Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

In summary, our contributions are:* We introduce self-supervised training of conditional neural groundplans, a hybrid discrete-continuous 3D neural scene representation that can be reconstructed from a single image, enabling efficient processing of scene appearance and geometry directly in 3D.

The review comment to be evaluated is:

Strength:

1. The authors tackle a challenging yet valuable problem, disentanglement of the movable and immovable components of the scene from a single image. They propose a neural scene representation called conditional neural groundplans and a self-supervised framework to disentangle static background and movable foreground objects given only a single image. The framework enables a variety of downstream tasks, such as extraction of object-centric 3D representations, novel view synthesis, instance-level segmentation, 3D bounding box prediction, and scene editing. The direction would interest a wide range of communities, including 3D scene understanding, 3D neural representation, disentangled representation learning, and novel view synthesis.
2. The proposed 3D persistent scene representation learning framework elegantly leverages ideas from BEV representation, neural representation learning, volume rendering, and compositing operation (Yuan et al., 2021). Moreover, the proposed method utilizes multi-view videos (in a self-supervised manner) at training time to learn to separately reconstruct static and movable components of the scene from a single image at test time. The authors present a self-supervised neural scene representation framework for general scene understanding tasks. The reviewer found the work valuable to the community.
3. The proposed 3D scene representations enable novel view synthesis and disentangle movable and immovable components of the scene via diverse qualitative evaluation on two datasets, CLEVR and CoSY. In particular, the qualitative results shown on CoSY are impressive, as shown in the manuscript and supplementary website.

Weaknesses:

1. Persistent scene representation: By sufficient qualitative analysis, the proposed 3D scene representations enable novel view synthesis and disentangle movable and immovable elements for different scene understanding tasks. One failure case shown on the top row of p.17 is that the framework cannot effectively synthesize the viewing perspective behind the box with a green door. The framework seems unable to capture the background correctly, yielding incorrect synthesis. Moreover, the box's location seems incorrect from the images on the left. The reviewer wonder if the performance can be improved with additional observations.
2. The authors propose to have two separate groundplans neural representations for static and dynamic, respectively. As we know from the literature (e.g., Yuan et al., 2021), it is possible to keep separate 3D neural representations for novel view synthesis. It seems reasonable to tackle the goal of this paper, i.e., achieve decent performance on a variety of tasks from a single image, with separate 3D neural representations based on the proposed framework. It would be great for the authors to elaborate on the technical challenge of this direction. That could motivate the community to tackle the direction collectively.
3. Differentiable rendering based on neural groundplans feature: the reviewer found it less intuitive to understand why the differentiable rendering would work using the groundplan features g_x. Specifically, g_x is obtained based on the weighted sum of the features along the y-axis. The groundplan feature g_x contains information in a particular pillar. Why is it a better feature for volume rendering? Empirically, the design choice renders better quality than STOA methods (i.e., PixelNeRF and uORF). Could the authors please elaborate more on this design choice?
4. The design choice of BEV representation: The authors utilize a particular operation to form BEV representations, i.e., the weighted sum of the features. However, there are other approaches, e.g., Roddick and Cipolla, 2020, Philion and Fidler, 2020 and Saha et al., 2022. It would be valuable for the audience to learn the difference between these operations for representation learning.
5. The reviewer is interested in the qualitative performance of novel view synthesis without using the contracted coordinate. With the analysis, readers would be able to visualize the difference.

The evidence to be evaluated is:Emerging neural scene representations enable reconstruction of geometry and appearance from images as well as high-quality novel view synthesis via differentiable rendering. A large part of recent work focuses on the case of reconstructing a _single_ 3D scene given dense observations (Cheng et al., 2018; Tung et al., 2019; Sitzmann et al., 2019; Lombardi et al., 2019; Mildenhall et al., 2020; Yariv et al., 2020; Tewari et al., 2021). Alternatively, differentiable rendering may be used to supervise encoders to reconstruct scenes from a single or few images in a feedforward manner. Pixel-aligned conditioning enables reconstruction of compositional scenes (Yu et al., 2020; Trevithick and Yang, 2021), but does not infer a compact 3D representation.

Hybrid discrete-continuous neural scene representations offer a compromise by factorizing a dense 3D field into several lower-dimensional representations that are used to condition an MLP (Chan et al., 2022; Chen et al., 2022).

