Title: Slot-guided Volumetric Object Radiance Fields
Venue: NeurIPS 2023
Accepted: yes
Keywords: 3D object-centric representation learning

NeRF

3D-aware slot
Abstract: We present a novel framework for 3D object-centric representation learning. Our approach effectively decomposes complex scenes into individual objects from a single image in an unsupervised fashion. This method, called \underline{s}lot-guided \underline{V}olumetric \underline{O}bject \underline{R}adiance \underline{F}ields~(sVORF), composes volumetric object radiance fields with object slots as a guidance to implement unsupervised 3D scene decomposition. Specifically, sVORF obtains object slots from a single image via a transformer module, maps these slots to volumetric object radiance fields with a hypernetwork and composes object radiance fields with the guidance of object slots at a 3D location. Moreover, sVORF significantly reduces memory requirement due to small-sized pixel rendering during training. We demonstrate the effectiveness of our approach by showing top results in scene decomposition and generation tasks of complex synthetic datasets (e.g., Room-Diverse). Furthermore, we also confirm the potential of sVORF to segment objects in real-world scenes (e.g., the LLFF dataset).  We hope our approach can provide preliminary understanding of the physical world and help ease future research in 3D object-centric representation learning.

Slot-guided Volumetric Object Radiance Fields

Abstract

We present a novel framework for 3D object-centric representation learning. Our approach effectively decomposes complex scenes into individual objects from a single image in an unsupervised fashion. This method, called slot-guided Volumetric Object Radiance Fields (sVORF), composes volumetric object radiance fields with object slots as a guidance to implement unsupervised 3D scene decomposition. Specifically, sVORF obtains object slots from a single image via a transformer module, maps these slots to volumetric object radiance fields with a hypernetwork and composes object radiance fields with the guidance of object slots at a 3D location. Moreover, sVORF significantly reduces memory requirement due to small-sized pixel rendering during training. We demonstrate the effectiveness of our approach by showing top results in scene decomposition and generation tasks of complex synthetic datasets (e.g., Room-Diverse). Furthermore, we also confirm the potential of sVORF to segment objects in real-world scenes (e.g., the LLFF dataset). We hope our approach can provide preliminary understanding of the physical world and help ease future research in 3D object-centric representation learning.

1 Introduction

As humans, we can understand scenes, perceive discrete objects within it, and interact with these objects in a 3D environment. This object-centric, geometric understanding of the 3D world is a fundamental ability in human vision [1]. In computer vision, researchers attempt to replicate this fundamental ability in machine learning models with a high interest, due to its wide application ranging from robotics [2] to autonomous navigation. To this end, machine learning models should bear two characteristics: unsupervised representation learning manner and 3D-aware generative mode [3].

Recently, with the advances of neural radiance fields (NeRFs) [4] and representation learning [5, 6, 7], there are some works [8, 9, 3] to achieve these two characteristics. These works learn to decompose objects and understand 3D scene geometry from RGB supervision via novel view synthesis in an unsupervised manner. To this end, volumetric-based methods [8] utilize volume rendering mechanism to implement a 3D-aware differentiable generative process without supervision. To avoid high computational cost of volumetric-based methods, light-field based methods [9, 3] use light field formulation [10] to scale its application to large numbers of objects in a scene. However, existing works suffer from some limitations. Light-field based methods lack strict multi-view consistency [10] and fall into mask bleeding issues [3], which are harmful for object-centric representation learning. Besides, volumetric-based methods fail to decompose scenes caused by attention rank collapse [8] and do not perform well in complex multi-object scenes.

In this paper, we propose a novel framework for 3D object-centric representation learning, alleviating the issues of existing works. Our method, called slot-guided Volumetric Object Radiance

Fields (sVORF), adopts volumetric rendering to synthesis novel views and use object slots as a guidance to compose volumetric object radiance fields. Concretely, we firstly use an efficient transformer module to extract object slots from a single image and learn object-aware slot features with the help of self-attention mechanisms [11]. Then we utilize a hypernetwork to map these slots to volumetric object radiance fields. Finally, at each 3D location, we compose object radiance fields with the guidance of object slots for volumetric rendering. Thus, sVORF can avoid instinctive limits of light field formulation and resolve mask bleeding issues. Meanwhile, with the benefits from the guidance of object slots, sVORF can learn 3D-aware slot features and facilitate network optimization, alleviating the issues faced by existing volumetric-based methods. Moreover, instead of rendering whole image [8, 9], sVORF only render a small amount of image pixels during the training phase, which significantly reduces the demand for training resources.

To validate the effectiveness of sVORF, we conduct experiments on four synthetic datasets to assess the ability of scene decomposition (e.g., segmentation in 3D) and scene generation(e.g., novel view sythesis, scene editing in 3D). Our results demonstrate that sVORF can precisely decompose 3D scenes into individual objects and produce high-quality novel view images. Specially, sVORF outperforms other state-of-the-art methods by a significant margin in complex multi-object scenes. In ablation experiments, we also analyze the effects of core components and show their strength. Besides, we show the robustness of sVORF on unseen object appearance and unfamiliar spatial arrangements. Furthermore, we extend our validation process to complex real-world LLFF data, confirming that our approach can segment objects in complex scenes with high accuracy.

To sum up, our contributions are three fold. First, we introduce a novel approach for 3D-centric representation learning, named sVORF, that effectively decompose objects from a single image. Second, our slot-guided scene composition method avoids the shortcomings of existing methods and significantly reduces the memory requirements during training phase. Third, we validate the effectiveness of our proposed method on synthetic datasets and confirm the extendability of our approach on real-world scenes.

2 Related Work

2.1 Neural Scene Representation and Rendering

Neural scene representations parameterize 3D scenes with a deep network that map xyz coordinates to signed distance functions or occupancy fields. Equipped with differentiable rendering functions, they can be optimized using only 2D images, relaxing the requirement of 3D ground truth. In particular, Neural Radiance Fields (NeRFs) [4] can use an MLP to compute radiance values (color and density) for a given 5D coordinate (spatial location ( x, y, z ) and viewing direction ( θ, ϕ )) and produce novel views with remarkably fine details. Numerous subsequent works have been introduced to address some its shortcomings and expand its applications, including rendering acceleration [12, 13, 14, 15, 16, 17, 18, 19, 20], NeRF with few images [21, 22, 23, 24], 3D reconstruction [25, 26, 27, 28, 29] and 3D scene semantic understanding [30, 31, 32, 33, 34]. However, these volumetric methods need hundreds of evaluations for a ray, leading to an expensive cost for rendering. To address this issue, Light Field Networks (LFN) [10, 24] directly map an input ray to an output color, making only a single evaluation of the MLP per ray.

