold range (see Eq. 8). The parameter selection in Line 200 considers this, ensuring that the rendered intensity within the positive and negative threshold range minimizes the loss, aligning with the theoretical analysis. We will add this analysis in the camera-ready version.\n\nQ3: The setting and optimization of $\\alpha$.\n\nA3: $\\alpha$ is a hyperparameter chosen to provide a good initial value for 3DGS. It doesn't need to be exactly 0, and any small value can work. While setting $\\alpha$ to the maximum value is possible, it may lead to local optima issues.\n\nQ4: The datasets setting and the length of the event sequences sampled.\n\nA4: We split each synthetic or real dataset, reserving a portion of the images for testing while using the rest for reconstruction training. The event sequences vary in length, but generally contain more than a million events. We will add these details in the experimental settings in the revised version.\n\nQ5: What is the impact of different values for $\\tau$? Is there a reason why it is set to 0.05?\n\nA5: This hyperparameter $\\tau$ controls the frequency range of the high-pass filter. A narrower range reduces noise but may discard more original event information. Besides, our tuning experiments show that setting this parameter to 0.05 yields better results.\n\nQ6: What is meant by \"$E(p, t)$ is ideal\" in Line 164?\n\nA6: \"The ideal\" means that an event perfectly represents intensity changes without any noise. In practice, events are affected by background noise, refractory periods, leak noise, and bandwidth limitations. We will provide more details in the revised version.\n\nQ7: What is the intuition of high pass filtering. Is the noise assumed to be low frequency?\n\nA7: Yes, due to the higher noise levels in event cameras compared to traditional RGB cameras, especially in low-light scenes, the noise primarily consists of low-frequency signals compared to the effective events.\n\nQ8: What is the purpose of the subscript $i$ in Eq. 14.\n\nA8: The symbol used here seems inappropriate, as it was intended only to differentiate it from the subsequent event loss. We will correct this in the camera-ready version.\n\nQ9: Line 253, in what sense is the threshold adaptive?\n\nA9: The threshold for detecting light changes in event cameras may not be directly obtained from event data, and it can be influenced by the scene environment (see Lines 148-150). Accurate threshold estimation is crucial for obtaining light intensity from a mathematical optimization perspective. To improve reconstruction quality, we design an adaptive threshold for each scene (see Table 3).\n\nQ10: Table 7, goes down as training progresses.\n\nA10: The training has essentially converged at a certain point, with subsequent steps involving only minor perturbations. In practice, although there are fluctuations after convergence, the overall performance remains stable.\n\nQ11: Explain how the combined method.\n\nA11: We have provided the combination of events and frames in the appendix (see Lines 469-488). Briefly, we compare the rendered image with the RGB frame to obtain a loss, which is then added to the total loss (see Eq. 16 and Eq. 19).\n\nQ12: Visualizations created.\n\nA12: In pure event-based imaging, restoring absolute light intensity is generally not possible. We specify the initial light intensity (e.g., setting the background intensity) as done in previous methods. Typically, this value can be set to 0, representing pure black.\n\nQ13: Colors is not realistic.\n\nA13: We assume each pixel has three channels of events, differing from the Bayer pattern. Therefore, our algorithm first interpolates the raw data into a three-channel format. In the future, we could extend our Event-3DGS to handle raw color event data in the Bayer pattern.", "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": "HfnDUyFTgi", "reviewer": "Reviewer_tU43", "summary": "This paper proposes a 3D reconstruction method from event cameras using 3D Gaussian Splatting (3DGS). The authors propose an innovative framework that takes a stream of events as input and optimize 3D appearance model with 3DGS. In particular, the authors propose differentiable rendering of event images and photovoltage contrast image with corresponding losses. Using photovoltage contrast images allow to handle noisy inputs with make the proposed method applicable to real data.", "questions": "Please clarify equation (7)", "limitations": "Yes limitations such as dynamic scenes have are included", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-\tThe paper is well written and easy to follow. Although I am not expert in the domain, I found the proposed method interesting and novel (as far as I know). The high pass filtering technique to handle noisy images makes much sense and it is also modeled in the rendering of Gaussians Splatting. The proposed losses seem correct and allow to achieve state-of-the-art results.