We similarly use axis-aligned 2D grids of features for self-supervised scene representation via neural rendering, but reconstruct them directly from few or a single 2D image observations.

In contrast, we present a self-supervised conditional groundplan representation, learned only from images via neural rendering.

Our approach is similar in using object motion as cue for disentanglement and multi-view as cue for 3D reconstruction, but uses it as supervision to train an encoder-based approach that enables reconstruction from a _single_ image instead of scene-specific disentanglement from multiple video frames.

Prior work has aimed to infer object-centric representations directly from images, with objects either represented as localized object-centric patches (Lin et al., 2020; Eslami et al., 2016; Crawford and Pineau, 2019; Kosiorek et al., 2018; Jiang et al., 2019) or scene mixture components (Engelcke et al., 2020; Burgess et al., 2019; Greff et al., 2019, 2016; 2017; Du et al., 2021), with the slot attention module (Locatello et al., 2020) increasingly driving object-centric inference. Resulting object representations may be decoded into object-centric 3D representations and composed for novel view synthesis (Yu et al., 2022; Smith et al., 2022; Elich et al., 2022; Chen et al., 2021; Bear et al., 2020; Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Du et al., 2021).

Several scene reconstruction methods (Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Nie et al., 2020) use direct supervision to train an object representation and detector to infer an editable 3D scene from a single frame observation.

In this work, we demonstrate that a representation factorized into static and movable 3D regions can serve as a powerful backbone for object discovery.

In this section, we describe the process of inferring a neural ground plan given one or several image observations in a feed-forward manner, as well as subsequent novel view synthesis.

A neural groundplan is a 2D grid of features aligned with the ground plane of the 3D scene, which we define to be the \(xz-\)plane. A 3D point is decoded by projecting it onto the groundplan and retrieving the corresponding feature vector using bilinear interpolation. This feature is then concatenated with the vertical \(y\)-coordinate of the query point and decoded into radiance and density values via a fully connected network, enabling novel view synthesis using volume rendering (Mildenhall et al., 2020).

We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021).

**Reconstructing neural groundplans from images**. Inferring a neural groundplan from one or several images proceeds in three steps: (1) feature extraction, (2) feature unprojection, (3) pillar aggregation. Given a single image \(\mathbf{I}\), we first extract per-pixel features via a CNN encoder to yield a feature tensor \(\mathbf{F}\). We define the camera as the world origin and center the neural groundplan accordingly, approximately aligned with the ground level. The image features are unprojected to a 3D feature volume \(\mathbf{v}\) in contracted world space using the inverse of the contract function defined earlier. We extract the feature at a contracted 3D point \(\mathbf{x}^{\prime}\) in \(\mathbf{v}\) as \(\mathbf{v}(\mathbf{x}^{\prime})=\mathbf{F}[\pi(C^{-1}(\mathbf{x}^{\prime}))]\), where \(C^{-1}(\mathbf{x}^{\prime})\) first maps the contracted point to linear world space and \(\pi(\cdot)\) projects it onto the image plane of the context view using camera extrinsics and intrinsics.

We first use a coordinate-encoding MLP \(D(\cdot)\) to transform the volume as \(\mathbf{f}(\mathbf{x}^{\prime})=D(\mathbf{v}(\mathbf{x}^{\prime}),\mathbf{x}_ {\mathbf{c}},\mathbf{d})\), where \(\mathbf{x}_{\mathbf{c}}\) denotes the 3D point in linear camera coordinates of the context camera, and \(\mathbf{d}\) denotes the ray direction from the camera center to that point. Since all features along a camera ray are identical in \(\mathbf{v}\), coordinate encoding is used to add the depth information to the features. In the case of multi-view input images, the volumes corresponding to each input view are mean pooled. Associated to each 2D vertex of the groundplan is now a set of features \(\{\mathbf{f}_{i}\}_{i=1}^{N}\), where \(N\) is the number of samples along the \(y\)-dimension. We use a "pillar-aggregation" MLP to compute softmax scores as \(\alpha_{i}=P(\mathbf{f}_{i},\mathbf{x}_{i})\), where \(P(\cdot)\) denotes the MLP and \(\mathbf{x}_{i}\) is the linear coordinate of the \(i\)-th point on the pillar. Finally, the features are aggregated by computing the weighted sum of the features, \(\mathbf{g}=\sum_{i}\alpha_{i}\mathbf{f}_{i}\).