2.2 3D Object-centric Representation Learning

Driven by the effectiveness of NeRF, recent research has attempted to combine 2D self-supervised object-centric models [5, 6, 7] with neural scene representations to decompose a 3D scene to individual objects. Earlier work [35] utilizes a slot-based encoder and NeRFs as 3D representations to decompose 3D scene with extra multi-view dense depth supervision. Likewise, uORF [8] explicitly model the separation of objects and background with only images in training to address complex scenes. In order to avoid expensive cost of volume rendering, OSRT [3] and COLF [9] further replace the volumetric parametrization with a light field formulation. However, existing methods face some limitations. ObSuRF [35] need dense depth as supervision and can not handle complex scenes, while uORF [8] encounters expensive computation cost during training. Although light field formulation method [3, 9] resolve computation cost issues, they lack strict multi-view consistency [10] and easily fall into mask bleeding issues [3].

M

Hyper

network

MLP

MLP

MLP

MLP

Attention

Block

Aggregation

Block

(

𝛾

(x), d

)

(

𝜎1, 𝒄 1

)

(

𝜎𝐾, 𝒄𝐾

)

…

(𝑚1, … , 𝑚 𝐾

)

(

ത

𝜎,

ത 𝒄

)

Scene Composition

𝛾

(x)

Encoder

Global pooling

Self-Attention

Cross-Attention

Scene Decomposition

Target View

(

x, d

)

2D Prior

Input View

: Sum

: Mul

Volume Rendering

Target View

Positional

Encodings

FFN

Different from the above methods, our method adopts volume representation to parameterize 3D scenes, avoiding the limits of light field formulation. Also, our approach has low computation cost by only sampling a small amount of rays and avoids using depth supervision during training. Moreover, our method can be applied to object segmentation in real-world scenes (e.g. LLFF dataset) [36].

3 Method

The aim of our method is to decompose a scene to a set of object-centric 3D representations given a single input image. An overview of our approach is provided in Figure 1. We firstly extract image features from an input image and decompose object slots from image features. Then we map these slots to volumetric object radiance fields and compose these object radiance fields with the guidance of object slots for novel view synthesis.

3.1 Preliminaries: NeRF

We begin by briefly reviewing the Neural Radiance Fields (NeRFs). A radiance field encodes a scene as a continuous volumetric radiance field f . The input to f is a location x ∈ R 3 and a viewing direction d ∈ R 2 , while the output is an RGB color value c ∈ R 3 and a volume density σ ∈ R + . NeRFs parameterize f as an MLP Φ ϕ . To make MLP learns high-frequency functions, the input coordinates x and viewing directions d are mapped into a higher dimensional space with sinusoids function γ ( · ) before being passed into the MLP [37]. This process, known as positional encoding, allows the MLP to better capture high-frequency scene content. Therefore, the function Φ ϕ can be formulated as:

Given N sampled points along a ray r and its predicted color and volume density { ( c i , σ i ) , i ∈ { 1 , . . . , N }} , the expected color C ( r ) of camera ray r can be derived from volume rendering:

where δ i indicates the distance between adjacent samples. The reconstruction loss between the rendered and true pixel colors is used during training to optimize the parameters ϕ of MLP.

3.2 Scene Decomposition from 2D Prior

Following [35, 9], we define the scene as a combination of K entities, where the first K -1 represent the objects and the last one represents the background. To obtain these entities, we first extract image feature as a 2D prior using an encoder E ( I ) from a scene image I . Instead of using slot attention module as existing methods, we adopt an efficient transformer module T to infer object and

background slots from image feature, termed as S = { s i } K i =1 . Compared to slot attention module, this transformer module is simple and easy to train without Gated Recurrent Unit (GRU) block. For this transformer module, we take a global image feature ¯ v = avg_pool ( E ( I )) as initial object slots Z = { z i } K i =1 . Combining with K learned positional encodings, these slots explicitly model all pairwise interactions between all slots and learn object-aware features via self-attention, which avoids inherent ambiguities in estimating color and geometry at occluded views, see Section 4.4 for details. Then these slots bind and explain the input image representation with cross-attention to image feature. Finally, the slots are transformed to S = { s i } K i =1 via feed forward network (FFN). The whole process can be formulated as follows:

3.3 Scene Composition

Given the infered slots S = { s i } K i =1 , we recompose these slots to novel views of the same scene, which is critical for achieving 3D object-centric representation learning. To achieve it, there are two forms: Spatial Broadcast (SB) [35, 8, 9, 3] and Slot Mixers (SM) [3]. SB and SM do scene composition on RGB space and feature space, respectively. SB can utilize 3D geometric bias (3D point or 3D ray) in the scene composition, facilitating the network optimization. Conversely, due to composition on feature space, SM is hard to optimize without 3D geometric bias. But SM can learn 3D-aware slot features, which is useful for scene decomposition. Combining the advantages of two forms, we propose a new method for scene composition. We transform slots into volumetric neural radiance fields to utilize explicit geometric bias and avoid the limits of light field formulation [10]. Then, we compose all volumetric neural radiance fields with the guidance of slots, making slot features 3D-aware.

Objects as Neural Radiance Fields To transform a slot to its radiance field, we utilize a hypernetwork [38, 39] H to map the slot s i directly to the parameters ϕ i of the associated object Neural Radiance Field. The mapping process is formulated as:

where i = 1 , · · · , K , K is the number of object slots.

With the radiance field Φ ϕ i , we can map a location x ∈ R 3 with a viewing direction d ∈ R 2 to a tuple of color c i and density σ i of corresponding object:

In this way, we transform feature space to RGB space, introducing 3D geometric bias for scene composition.