\n\n-\tThe experimental section is convincing. The results are clearly superior to previous methods and the ablation part shows that the losses are working well. The authors also propose a concrete application for the task of image deblurring.", "weaknesses": "-\tIn the writing, it is better to avoid abbreviations like “it’s” and write “it is” (l. 129 for example). \n\n-\tA word is missing l. 147\n\n-\tIn equation (7), I cannot understand the meaning of i^p. I understand from l. 139 that p is 2D pixel coordinate, but I am not sure what is an integer at the power of a 2-dimensional vector.\n\n-\tIn the experiments it seems that numbers in the text l.230 do not match the numbers in table 2.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your positive evaluation.\n\nW1: In the writing, it is better to avoid abbreviations like “it’s” and write “it is”.\n\nR1: we will add the missing words and change “it’s” to “it is” in the camera-ready version. \n\nW2: A word is missing in Line 147.\n\nR2: We missed \"event sensor\" in Line 147, and will correct it in the camera-ready version.\n\nW3: Questions about Equation (7).\n\nR3: Our intention is to use $t$ as the subscript and $p$ as the superscript to represent the time when the $i$-th event is triggered at pixel $p$, without implying an exponent. We will correct this in the camera-ready version.\n\nW4: It seems that numbers in the text Line 230 do not match the numbers in Table 2.\n\nR4: Actually, Line 230 corresponds to the numbers in Table 1, not Table 2. The statement \"our Event-3DGS has improved by 0.017 and 2.227, respectively\" refers to the performance metrics for the synthetic dataset shown in Table 1, not the real-world dataset in Table 2.", "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": "ClZyUk9YlJ", "reviewer": "Reviewer_nxFk", "summary": "The paper introduces Event-3DGS, a framework that leverages event cameras and 3D Gaussian Splatting (3DGS) for efficient and robust 3D reconstruction in challenging real-world scenarios. The authors propose: a high-pass filter-based photovoltage estimation module and a novel event-based 3D reconstruction loss to enhance performance. Experiments with both real and synthetic datasets are used to evaluate the performance of the proposed method. The results demonstrate it performs better than prior works.", "questions": "n.a.", "limitations": "n.a.", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "1: The combination of event camera with 3D-GS is interesting and enable the leverage of efficient rendering capability of 3D-GS;\n\n2: The experimental results, which conduct on both real and synthetic datasets, demonstrate the proposed method performs better than baseline methods, in terms of visual quality;\n\n3: Additional experiments which integrate the proposed method with motion blurred RGB images, as well as for color reconstruction, are presented; The experiments demonstrate its advantage for more practical applications.", "weaknesses": "1: The paper is not well written and contains many errors, it is very difficult to follow for certain parts. For example: \n* why it holds for Eq. 9, based on the reviewer's understanding, the uncertainty term or noise term is usually a random gaussian noise. why it equals to the negative of E?\n* the notation is confusing, V is used to denote signal after Laplace transformation, while it is used as photovoltage and photocurrent contrast in Eq. 10.\n* Eq. 12 conflicts with Eq. 10, why the same term, i.e. \\hat{V}_d, can equal to E's integration in Eq. 10 and E + plus a differential term in Eq. 12? \n* It is confusing on \"when the time is sufficiently close, we consider the relationship between time t and pose T as a one to one mapping\" in Line 127.\n* Line 147, \"V_th is a fixed constant\" -> typos, same for Eq. 7.\n\n2: Experimental evaluations against prior methods are not sufficient. The paper exploits E2VID, E2VID+3DGS, PI-3DGS as the baselines. However, it misses several important baselines which are on event based NeRF. Although the authors present additional comparisons against EvNeRF in the appendix. It misses the comparisons on the synthetic datasets. The evaluations on real data against EvNeRF also misses some sequences which presented in Table 2. \n\n3: In terms of the ablation studies on the contribution of each component, why the authors chose the baseline that integrates E2VID and 3DGS for event based 3D reconstruction. It should be experiments for the proposed method instead of E2VID. \n\n4: Dependency on known poses: the approach requires ground truth poses, which limit its practical usage of the proposed method. Different from frame-based methods, which can exploit COLMAP to obtain GT poses, it is usually difficult to obtain GT poses for event camera alone. \n\nMain reasons on current rating:\n\nBased on the poor presentation of the paper, and insufficient evaluations to fully demonstrate the advantages of the proposed method, the reviewer gives his current rating.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "The figures (i.e., Fig. R1 and Fig. R2) mentioned below can be found in the attached PDF.\n\nQ1: The paper is not well written and contains many errors, it is very difficult to follow.