We can render images from novel camera views via differentiable volume rendering (DeVries et al., 2021; Lombardi et al., 2019; Mildenhall et al., 2020).

Furthermore, we describe a method for performing self-supervised 3D object discovery and 3D bounding box prediction using the geometry encoded in the dynamic groundplan representation.

We leverage the fact that objects move in the given multi-view videos as the training signal.

For each frame, we infer an _entangled_ neural groundplan as described in the previous section. Features in this entangled neural groundplan parameterize both static and dynamic features of the scene, for instance, a car as well as the road below it. We feed this groundplan into a fully convolutional 2D network, which disentangles it into two separate groundplans containing _static_ and _dynamic_ features. The per-frame static groundplans are mean-pooled to obtain a single, time-independent static groundplan.

To render a scene using the disentangled static and dynamic groundplans, we first decode query points using both groundplans, yielding _two_ sets of (density, color) values for each point. We use the compositing operation proposed by Yuan et al. (2021) to compose the contribution from static and dynamic components along the ray. Given the color and density for static \((\mathbf{c}^{S},\sigma^{S})\) and dynamic \((\mathbf{c}^{D},\sigma^{D})\) parts, the density of the combined scene is calculated as \(\sigma^{S}+\sigma^{D}\). The color at the sampled point is computed as a weighted linear combination \(w^{S}\mathbf{c}^{S}+w^{D}\mathbf{c}^{D}\), where \(w^{S}=(1-\exp(-\delta\sigma^{S}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), \(w^{D}=(1-\exp(-\delta\sigma^{D}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), and \(\delta\) is the distance between adjacent samples on the camera ray.

We train our model on multi-view video, where multi-view information is used to learn the 3D structure, while motion is used to disentangle the static and dynamic components in the scene. During training, we sample two time-steps per video. For each time-step, we sample multiple images from different camera views; some of the views are used as input to the method while others are used to compute the loss function. We use the input images to infer static and dynamic groundplans, and use them to render out per-frame query views.

Our formulation yields a model that maps a single image to two radiance fields, parameterizing static and dynamic 3D regions respectively.

We now perform a search for connected components in the dynamic neural groundplan to perform 3D instance-level segmentation, monocular 3D bounding box prediction, and the extraction of object-centric 3D representations. Specifically, given a dynamic groundplan, we first sample points in a 3D grid around the groundplan origin and decode their densities. We now perform conventional connected-component labeling in the groundplan space using accumulated density values, identifying the disconnected dynamic objects. We perform 2D instance-level segmentation for a queried viewpoint using volume rendering based on the densities expressed by the dynamic groundplan and assigning a color to the points corresponding to each of the identified objects, see Fig. 1 for an example.

This approach is not limited to a fixed number of objects during training or at test time. As we will show, this simple method is at par with the state of the art on self-supervised learning of object-centric 3D representations, uORF (Yu et al., 2022). Note that our approach is compatible with prior work leveraging slot attention (Locatello et al., 2020; Kipf et al., 2021) and other inference modules, which can be run on the disentangled dynamic groundplan which, in contrast to image space, enables shift-equivariant processing free from perspective distortion and encodes 3D structure.

We demonstrate that our method infers a 3D scene representation from a single image while disentangling static and dynamic components of the scene into static and dynamic groundplans respectively.

Our method is trained on multi-view observations of dynamic scenes.

We present novel views rendered from groundplans inferred from a single image from CLEVR and CoSY. For single-shot 3D reconstruction and novel view synthesis, we compare against PixelNeRF (Yu et al., 2020), a state-of-the-art single-image 3D reconstruction method, and uORF (Yu et al., 2022), state-of-the-art unsupervised object-centric 3D reconstruction method.

Fig. 4 provides a qualitative comparison to PixelNeRF and uORF in terms of single-image 3D novel view synthesis on both CoSY and CLEVR. Note that our model produces novel views with plausible completions of parts of the scene that are unobserved in the context image such as the back-side of objects.

Given only a single image, our method computes separate static and dynamic groundplans that can be used to individually render the static and movable parts of the scene respectively. Fig. 5 shows results on single-image reconstruction of static and movable scene elements.