Composing Mechanism Given K Object NeRFs { Φ ϕ i } K i =1 , we compose their outputs { σ i } K i =1 and { c i } K i =1 at a 3D location with the guidance of object slots. Specifically, we firstly leverage a feature aggregation block D c to gather object slots and obtain an aggregate feature z for query location γ ( x ) :

where D c is a cross-attention layer [40] network. Then we pass z to an attention block D a and compute a normalized dot-product similarity between z and each slot feature in S :

where m = ( m 1 , · · · , m K ) , D a is a cross-attention layer without linear operation. Finally, we compute the combined density ¯ σ and color ¯ c as follows:

Note that our model can train with a small amount of sample rays, leading to a significant reduction for computation and memory cost during training. We speculate that this characteristic benefits from our composing mechanism. In order to decompose small objects from a scene, it is essential to sample much more rays to cover the regions of these small objects, resulting in heavy training cost. However, our composing mechanism can perform well on small objects with a small amount of rays, addressing this large sampling cost, see Section 4.4.

3.4 Loss Functions

Reconstruction Loss We train our model across multiple scenes and only take view images as the supervisory signal. The reconstruction loss is formulated as:

where R is the set of rays in each batch, and C gt ( r ) is the groundtruth color.

Connectivity Regularization We observe that some object radiance fields exist semi-transparent clouds, especially when the number of slots is much larger than the total number of objects in a scene. To solve this issue, we apply a connectivity regularization L connect to each Φ ϕ i by referring to the distortion loss presented in Mip-NeRF360 [41]:

where w = { T i (1 -exp( -σ i δ i )) } N i =1 is the weights along a ray and t is the normalized ray distance.

Total Loss The overall training loss function is formulated as follows:

where λ connect is the scale to balance the connectivity regularization L connect , which is set to be 0.01 in our experiments.

4 Experiments

Datasets Following uORF [8], we experiment on several datasets in increasing order of complexity.

CLEVR-567 [8]: The CLEVR [42] dataset is a widely used benchmark for evaluating object decomposition in computer vision. CLEVR-567 is a multicamera variant of this dataset with 1,000 scenes for training and 500 scenes for testing. Each scene consists of with 5-7 CLEVR objects that randomly positioned and oriented with a clean background. The objects in the scenes are comprised of three geometric primitives: cubes, spheres, and cylinders. We follow uORF's setup in using a 'Rubber' material with largely diffuse properties.

CLEVR-3D [35]: This dataset is also a variant of CLEVR dataset, in which each scene consists of 3-6 basic geometric shapes of 2 sizes and 8 colors. In particular, each scene includes 3 fixed views: the two target views are the default CLEVR input view rotated by 120 ◦ and 240 ◦ , respectively. Following ObSuRF [35], we train 35k scenes and test on the first 320 scenes of each validation set [43, 6].

Room-Chair [8]: This dataset contains 1,000 scenes designated for training and 500 for testing. In this dataset, each scene includes 3-4 chairs of identical shape with 3 different textures background.

Room-Diverse [8]: This dataset is an upgraded Room-Chair. Each scene contains 4 distinct chairs, whose shape chosen randomly from ShapeNet [44] chair shapes, and a range of background that is selected from 50 unique textures. There are 5,000 scenes for training and 500 for testing.

MultiShapeNet (MSN) [35]: This dataset comprises 11,733 distinct shapes, with each scene populated by 2-4 objects with different categories sourced from the ShapeNetV2 3D model dataset.

Local Light Field Fusion (LLFF) [36]: This dataset includes real scene scenarios with complex forground and background, making it highly challenging. We specifically utilize the forward-facing scenes Flower and Fortress from the LLFF dataset, with each scene consisting of 27 training images and 6 testing images.

Baselines We compare our model with a 2D object-centric learning method Slot-Attention [43] and four competitive 3D methods, namely uORF [8], COLF [9], ObSuRF [35] and OSRT [3], in terms of scene decomposition and novel view synthesis. Both COLF and OSRT are based on light field, while uORF and ObSuRF employ volumetric parameterization, which is similar to our approach.

(a)

3D Segmentation

.

(b)

Novel View Synthesis

.

Metrics To evaluate the quality of novel view synthesis, we use Learned Perceptual Image Patch Similarity (LPIPS) [45], Structural Similarity Index (SSIM) [46], and Peak Signal-to-Noise Ratio (PSNR). For scene segmentation in 3D, we measure clustering similarity using Adjusted Rand Index (ARI). The ARI score ranges from 0 to 1, with a score of 0 indicating random segmentation and a score of 1 indicating perfect segmentation. For a fair comparison, we evaluate two types of 2D ARI metrics: ARI and FG-ARI, as well as three types of 3D ARI metrics: NV-ARI, ARI ∗ , and FG-ARI ∗ . Specifically, both ARI and FG-ARI are computed on the source image to facilitate comparison with 2D methods. The FG-ARI is further calculated solely on the foreground regions, using ground-truth data. Similarly, ARI ∗ and FG-ARI ∗ are calculated on all images. Lastly, the NV-ARI is computed on synthesized novel views.

4.1 Scene Segmentation in 3D

Setup Given the soft slot masks of 3D locations, 2D segmentation masks are inferred through volume rendering. To clarify, we begin by mapping the pixel p in the rendered view to a ray r for sampling N points along it. Then, we calculate the soft mask m of each sampling point x at all object NeRFs and derive the composite density ¯ σ using the mask information. Finally, we render the segmentation mask along the ray based on the composite density to yield the segmentation of pixel p .