\n\nA1: Thanks. We will clarify the writing to improve reader understanding in the camera-ready version.\n\nQ1-1: In Eq. 9, why it equals to the negative of $E$?\n\nA1-1: Eq. 9 is a parameter set used to simplify assumptions, which is convenient for the theoretical derivation and representation of subsequent filtering. $w$  should not be treated as a Gaussian noise term. The negative term is reasonable, as it accommodates step-like changes in light intensity, which are typically within the feasible range of  $w$ . We will clarify this explanation in the revised version.\n\nQ1-2: $V$ is used to denote signal after Laplace transformation.\n\nA1-2: The notation $V$ should indeed be different after the Laplace transform. We will correct this in the camera-ready version.\n\nQ1-3: Eq. 12 conflicts with Eq. 10.\n\nA1-3: Eq. 10 represents the pure integration method, which estimates light intensity differences under ideal conditions but performs poorly in noisy environments. In contrast, Eq. 12 employs high-pass filtering, making it more robust to noise. Thus, Eq. 10 and Eq. 12 are two different approaches for estimating light intensity differences and are not contradictory. We will add the details in the revised version.\n\nQ1-4: It is confusing on \"when the time is ...\" in Line 127.\n\nA1-4: The camera pose $T$ can be regarded as a function of time $t$ , which is generally not one-to-one. For example, a camera might return to the same position with the same orientation at different times. However, within a sufficiently small time interval, this function can be treated as one-to-one, meaning each pose corresponds to a unique point in time. We will provide a more detailed description of this in Line 127 in the revised version.\n\nQ1-5: Line 147, the typo minor.\n\nA1-5: The omission of the subscript was a mistake, and we will correct it in the revised version.\n\nQ2: Experimental evaluations against prior methods are not sufficient. It misses the comparisons on the synthetic datasets. The evaluations on real data against Ev-NeRF also misses some sequences in Table 2.\n\nA2: Thanks for your comments. We have conducted additional experiments comparing our Event-3DGS with Ev-NeRF on both synthetic (see Table R1) and real-world datasets (see Table R2). Our Event-3DGS significantly outperforms Ev-NeRF in terms of SSIM, PSNR, and LPIPS. Additionally, we provide representative visualization examples for both the synthetic data (see Fig. R1) and the real-world dataset (see Fig. R2). Note that, we have added 3 additional sequences in the real dataset that are not shown in Table 6 of the appendix. These results demonstrate that Event-3DGS achieves superior reconstruction quality compared to Ev-NeRF. We will present these experimental results for Ev-NeRF in the camera-ready version.\n\nTable R1: Comparison of Ev-NeRF and our Event-3DGS in the synthetic dataset.\n\n|             ||Ev-NeRF||           |ours||          \n|-------------|------|-------|------|------|-----------|------|\n|             |SSIM|PSNR|LPIPS|SSIM|PSNR|LPIPS|\n|**mic**|0.858|16.939|0.316|0.952|21.127|0.063|\n|**ship**|0.656|16.521|0.398|0.818|17.815|0.147|\n|**materials**|0.692|11.272|0.482|0.933|20.506|0.060|\n|**lego**|0.743|18.526|0.303|0.925|23.046|0.058|\n|**ficus**|0.794|13.368|0.244|0.940|19.939|0.049|\n|**drums**|0.797|16.793|0.315|0.951|22.568|0.042|\n|**chair**|0.786|10.945|0.239|0.953|27.336|0.050|\n|**average**|0.761|14.909|0.328|**0.925**|**21.762**|**0.067**|\n\n\nTable R2: Comparison of Ev-NeRF and our Event-3DGS in the real-world dataset.\n\n|                      ||**Ev-NeRF**||           |**Ours**||       \n|----------------------|------|----------|------|------|-----------|------|\n|                      |SSIM|PSNR|LPIPS|SSIM|PSNR|LPIPS|\n|**slider_depth**|0.282|6.033|0.442|0.497|12.448|0.261|\n|**outdoors_walking**|0.208|8.595|0.409|0.271|10.583|0.300|\n|**calibration**|0.114|12.023|0.712|0.312|11.065|0.222|\n|**average**|0.201|8.883|0.521|**0.360**|**11.365**|**0.261**|\n\nQ3: In terms of the ablation studies on the contribution of each component, why the authors chose the baseline that integrates E2VID and 3DGS for event based 3D reconstruction. It should be experiments for the proposed method instead of E2VID.\n\nA3: Sorry for the writing mistake that may have misled you. We confirm that the data in Table 3 is correct, but the description of the baseline in Lines 250-251 is incorrect. The baseline should be described as a pure integration image without the adaptive threshold and event loss, not E2VID+3DGS. Additionally, comparing Table 2 and Table 3 shows that the ablation baseline performance in Table 3 does not match the E2VID performance in Table 2, confirming that the baseline is not E2VID. We will correct the baseline description in Lines 250-251 in the camera-ready version.\n\n\n\nQ4: Dependency on known poses. It is usually difficult to obtain GT poses for event camera alone.