The separate reconstruction of movable scene components in the dynamic groundplan enables object detection via instance-level segmentation and bounding box prediction. Fig. 6 presents the instance-level segmentation and 3D bounding box prediction results of the proposed 3D object discovery via connected component discovery using the density inferred using the dynamic groundplan from the bird's-eye view.

As the dynamic groundplan does not encode static scene regions such as the street below cars, cars can easily be moved from one scene to another.

Our paper demonstrates self-supervised learning of 3D scene representations that are disentangled into movable and immovable scene elements. By leveraging multi-view video at training time, we can reconstruct disentangled 3D representations from a single image observation at test time. We show the potential of neural ground plans as a representation that may enable data-efficient solutions to downstream processing of the 3D scene, such as completion, instance-level segmentation, 3D bounding box prediction, and 3D scene editing. We hope that our paper will inspire future work on the use of self-supervised neural scene representations for general scene understanding tasks.

* Yu et al. (2020) Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one or few images. _Proc. CVPR_, 2020.

* Yu et al. (2022) Hong-Xing Yu, Leonidas J Guibas, and Jiajun Wu. Unsupervised discovery of object radiance fields.

* Yuan et al. (2021) Wentao Yuan, Zhaoyang Lv, Tanner Schmidt, and Steven Lovegrove. Star: Self-supervised tracking and reconstruction of rigid objects in motion with neural rendering. In _Proc. CVPR_, pp. 13144-13152, 2021.

We populate a coarse 3D feature volume of shape \(64\times 16\times 64\) with 128-dimensional latents for points in the camera frustum by bilinearly sampling the aggregated encoder feature tensor. This volume is processed as explained in the main paper: a coordinate encoding MLP transforms each feature into a new \(128\) dimensional feature vector.

To construct an entangled groundplan, we aggregate the 3D feature volume into a 2D groundplan using a pillar aggregation MLP. Consider a pillar of features orthogonal to the groundplan for a particular point \((x,z)\), in our case that is \(128\times 16\). The MLP takes in each latent with its corresponding 3D coordinate in the world coordinate system. It outputs the softmax scores for each of these latents which can be used to sum these latents along the pillar into a single 128-dimensional latent, as explained in the main paper.

We use a shallow CNN with 4 hidden convolutional layers to disentangle the entangled groundplan of shape \(128\times 64\times 64\).

This shallow CNN outputs groundplan of shape \(256\times 256\times 256\), in which the first 128 channels of the feature tensor are attributed as the static groundplan and the rest of the 128 channels are used as the dynamic groundplan for that timestep.

Our method performs project of a 3D point on the image plane to get the corresponding feature tensor. This is performed using the intrinsic matrix of the camera. For a given 3D point in camera coordinates \(\mathbf{x_{c}}\) and intrinsic matrix \(\mathbf{K}\), the resulting 2D point on the image plane is computed as \(\mathbf{Kx}\). For projecting a 3D query point \(\mathbf{x}\) on the groundplan, we use grid sample using \((x,z)\)-coordinates of the 3D query points \(\mathbf{x}\).

Our model supports multi-view, as well as monocular reconstruction. We start our training only using multi-view reconstruction with 5 input views for the first 200 epochs, and then switch to a variable mode where the model is given a varying number of input views ranging between 1-5 views. Thiscurriculum approach helps the network to first learn the relevant scene priors, before learning to complete the 3D structure of the scene. For localization of objects, we consider the dynamic groundplan and render it from an orthographic bird's-eye view. Along with the bird's-eye view RGB image, we also generate the occupancy map (per-pixel accumulated alpha) as shown in the manuscript in Fig. 5.

Given the localization in the orthographic bird's-eye view, we can find the height of the objects by computing the depth within each region. This information gives us a 3D bounding box around each of the localized object. The instance level segmentation is produced via volume rendering, by overriding the RGB values within the detected region to a chosen color for the object.

Scene editing is performed by editing the dynamic groundplan.

Our method successfully integrates information across observations into a single, multi-view consistent representation.

First, our method is in the regime of prior-based reconstruction from a few images. This is in contrast to the regime of single-scene overfitting (e.g. NeRF) in which prior work has demonstrated photo-realistic results. In our task setup of prior based reconstruction, a certain degree of uncertainty exists. For instance, there is uncertainty about the exact depth and geometry of the 3D scene given the input images. In these cases, the model will learn to blur proportionate to the amount of uncertainty.