Results We compare our method with uORF and COLF, and present the results in Table 1. The comparison reveal that our method outperforms all baselines in terms of NV-ARI and ARI values, particularly the NV-ARI, in both Room-Chair and Room-Diverse scenes. It provides evidence that sVORF can effectively identify 3D objects from a single image with better multi-view consistency. Furthermore, in the more complex Room-Diverse scene, our approach achieves comprehensive and distinct improvements over other methods, indicating the robustness of our design. Moreover, we report the performance on CLEVR-3D in Table 2a to ensure equitable comparisons with ObSuRF and OSRT. Compared with OSRT, sVORF achieves significantly higher ARI ∗ and similar FG-ARI ∗ without using depth information, which further proves that our volume parameterization can alleviate mask bleeding problems, as shown in Figure 3. However, we encounter exceptions in the ARI and NV-ARI scores on the CLEVR-567 dataset, and the ARI ∗ on CLEVR-3D dataset. Our benchmark scores are slightly lower than those of uORF and ObSuRF. We attribute this to the penalty imposed on reconstructing shadows of foreground objects, which are not included in the ground truth object masks. This inadequacy is illustrated in Figure 3. Since the light source remains fixed in the CLEVR dataset, it is straightforward to model the shadow as a translucent layer belonging to the object. Nonetheless, the high FG-ARI indicates that our proposed method is proficient in forming factorized representations, which can segment objects in a scene effectively.

Furthermore, to validate our method on more challenging scenarios, we conduct experiments on the MSNdataset and show the results in Table 4. Compared with ObSuRF, sVORF achieves significantly higher Fg-ARI and comparable ARI without using depth information, which demonstrates the model's ability to decouple more complex scenarios. Qualitative results are shown in Figure 2.

Reconstruction

Segmentation

M

4.2 Novel View Synthesis

Setup For each test scene, we reserve one view as an input and use the other views to evaluate the the quality of reconstruction.

Results In Table 3, sVORF outperforms all baselines on most metrics, despite not employing the coarse-to-fine training schedule. These findings suggest that our method is effective in producing high-quality images. The slightly lower LPIPS performance on Room-Chair and Room-Diverse can be attributed to the lack of perceptual loss in the sVORF training process, which does not explicitly optimize the LPIPS performance. Moreover, there exists a trade-off between structural and perceptual loss within the model. The excellent SSIM performance of our model indicates that the sVORF can generate complex object shapes. Specifically, as illustrated in Figure 3, our method generated diverse chair shapes with higher accuracy than COLF and uORF, even though it did not fully recover the background texture. In addition, the results presented in Table 2b indicate that sVORF outperforms OSRT in all metrics, despite using nearly half of the parameters as OSRT (48.73M v.s. 83.11M). Without the addition of depth information, our method synthesizes multi-view images with higher quality than obsurf, as shown in Table 4.

4.3 Scene Design and Editing in 3D

Setup We examine the potential of our method for basic scene editing on the Room-Chair dataset. Following uORF, our investigation involves two types of modifications, namely, moving objects and changing backgrounds. For editing the position of a foreground object, we move all query point coordinates on its object NeRF, based on the targeted movement. In order to relocate the slot, an affine transformation is applied to the 3D sample points before passing them to the corresponding object NeRF.

Move

Input image

Input view

Novel view

GT

Meanwhile, for changing the background, we substitute the original background texture by replacing the original background slot feature with that of the target image.

GT

Ours

uORF

COLF

Input view

Novel  view

Novel seg.

GT

Ours

uORF

COLF

Novel  view

Novel seg.

Input view

GT

Ours

uORF

COLF

GT

Ours

OSRT

Results Figure 4 shows that edited images maintain a harmonious quality while accurately executing object movement and background replacement, affirming the strong correlation between slots and 3D objects in sVORF, as well as the accuracy of our model in 3D scene segmentation.

4.4 Ablation Studies

In this section, we conduct ablation studies on the CLEVR-567 dataset to gain a deeper understanding of how the various parts contribute to the overall effectiveness of our approach. More ablation studies on architectures are detailed in Appendix C.

Role of Novel View Synthesis To investigate the influence of the novel view synthesis setup on the training process, we modify our reconstructed target view to equal with the input view, i.e. , we turns sVORF into a 2D image auto-encoder. As shown in Figure 5, the model divides images based on areas rather than objects. This division led to substantially lower ARI results, presented in Table 5. Above observations confirm the crucial role of viewpoint changes in scene decomposition. Specifically, the mapping between slots and 3D representations captures changes occurring in various regions due to differences in viewing angles between the target and source views. Changes that occur within regions belonging to the same object are more closely approximated, which allows the model to converge to K slots based on object clustering.

Connectivity Regularization As previously mentioned, novel view synthesis setup ensures distinctiveness between objects, while implementing Connectivity Regularization guarantees connectivity within the same objects. These two factors work together to achieve a clear decomposition of the scene. Figure 5 visualizes that our Connectivity Regularization ensures that points on an object belong to the same slot by preventing semi-transparent clouds from being modeled by object NeRFs.

Numerically, as shown in Table 5, the model's FG-ARI displays a significant increase from 89.3 to 92.0 when implementing connectivity regularization compared to the model without it.

Composing Mechanism As described in Section 3.3, our composing mechanism can perform well on small objects with few rays. To verify this, we implement the common density-weighted mean combination mode on our model and present the visualization in Figure 5. Our composing mechanism outperforms the density-weighted mean combination mode in decoupling effect, especially for small objects that may otherwise be segmented into attachments of other objects.

Self-Attention in Scene Decomposition If an object in the input image is occluded, it may be mistakenly segmented into the slot of another object that corresponds to the occluded area. This issue can be resolved by leveraging the self-attention layer in the decomposition module as it facilitates the interaction between slots. As illustrated in the Figure 5, removing the self-attention layer leads to incorrect division of the occluded object, highlighting the importance of inter-slot interaction in preventing the collapse of the corresponding slot of the occluded object.

Input view

Novel view

Image

Ours

w/o NVS

w/o CR

Density-weighted

w/o SA

GT

4.5 Generalization

We conduct three sets of generalization experiments. The three subsets assess the ability of sVORF to generalize to unseen object appearances, unfamiliar spatial arrangements and grayscale images respectively.

Object Appearance For unseen object appearance, we follow the dataset in uORF, which is similar to CLEVR-567. The training set of this dataset excludes red cylinders and blue spheres, while the testing set includes only these types of objects. The results are presented in Table 6. It is noteworthy that our approach has never encountered the appearance of test objects but achieves comparable results to the models trained on a standard CLEVR-567 dataset.

Spatial Arrangements To assess the model's ability to generalize to a greater number of objects with unseen, challenging arrangements, we train our method using 11 slots on the CLEVR-567 dataset and evaluate on the packed-CLEVR-11 dataset provided by uORF. During training, we randomly mask off four slots to prevent slot collapse, but we utilize all slots during testing. The

performance of our method on the unseen object arrangements test set is shown in Table 7 and is found to be reasonably well.