\n\nA4: In general, obtaining accurate camera poses in normal scenes using only event cameras is challenging compared to RGB frames, due to the sparse sampling of event cameras. However, recent works [1, 2] show that event cameras can be effective for pose estimation, particularly in challenging scenarios such as high speeds or low light. For example, Muglikar et al. [1] developed the E2Calib tool, which uses E2VID to reconstruct gray frames, calibrate camera extrinsics, and estimate poses. In our work, we use E2VID to reconstruct frames and then apply COLMAP to process frames to estimate camera poses. Thus, the camera poses estimated using event data enable our Event-3DGS to produce high-quality reconstructions in real-world applications.\n\n[1] How to calibrate you event camera, CVPRW 2021.\n\n[2] EVO: A geometric approach to evnet-based 6-DOF parallel tracking and mapping in real time, IEEE RAL 2017.", "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": "aiEyDEWLP9", "reviewer": "Reviewer_bZpj", "summary": "The paper introduces Event-3DGS, the first framework for event-based 3D reconstruction using 3D Gaussian Splatting (3DGS). The method demonstrates superior reconstruction quality, robustness, and efficiency", "questions": "1. Can the author provide rendering speed and training times on various datasets? Based on my experience, optimizing 3DGS scene representations often requires more time. Please clarify this.\n2. How is the threshold initialized? How can it be optimized with the scene? Is there any difference in the learning rate schedule?\n3. In Figure 6, how does the experiment generate blurred images through integration? Can the author more detailed illustration? Besides, I believe that a real-scene blur dataset should be used to support the superiority of Event-3DGS.", "limitations": "Combining 3DGS with Event cameras may be ineffective due to the loss of crucial information in Event cameras, such as color and resolution, which are incompatible with the high-quality rendering required for tasks like VR.\nSetting the threshold as a global learnable variable for all shooting positions is unreasonable due to dynamic changes with camera movement and lighting; encoding the threshold into (x,y,z,θ) for optimization would be more appropriate.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. By addressing the challenges of fast-motion and low-light scenarios with event cameras and 3DGS, the paper opens new avenues for high-quality, efficient, and robust 3D reconstruction.\n2. The quality of the work is demonstrated through extensive experimental evaluations. The authors provide a thorough comparison with state-of-the-art methods, showing significant improvements in reconstruction quality on both simulated and real-world datasets\n3. Experiments are conducted thoroughly, including experiments on synthetic and real-world datasets. The ablation study is also conducted", "weaknesses": "1. In my opinion, combining 3DGS with Event cameras is somewhat meaningless. The reason is that 3DGS can achieve very high FPS rendering speed and quality, which is essential for real-time tasks like VR and avatar rendering. However, the Event camera modality loses much information, such as color and resolution, which is incompatible with the downstream tasks of 3DGS. In other words, no one would want to experience low-resolution black-and-white VR scenes through a Vision Pro headset.\n2. The paper's experimental setup is insufficient, as it does not sufficiently compare reconstruction methods based on Event NeRF. The authors should provide a more comprehensive comparison in Table 2, including [1,2,3]. Furthermore, the datasets used for evaluation are very limited. The authors should include a wider range of real-world data, such as real data capture used in EventNeRF[1].\n3. Setting the threshold as a learnable variable and optimizing it together with the 3DGS scene representation may be unreasonable. The threshold dynamically changes with camera movement, scene lighting, and shooting position. Therefore, using a global consistent threshold for all shooting positions is clearly not reasonable. I believe encoding the threshold into (𝑥,𝑦,𝑧,𝜃) for optimization would be more appropriate.\n\n[1] EventNeRF: Neural Radiance Fields from a Single Colour Event Camera\n\n[2] E-NeRF: Neural Radiance Fields from a Moving Event Camera\n\n[3] Ev-NeRF: Event-Based Neural Radiance Field", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your suggestions and affirmation. The figures mentioned below can be found in the attached PDF.\n\nW1: Combining 3DGS with Event cameras is somewhat meaningless.\n\nR1: The combination of these two approaches is meaningful:\n\n(1) Pure event data excels in SLAM, 3D reconstruction, and autonomous driving, especially in high-speed or low-light scenes where it outperforms RGB frames.\n\n(2) For high visual quality, our method can be extended to a multimodal framework combining RGB and event data. This joint approach is useful for tasks like high-speed motion de-blurring (see Fig. 6) and HDR imaging.\n\nW2: A more comprehensive comparison, including EventNeRF, E-NeRF, and Ev-NeRF.