We outperform pixelNeRF, a strong baseline in this regime of 3D reconstruction from few images, both quantitatively and qualitatively.

In contrast to single-scene methods, our method needs to fit not only the differentiable rendering in GPU memory, but also the whole inference pipeline - CNNs, 3D lifting, groundplans, etc.

Fig. 11 provides rendered images from edited groundplans where the cars are rotated at different angles. Note that the representation only allows for rotations in the \(xz\)-plane. The dynamic groundplan can be further used to perform motion interpolation in 3D, using optical flow for groundplan interpolation prediction using off-the-shelf, state-of-the-art optical flow and frame interpolation methods.

We first trained our model on the GQN dataset and used the output dynamic groundplans to train the frame interpolation method.

Firstly, we extracted dynamic groundplan for the samples over different timesteps by passing the multi-view observation through our groundplan generation pipeline. Two dynamic groundplans at different timesteps were given as input to RIFE, and an intermediate timestep was queried.

The proposed method succeeds at inferring the correct object motion, and enables novel view synthesis through space and time.

Input: Figure 1: Given a single image, our model infers separate 3D representations for static and dynamic scene elements, enabling high-quality novel view synthesis with plausible completion, unsupervised instance-level segmentation, 3D bounding box prediction, 3D scene editing, and extraction of objectcentric 3D representations. Our model is trained self-supervised using unlabeled multi-view videos.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 4: Qualitative comparisons. Comparison for novel-view synthesis given a single context view with PixelNeRF (Yu et al., 2020) and uORF (Yu et al., 2022).

Input: Figure 5: Single-image reconstruction, disentanglement of static and dynamic objects, and novel view synthesis. Given a single input image, our method can disentangle the observed scene into static and object components based on what the model observed as not-moving and moving in the training data. In these examples, the cars are isolated in the object component as the model was training on video data of cars moving on the road.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 6: Object Localization. Given a single input image, we can use our inferred 3D representation of the scene to compute (a) bird’s-eye view rendering, (b) object localization in the bird’s-eye view space, (c) instance-level segmentation, and (d) 3D bounding box prediction.

Input: Figure 2: Groundplan inference. Given a context image, we first extract a set of CNN features. We unproject the features into 3D and re-sample them at “pillars” on top of the location of groundplan vertices. Pillars are aggregated into groundplan features using a softmax-weighted sum. The resulting 2D grid of features is decomposed into separate dynamic and static groundplans by a 2D CNN. The coordinate-encoding MLP is not visualized in this figure. Please refer to Sec. 3 for details.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 9: Visual quality of views for a given input image.

Input: Figure 8: Object-centric representations and scene editing. The proposed static-dynamic neural groundplans enables object discovery using connected components labeling on the density of objects encoded in the dynamic groundplan (left). This enables straight-forward scene editing such as deletion, addition, or rigid-body transformation via directly editing the neural groundplan (right).

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 3: Learning Static-Dynamic Disentanglement. Given multiple frames of a video, we extract per-frame, compactified, static and dynamic groundplans according to Fig. 2. Static groundplans are pooled into a time-invariant groundplan. We then composite per-frame dynamic and static time-invariant groundplans via differentiable volume rendering. Our model is supervised only via a re-rendering loss on video frames. We encourage the model to explain as much of the scene density as possible with the static groundplan via a sparsity loss on per-frame dynamic volume rendering densities. The surface loss is not visualized here.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I'll evaluate how well the claim aligns with the evidence:

The claim outlines a contribution of introducing self-supervised training of conditional neural groundplans for single-image 3D scene reconstruction. The extensive evidence, including detailed methodology descriptions, architectural diagrams, and numerous experimental results across multiple figures, strongly supports this claim. The evidence demonstrates:

1. The method successfully reconstructs 3D scenes from single images
2. Clear disentanglement of static/dynamic elements is achieved
3. Self-supervised training is thoroughly documented
4. The hybrid discrete-continuous nature is well-explained
5. Novel view synthesis and scene editing capabilities are compellingly demonstrated

The claim is conservatively stated and fully supported by comprehensive evidence. It accurately reflects the technical contribution without exaggeration of capabilities or results.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

In summary, our contributions are:* We introduce self-supervised training of conditional neural groundplans, a hybrid discrete-continuous 3D neural scene representation that can be reconstructed from a single image, enabling efficient processing of scene appearance and geometry directly in 3D.