RGB color To explore whether the sVORF mainly relies on RGB color for scene decomposition, we conduct an evaluation on a grayscale version of CLEVR-567 dataset. The model used in the evaluation is only trained on RGB CLEVR-567 dataset. The model achieves 87.5 FG-ARI on the grayscale test set, which is on par with 92.0 FG-ARI on the default RGB images. The evaluation results demonstrate that sVORF really learns to decompose the scene intrinsically. For qualitative results, see details in Appendix D.

4.6 Object Segmentation on Real Images

We demonstrate the effectiveness of our approach in real-world scenarios by validating it on LLFF datasets. To handle complex scenarios, we implement VIT-Base [47] as the backbone instead of ResNet34 [48] and train the network from scratch. Qualitative visualizations displayed in Figure 6 show that sVORF effectively segments the object within the scene, demonstrating the potential of our approach to understand general real scenarios.

4.7 Training Speed and Memory Consumption

Setup We compare sVORF with uORF [8] and COLF [9] in terms of memory consumption and training speed. For all three methods, we train models on the CLEVR-567 dataset using a batch size of 1 on V100 and record their memory usage and time taken for one epoch. Since both COLF and uORF render and supervise images at 64 × 64 resolution to learn the coarse structure first before supervising them at 128 × 128 resolution, we record their performance during both stages.

Results As shown in Table 8, sVORF offers substantially shorter training time (3m24s vs. 9m2s) and lower memory consumption (4.6G vs. 23.7G) than the volumetric-decoder based uORF method, while displaying comparable performance to the light field-based COLF.

In terms of total training time, for the CLEVR-567 and Room-Chair datasets, we train sVORF for approximately 7 hours using 8 Nvidia RTX 2080 Ti GPUs with batch size 16. The uORF and COLF models are trained on an Nvidia RTX V100 GPU for approximately 7 and 2 days, respectively, with a batch size of 1. For the CLEVR3D dataset, sVORF is trained for approximately 2 days using 8 Nvidia RTX V100 GPUs with batch size 16, while OSRT is trained for approximately 1 day on 8 A100 GPUs with a batch size of 256. These results demonstrate the effectiveness of sVORF in overcoming the challenges of volumetric decoders that demand extensive resources, while also contributing to enhanced training efficiency.

5 Conclusion

We present sVORF, a novel method for 3D object-centric representation learning. By adopting volumetric rendering to synthesis novel views and using object slots as a guidance to compose volumetric object radiance fields, sVORF precisely decompose 3D scenes into individual objects with limited training resources. It significantly outperforms existing SOTA methods, particularly in complex multi-object scenes. In addition, we demonstrate sVORF's ability for realistic scenario decomposition, indicating a promising direction for understanding the physical world.

Input view

Novel view

Ours

Image

GT

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A Additional Training and Architecture Details

A.1 Training details

We utilize the Adam optimizer with a learning rate of 0.0001, β 1 = 0.9, and β 2 = 0.999. Additionally, we implement learning rate warm-up for the initial 1,000 iterations. The minimum number K of objects in each scene is customized separately as follows: K = 8, 7, 5, 5, 2, and 5 for the CLEVR-567, CLEVR-3D, Room-Chair, Room-Diverse, LLFF, and MSN datasets, respectively.

To allow training on a high resolution, such as 256 × 256, we render individual pixels instead of large-sized patches. Specifically, we randomly sample a batch of 64 rays from the set of all pixels in the dataset, and then follow the hierarchical volume sampling [4] to query 64 samples from the coarse network and 128 samples from the fine network.

In addition, we train our model from scratch, with the exception of the Room-Diverse dataset. The Room-Diverse dataset is more complex and requires an incremental learning approach. Specifically, we initialize our models for Room-Diverse using weights from a model that have previously been trained on the CLEVR-567 dataset.

A.2 Architecture details

Image encoder For the image encoder E , we utilize the well-known ResNet34 [48] architecture as the backbone, followed by three upsampling layers. Specifically, given the source image I ∈ R 256 × 256 × 3 , we extract features F 1 ∈ R 128 × 128 × 64 , F 2 ∈ R 64 × 64 × 128 , and F 3 ∈ R 32 × 32 × 256 from the conv 2 , conv 3 and conv 4 layer of the ResNet34 architecture, respectively. Note that the max-pooling layer in conv 2 is not used. Subsequently, these features are fed into the following three up-sampling layers within a U-net expansive path, resulting in the feature F ∈ R 128 × 128 × 512 . The architecture of upsample layers is shown in Table 9.

Object NeRF To represent each object NeRF, we employ a simple 4-layer MLP that each layer has 128 channels and is followed by a ReLU activation. In addition, we use skip connection mechanism that add the first layer's activation to the third layer's activation. Note that the last layer outputs the RGB value with a sigmoid activation function.

Transformer-based module The efficient transformer module is a standard transformer decoder. Specifically, we firstly use each slot z i as query and interact with other object slots with multi-head self-attention operation. Then we employ multi-head cross-attention operation to attend into and aggregate features from the flattend image features E ( I ) . Finally, we pass the resulting slot features into a feed forward network (FFN) to get the final slots. This transformer module is simple and easy to train than the slot attention module, as it does not contain a Gated Recurrent Unit (GRU) block.

Composition module The aggregation block performs a cross-attention operation, which aggregates object representations S with the 3D location x as the query to obtain the corresponding feature z . The attention block computes the similarity between S and z after mapping them into the same space through a linear layer, thus obtaining the probability distribution of x belonging to each slot. In the initial stages of our experiments, we observed that utilizing both modules simultaneously yielded superior results. We speculate that this improvement may be attributed to a good feature space alignment between 3D points and slot features using the proposed aggregation block.

B Object Segmentation on Real Images

Setup In this study, we use VIT-Base [47] as the feature extractor for complex datasets of size 1008 × 756 with intricate textures. The adopted backbone networks are trained from scratch, and the method strictly follows unsupervised learning. To conserve memory, we resize the source image to 256 × 256 and select only 7168 rays from the target view during each training iteration. Moreover, we define the task as foreground-background segmentation. As such, we set the number of slots to 2 and map it to two NeRFs. Each NeRF consists of a simple 4-layer MLP.