\n\nR2: Per your suggestion, Ev-NeRF and EventNeRF can be used for comparison, but E-NeRF has a bug that prevents it from being tested. \n\n(1) For Ev-NeRF, we report experimental results on both synthetic datasets (see Table R1 and Fig. R1) and real-world datasets (see Table R2  and Fig. R2). Note that, our Event-3DGS significantly outperforms Ev-NeRF in terms of SSIM, PSNR, and LPIPS.\n\nTable R1: Comparison of Ev-NeRF and our Event-3DGS in the synthetic dataset\n\n|             ||Ev-NeRF||           |ours||          \n|-------------|------|-------|------|------|-----------|------|\n|             |SSIM|PSNR|LPIPS|SSIM|PSNR|LPIPS|\n|**mic**|0.858|16.939|0.316|0.952|21.127|0.063|\n|**ship**|0.656|16.521|0.398|0.818|17.815|0.147|\n|**materials**|0.692|11.272|0.482|0.933|20.506|0.060|\n|**lego**|0.743|18.526|0.303|0.925|23.046|0.058|\n|**ficus**|0.794|13.368|0.244|0.940|19.939|0.049|\n|**drums**|0.797|16.793|0.315|0.951|22.568|0.042|\n|**chair**|0.786|10.945|0.239|0.953|27.336|0.050|\n|**average**|0.761|14.909|0.328|**0.925**|**21.762**|**0.067**|\n\n Table R2: Comparison of Ev-NeRF and our Event-3DGS in the real-world dataset.\n\n|                      ||**Ev-NeRF**||           |**Ours**||       \n|----------------------|------|----------|------|------|-----------|------|\n|                      |SSIM|PSNR|LPIPS|SSIM|PSNR|LPIPS|\n|**slider_depth**|0.282|6.033|0.442|0.497|12.448|0.261|\n|**outdoors_walking**|0.208|8.595|0.409|0.271|10.583|0.300|\n|**calibration**|0.114|12.023|0.712|0.312|11.065|0.222|\n|**average**|0.201|8.883|0.521|**0.360**|**11.365**|**0.261**|\n\n(2) For EventNeRF, it processes color event data unlike our format. Thus, we converted its synthetic data to our classic event data format. Table R3 and and Fig. R3 shows that EventNeRF and our Event-3DGS perform comparably. Note that, EventNeRF’s data differs from the original paper due to additional color adjustments made before metric calculation. This adjustment may be not entirely reasonable, so we compare only the raw reconstructed images in the two methods. Besides, while EventNeRF requires a long training time for each scene, our Event-3DGS trains each sequence in under 10 minutes. In short, Event-3DGS offers better efficiency while maintaining comparable reconstruction quality. \n\nTable R3: Comparison of EventNerf and our Event-3DGS in the synthetic dataset.\n|           ||EventNeRF||           |**Ours**||\n|-----------|------|----------|------|------|--------|------|\n|           |SSIM|PSNR|LPIPS|SSIM|PSNR|LPIPS|\n|**lego**|0.894|23.137|0.076|0.914|23.694|0.111|\n|**drums**|0.923|26.917|0.054|0.942|24.394|0.055|\n|**chair**|0.952|28.905|0.047|0.958|24.449|0.035|\n|**average**|0.923|**26.320**|**0.059**|**0.938**|24.179|0.067|\n\n(3) For E-NeRF, we attempt deployment but faced insurmountable issues. A review of related GitHub discussions reveal that others have encountered similar problems without resolution from the authors, leading us to abandon this comparison.\n\nOverall, we have tested many sequences with high-noise real event data, proving its practicality. The real object data used in EventNeRF comes from a different color event camera, which makes it unsuitable for our algorithm.\n\n\nW3: Making the threshold a learnable variable and optimizing it with the 3DGS scene representation may be unreasonable.\n\nR3: Emphasizing adaptive thresholds is valuable. We explore a basic approach using an adaptive threshold for a single sequence. While varying scene or pixel-level thresholds could improve reconstruction quality, this would likely increase computational complexity, which we acknowledge as a limitation. These points are important and could be explored further in future work.\n\nQ1: Can the author provide rendering speed and training times on various datasets?\n\nA1: Our Event-3DGS optimization is fast. For instance, using the Ficus sequence, we achieved the reported results in approximately 9 minutes and 47 seconds on an RTX 3080 Ti. However, the original 3DGS has high GPU memory requirements, and running out of memory can significantly slow down subsequent reconstructions.\n\nQ2: How is the threshold initialized? How can it be optimized with the scene?\n\nA2: We can start by setting the threshold to the manufacturer’s standard value or an estimated range (typically between 0 and 1). During training, this threshold can then be optimized as a learnable parameter alongside the scene parameters. This approach differs from a learning rate schedule, which is a manually designed strategy not directly tied to backpropagation or training but helps facilitate the training process. We will add these details in the revised version.\n\nQ3: How does the experiment generate blurred images through integration in Fig. 6?\n\nA3: To accurately simulate the blur effect, we start with a high-quality 3D model and render the blurred images. During rendering, we calculate the spectral integration of the camera's motion based on its speed to produce the final blurred image. Given the ground truth data of the 3D scene distribution, the resulting blurred images closely approximate real-world conditions.", "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:
Thank you to the area chairs and all the reviewers for your valuable comments!