Unlike the setup on other datasets, we train sVORF on both LLFF scenes as two separate models Following the setup in NeRF-SOS, we divide the data of each scene into training and testing sets, ensuring there is no overlap between these two sets.

Results Figure 7 shows the complete segmentation results of sVORF on both Flower and Fortress datasets. The results demonstrate the potential of sVORF for 3D segmentation on non-object-centric real scenes with cluttered backgrounds. Additionally, we use ResNet34 as the backbone and provide the segmentation results in Figure 8. Unlike sVORF with ViT-Base, sVORF with ResNet34 produces a coarse segmentation and still segments foreground object from complex scenes.

Novel views

Input view

Color Images

Ours

GT

Color Images

GT

Ours

C More Ablation Studies

This section provides more ablation studies on architecture, assessing the efficacy of the transformerbased module (Section 3.2), hypernetwork (Section 3.3) and combination module (Section 3.3), respectively. The quantitative results are reported in Table 10.

Transformer-based module We substitute the transformer with slot attention and observe that slot attention fails to achieve the decomposition task in our model, as shown in the second row of Table 10.

Reconstructions

Segmentations

Based on this comparison, we can conclude that our transformer-based module has a better scene decomposition than slot attention in our training setting.

Hypernetwork We replace the hypernetwork with directly using the slots for conditioning the radiance fields per object like uORF [8]. As shown in the first row of Table 10, the model's performance significantly decreases. We speculate that using hypernetwork can provide stronger 3D geometric bias than directly using the slots for conditioning the radiance fields per object.

Our composition module v.s. Slot Mixers To compare our composition method with Slot Mixers decoder, we have some modifications on the SM decoder [3]. First, we use a 3D point x instead of the target ray as the query to aggregate the weighted slot feature. Second, we transform the weighted slot feature into the corresponding radiance field. Third, based on the radiance field, we can obtain the density and color of the 3D point x . In the experiment, we find that the composition performance of the SM method is lower than our proposed composition method. Specifically, the SM method exhibits 3D-inconsistent segmentation results, as shown in the third row of Table 10. It proves that the introduction of 3D geometric bias is really important for scene decomposition.

D More Qualitative Results

Depth maps We illustrate the depth maps of sVORF on different datasets in Figure 9. The results show that our method can learn a high quality of 3D geometry.

RGB

Depth

L

.9

-

Object-level radiance fields. We provide the visualization of learned object-level radiance fields on CLEVR-567 dataset in Figure 10. It is further demonstrated that our method can achieve very clean scene decomposition.

Reconstruction

Slots

RGB

Depth

..

D

D

0

Grayscale images. We provide the multi-view results of the qualitative evaluation of the model on a grayscale version of the CLEVR-567 dataset in Figure 11.

sVORF

Gray

test

Hyper network

E Limitations

w Slot-

Attention w SM There are three limitations in sVORF. First, although sVORF can generalize to more objects at test time, as shown in Section 4.7, the maximum slot number of test scenes is restricted by the training setting. In other words, we need know the maximum number of objects/slots in the scene, and ensure that the number of slots set is equal to or exceeds this maximum value. Second, like other 3D representation learning methods, the model's training process requires curated multi-view images, which are difficult to obtain and necessitate specialized equipment, particularly in real scenes. Finally, although our method performs well on some complex scenes, such as MSN, it is still a challenge for our method to decompose and understand real-world scenes like a human. Addressing the limitations related to the slot number, training dataset and the generalization capabilities on real scenes is a potential area for future research.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents slot-guided volumetric object radiance fields (sVORFa), a learning method for 3D object-centric representation. They proposed three key techniques, scene decomposition based on global pooling and slot-based representations, hyper-network to generate per-object radiance fields, and scene composition module. They have tested the method on various tasks on synthetic datasets, such as CLEVR and Room, showing superior performance to prior arts. Finally, they provided the simple experiment results on real images (LLFF), highlighting the broader effectiveness of the methods.\n\nSTRENGTHS:\n1. The proposed method improved the prior methods by a large margin, especially on Room-Chair and Room-Diverse datasets (segmentation task)\n2. The newly suggested modules seem very efficient. and I think the global pooling features combined with the slot-guided method is a reasonable and better approach than the previous slot-attention method, at least in these particular tasks.\n\nWEAKNESSES:\n1. From my understanding, three modules were newly adopted or introduced to object-centric representation learning tasks. They are 1. ‘global pooling’ with slot-guided scene decomposition module, 2. hypernetwork, and 3. scene composition modules. However, throughout the experiments, I do not see which components are actually effective compared to prior methods. For example, they could have introduced ‘hypernetwork’ to uORF, or they could have tested ‘slot-attention’ in the proposed sVORF to see the effectiveness of the 'hypernetwork' or ‘global-pooling’ slot-guide method. Hence, it is hard for the readers to know every component actually contributes to the final performance.\n2. It seems connectivity regularization (CR) is very important, I would like to see how much CR can improve the performance of the previous methods, such as uORF and others.\n3. Similarly, I believe we can easily incorporate spatial broadcast (SB) or slot mixers (SM) in the proposed method sVORF, which could clearly show the effectiveness of the proposed scene composition module.\n4. Although the newly introduced modules are well orchestrated into a single model and improve performance, I do not see significant technical novelty.\n\nQUESTIONS:\n1. In Table 2, why did you have to use different settings and re-evaluate the previous methods?\n\nOther questions are embedded in the weaknesses section.\n\nLIMITATIONS:\nI do not see any potential negative societal impact from this work.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method, sVORF, for unsupervised object-centric 3D representation learning. Given a single image as input, it decomposes the scenes into individual 3D objects and 3D backgrounds which thus support object segmentation, novel view synthesis (named scene generation in the paper), and scene editing (including object moving and background repainting). \nThe key idea of the paper is to combine object slot with object radiance fields together in a framework, in which the object slot is responsible for decomposing the scene into objects. In contrast, the object radiance fields are used to re-compose the scene for volumetric rendering. The only cue for training the network is the rendering loss between the re-composed and volumetric rendered image with the input single-view image. The overall performance of sVORF is plausible and thorough experiments and ablation studies well validated the effectiveness of the proposed method.\n\nSTRENGTHS:\n+The task of reconstructing each object and the background in 3D given only a single RGB image is very challenging and with great importance for practical applications in robotics and CHI, etc. \n+The overall performance of the proposed method is strong when compared with existing approaches. \n+The idea of using the attention mechanism for scene decomposition and re-composition as well as the use of HyberNetwork for object-level NeRF generation is sound and practical. \n+The demonstration of segmentation on real captured dataset LLFF is important to help the readers to qualify the performance of the method. \n+The paper is well written and easy to follow.\n\nWEAKNESSES:\n- The dataset used for validating the proposed method is quite simple, with obvious color or shape differences between objects and simple backgrounds, which is very convenient for segmentation and decomposition. In the LLFF Dataset, the segmented foreground color is also very different from the background. So maybe more complex scenes should be used to demonstrate the effectiveness of the proposed method. \n- The HyperNetwork produces MLP parameters of NeRF. However, the MLP representation of NeRF is very ambiguous, so learning such a hyberNetwork for NeRFs may not be very robust, please explain how to deal with this problem, especially for real-world scenes with complex objects in it. \n- In Fig.5, only segmentation results are provided on the LLFF dataset, is it possible to also provide the NVS results? why not? \n- The main paper should clarify the training strategies and key implementation details like how to set K for each dataset.\n\nQUESTIONS:\n- Line 224, please provide the full name of FFN since this is the first time you use FFN. \n- In Table 2(a), it seems ObSURF works generally better on 3D segmentation, does this mainly benefit from the depth input? \n- Line 149, a->an\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a method called sVORF for learning 3D object centric representations. A transformer decompose a single input image into slots which are then each mapped to volumentric radiance fields by a hypernetwork. These object-radiance fields are then composed into a 3D scene. The effectiveness of sVORF is demonstrated on a set of simple synthetic datasets and two real world scenes. It achieves SOTA or at least competitive results on CLEVR567, CLEVR3D, Room-Chair, and Room-diverse datasets, compared to SlotAttention, uORF and COLF.\n\nSTRENGTHS:\n* The problem of unsupervised 3d object decomposition is quite challenging. The fact that sVORF performs so well with only a single input image, and no depth or segmentation supervision is remarkable.\n* The writing is clear and easy to follow. The figures look nice, are helpful and are easy to understand. \n* The individual parts of the method are well motivated and their individual contributions are established through systematic ablations.\n\nWEAKNESSES:\n* The paper stresses the low computational costs and memory footprint of sVORF, but fails to report any data on them in the main paper. Memory consumption is mentioned in the appendix, alongside training time per epoch. But information about the length of training is lacking so the real computational costs remain unclear. \n\n* The studied scenes are visually simple (yes even Room-diverse which is advertised as complex). The only exception are the two scenes from LLFF. It is encouraging that sVORF succeeds on these two scenes, but in this setting it appears to me that the model is effectively overfitting on the given scene, and there is no evidence for generalization to novel scenes in that setting. \n\n* The restriction to a single input image is rather limiting. The 3D structure of a general scene is highly underspecified from a single image, which should lead to large uncertainties (e.g. in occluded areas). For simple scenes like CLEVR and Room-Chair this is not a problem because none of the elements is ever fully occluded, and they come from a small set of known objects. But I expect this to become a severe limitation for scaling to more complex scenes. Especially since sVORF and its training objective are not designed to be probabilistic / generative, and its fidelity will thus likely suffer substantially from complex ambiguities.\n\nQUESTIONS:\n- How many samples are used per scene during training. Appendix A mentions 64 rays with 64 coordinates in the coarse volume and 128 additional coordinates in the fine volume. What are the coarse and the fine volumes? \n- For how long (number of updates / epochs) was sVORF trained? How does that compare to uORF, COLF, OSRT?\n- The LLFF results use only two scenes. Does that mean the shown results are training images? Is sVORF trained on both scenes at once or as two separate models. In the latter setting it seems to me that sVORF is essentially equivalent to a simple volumetric NeRF, since the model could in principle learn to produce the correct target views during inference without even looking at the input view. Is there any evidence for generalization in this setting?\n\nLIMITATIONS:\nThere is a brief discussion of limitations in the supplementary that touches on two important limitations of the method. \nIt does however not discuss any concerns regarding generalization to more complex real-world scenes.