To further verify the effectiveness of our Event-3DGS, we conducted six experimental tests using two event-based NeRF methods (i.e., Ev-NeRF [1] and EventNeRF [2]). The quantitative results and visualization figures are available in the attached PDF file. Specifically:

- **Table R1** and **Table R2** provide a quantitative comparison of Ev-NeRF and our Event-3DGS on synthetic and real-world datasets.

- **Fig. R1** and **Fig. R2** showcase representative visualization examples for Ev-NeRF and our Event-3DGS on synthetic and real-world datasets.

- **Table R3** and **Fig. R3** show the quantitative and visual experimental results of EventNeRF and our Event-3DGS, respectively.

For convenience, we highlight the tables and figures relevant to each reviewer's comments as follows:

- **Reviewer kCE4**: Table R1, Table R2, Fig. R1, and Fig. R2.

- **Reviewer nxFk**: Table R1, Table R2, Fig. R1, and Fig. R2.

- **Reviewer bZpj**: Table R1, Table R2, Table R3, Fig. R1, Fig. R2, and Fig. R3.

We have provided point-by-point responses to each reviewer's comments in the corresponding rebuttal. Please review these responses.

Thank you again for your insightful comments. We sincerely hope the rebuttal will address the reviewers' concerns and convince the reviewers to give more convincing decisions.



[1] Ev-NeRF: Event-Based Neural Radiance Field, WACV 2023.

[2] EventNeRF: Neural Radiance Fields from a Single Colour Event Camera, CVPR 2023.

Meta-review: All reviewers agreed to accept the paper. The paper originally got BA, A, BR, and BA, and, after the rebuttal period, the last two reviewers raised the ratings, leading to final ratings of BA, A, BA, and WA. 

Reviewers recognized that the paper has clear contributions in applying 3DGS for event cameras, considered the first in the field. 
However, reviewers are also concerned about the unsatisfactory readability and issues in evaluations. After the authors' rebuttal and discussion period, most reviewers’  concerns have been resolved, and all reviewers agreed that the paper's shape is above the bar for NeurIPS. 

The AC also supports accepting the paper and strongly suggests the authors to follow the reviewers’ feedback in the camera-ready version.
Decision: Accept (poster)