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces sVORF, a compositional method for representing scenes as a collection of slots that are parametrized as per-object radiance fields. The proposed model can be used to perform novel-view synthesis, as well as semantic segmentation in 3D. Moreover, the proposed compositional representation, also enables performing simple editing operations in the scene. In more detail, given an input image, sVORF first extracts image features from the image and passes them to a transformer encoder-decoder module that extracts slots for the objects in the scene and the background. Subsequently, these slots are mapped to volumetric object radiance fields using a hypernetwork. Using the per-object radiance fields, the scene is rendered by simply compositing their outputs at a 3D location with the guidance of each slot. Unlike [8] that was the first work that explored discovering slots in 3D data, sVORF maps slots to per-object radiance fields using a hypernetwork. The authors evaluate the performance of their model on the CLEVR-567, CLEVR-3D, Room-Chair, Room-Diverse and the LLFF datasets and compare with several compositional representations that represent slots as radiance fields [8, 35] or as light fields [9]. From their experimental results, it seems that the proposed model outperforms all baselines both on the novel view synthesis task as well as on the 3D segmentation task.\n\nOverall, I think the proposed idea for discovering slots in 3D is interesting and the authors show that their approach is working for simple scenes with a few objects. In terms of novelty, the proposed pipeline is quite similar to [8], with the main difference being the use of the hypernetwork for mapping slots to per-object radiance fields. Looking at the quantitative results, it seems that the proposed model is better than the baselines on most tasks, thus I am leaning towards accepting the paper but I am still a bit concerned by the fact that the proposed model and [8] are relatively similar and that the proposed model is only evaluated on extremely simple scenes.\n\nSTRENGTHS:\n1. The authors conduct multiple experiments and compare their model with several baselines on multiple datasets. From the quantitative evaluation, we note that the proposed model outperforms all baselines on most tasks. I particularly liked the scene editing experiment in Sec. 4.3.\n\n2. Although some things are not 100% clear I think the paper is easy to read and relatively nicely written. I really liked Figure 1 that is a pictorial representation of the overall pipeline.\n\nWEAKNESSES:\n1. One of the major weaknesses of this work is that the authors only demonstrate the performance of their model on very simple datasets that consist of few objects that in most cases belong to the same object class e.g. chairs. Although I am aware that all baselines evaluate their models on similar setups I think it would have been great if the authors could show that their model works on more challenging scenarios, with different objects and more diverse backgrounds. A rather simple indoor dataset that the authors could consider is the 3D-FRONT dataset. Another less exciting alternative would be to also show results on the City-Block dataset introduced in [9]. However, since also this dataset contains scenes with cars, I think that the 3D-FRONT would be a more appropriate benchmark.\n\n2. In Sec. 3.2 and in L116-117 the authors state that the adopt an efficient transformer module to infer the object and the background slots form the image features. Can the authors describe how this efficient transformer module compares to the classical slot attention module used in [8]? Is the efficient transformer module a standard transformer encoder/decoder? I think that to make things very clear, it would have been very useful to properly define (e.g. using a math expression) how is the cross-attention defined? In addition, can the authors also clarify why/how is this model efficient?\n\n3. Although, the authors provide several ablation studies, I believe that they should have ablated the impact of using a hypernetwork as opposed to directly using the slots for conditioning the per-object radiance fields. This is more similar to [8] and it could better explain why is the proposed model outperforming [8], although their quite similar.\n\n4. I am bit concerned regarding the limited technical contribution of this work. Unless I am missing out something I think the proposed paper is quite similar to [8]. That being said, the proposed method seems to be significantly better than [8]. This could be either due to the use of the hypernetwork or the use of the attention module for inferring the slots. I believe that it is very important to clarify what are the differences and also try to justify the improvement in performance though ablations e.g. ablate the use of a hypernetwork for mapping slots to per-object radiance fields.\n\nQUESTIONS:\n1. Unless I am missing out something, I think that the proposed model assumes that the number of objects/slots is known right? In other words, although we might not know what are the objects, we know how many objects/slots exist in the scene, right? This is never clearly mentioned in the text. I think the authors should clarify it.\n\n2. I think that the per-object NeRFs should be locally defined, namely each NeRF is augmented with a local affine transformation defining its pose in 3D. Otherwise, it would not be possible to change the location of a specific object/slot to a new position. Is this really the case?\n\n3. I think that from the provided information for the composing mechanism in L146-150 it is not 100% clear how are the aggregation $D^c$ and the attention bloc $D^a$ really implemented. One thing that is not very clear to me is why do we need both? Can the authors please explain?\n\n4. In L264-272, the authors present an ablation study that tries to investigate the impact of the Novel View Synthesis setup. To be honest, I am not 100% sure that I understand what the authors mean by \"we modify our reconstructed target view to equal with the input view\". Can the authors please clarify?\n\n5. I am wondering what is the quality of the 3D geometry of the proposed model and how does it compare to baselines. Since the authors represent the scene using a compositional NeRF-based representation I think it would be useful to also show some depth maps at least in the supplementary.\n\nLIMITATIONS:\nThe authors discuss the limitations of their work in their supplementary material but I was not able to find any discussion about the potential negative societal impact of their work. That being said, I think that for this paper this discussion is not 100% necessary.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-08"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes sVORF to tackle the challenging problem of ‘unsupervised’ scene decomposition by learning a series of slot-guided neural radiance fields. Inferring object-level NeRF from a hyper-network instead of costly GRU modules, the overall pipeline can be efficiently trained with on a collection of multi-view images and produce promising segmentation results on several synthetic benchmark datasets.\n\nSTRENGTHS:\n- The overall ideas is well motivated and easy to follow, and the main pipeline could be well taken.\n\n- Extensive experiments on adequate synthetic datasets are conducted. The numerical results are promising  compared to SOTA baselines, with detailed ablations.\n\nWEAKNESSES:\n- Limited unique contribution compared to previous work like uORF.\n\n   I think this paper proposes a good extension on top of uORF while my main concern is that the unique contributions are somewhat limited. The overall pipeline is built on top of previous work uORF by replacing the expensive GRU modules to hyper-network inferred compositional object-level NeRFs, which I see as the main difference bringing efficiency advantages.\n\n- I do appreciate the promising performance on synthetic datasets, however I think more discussions and results towards the main statements (consistency, efficiency against current baselines) need to be further strengthened.\n    - The method of using radiance fields instead of light-fields stand out in terms of strict multi-view consistency. Therefore, discussions and analysis of multi-view consistency of segmentation masks (on synthetic and real-world cases) are expected to show to validate this point.\n\n\n- Are the adopted backbone networks (ResNet34 and ViT-Base of real-world image segmentation) pre-trained in any way or trained from scratch (L318)? As I am not sure if the used datasets are sufficient to train such large network. If so, is the method strictly unsupervised anymore? More clarifications are expected. Also, for real-world segmentation, I am wondering how does the backbone impact the performance if ResNet34 is used. \n\n- How does appearance affect the perform? Does the mode really learn to decompose the scene intrinsically or a very good ‘colour/apperance’ segmentor? I see some good evidence from fig2 but find the networks struggles to separate close-by objects with similar colour as well as shadows. Moreover, related to last point of consistency, is this ‘incorrect pattern’ also consistent across view?\n\n\n - Related to last point, visualization of learned object-level radiance fields are expected. Readers could know if the method indeed decompose the scenes into objects and background as we expect.\n\n- It would be more exciting to see how the methods work on real-world images with more than 1 foreground objects.\n\n- What is the total training time required to converge sVORF as only per-epoch time is provided.\n\n-L118. (GEU) --> (GRU)?\n\nQUESTIONS:\nPlease see the weaknesses above.\n\nLIMITATIONS:\nLimitations have been discussed in the supplement.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-08"}