The review comment to be evaluated is:

====> Strength
1. The authors introduced the bird’s eye-view (BEV) representation as a scene representation, which is novel in the area of neural rendering.
2. The disentanglement of the static and moving component of the scene adds more contribution to the proposed method. Although it is not new to automatically separate these components in the neural rendering community, using a vanilla 2D CNN to separate the feature representation is new to the reviewer.
3. The authors show that using a simple heuristic method, they can generate instance segmentation and bounding boxes for the dynamic components in the scene.
4. Good qualitative results are given.

====> Weakness
1. The details of the neural groundplans is confusing:

    i. In page 4, there are multiple $x$ such as $x'$, $x$, $x_c$, $x_i$. Their shape should be clarified. Whether they belong to 2D or 3D point, and also their coordinate system (i.e., the image frame coordinate or the world coordinate, and how to transform between these coordinates using the camera intrinsic)

    ii. For equation like $v(x ′ ) = F(π(C^{-1}(x ′ )))$, $f(x ′ ) = ...$, the parentheses here denote indexing the feature volume $v$ and feature tensor $F$. However, it is easy to confuse them with the functions like $\pi()$ and $D()$. The authors should consider using other formulation.

    iii.The $\pi(\cdot)$ is not clear. What is the meaning of it and how to learn $\pi(\cdot)$, is it learned per image I?

    iv. ``$g_x$ are the groundplan features for the point $x$ computed by projecting the coordinates onto the groundplane...'' How is the projection conducted? Is it projected by the camera extrinsic？

    v. In page 5, the authors say ``The per-frame static groundplans are pooled to obtain a single, time-independent static groundplan.'' How is the pooling process performed? The authors need to detail it.

2. The task setting is not clear. The authors should consider formulate the problem setting in a separated subsection (e.g., train one model for multiple scenes, all images are calibrated, the view density per scene, etc.)

3. It seems the compared baselines like pixelNerf and uORF are not proposed for the topic of separating dynamic and static representation. It would be fairer to compare with ``Neuraldiff: Segmenting 3d objects that move in egocentric videos.'' that used different components for the moving and static objects.

The evidence to be evaluated is:Emerging neural scene representations enable reconstruction of geometry and appearance from images as well as high-quality novel view synthesis via differentiable rendering. A large part of recent work focuses on the case of reconstructing a _single_ 3D scene given dense observations (Cheng et al., 2018; Tung et al., 2019; Sitzmann et al., 2019; Lombardi et al., 2019; Mildenhall et al., 2020; Yariv et al., 2020; Tewari et al., 2021). Alternatively, differentiable rendering may be used to supervise encoders to reconstruct scenes from a single or few images in a feedforward manner. Pixel-aligned conditioning enables reconstruction of compositional scenes (Yu et al., 2020; Trevithick and Yang, 2021), but does not infer a compact 3D representation.

Hybrid discrete-continuous neural scene representations offer a compromise by factorizing a dense 3D field into several lower-dimensional representations that are used to condition an MLP (Chan et al., 2022; Chen et al., 2022).

We similarly use axis-aligned 2D grids of features for self-supervised scene representation via neural rendering, but reconstruct them directly from few or a single 2D image observations.

In contrast, we present a self-supervised conditional groundplan representation, learned only from images via neural rendering.

Our approach is similar in using object motion as cue for disentanglement and multi-view as cue for 3D reconstruction, but uses it as supervision to train an encoder-based approach that enables reconstruction from a _single_ image instead of scene-specific disentanglement from multiple video frames.

Prior work has aimed to infer object-centric representations directly from images, with objects either represented as localized object-centric patches (Lin et al., 2020; Eslami et al., 2016; Crawford and Pineau, 2019; Kosiorek et al., 2018; Jiang et al., 2019) or scene mixture components (Engelcke et al., 2020; Burgess et al., 2019; Greff et al., 2019, 2016; 2017; Du et al., 2021), with the slot attention module (Locatello et al., 2020) increasingly driving object-centric inference. Resulting object representations may be decoded into object-centric 3D representations and composed for novel view synthesis (Yu et al., 2022; Smith et al., 2022; Elich et al., 2022; Chen et al., 2021; Bear et al., 2020; Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Du et al., 2021).

Several scene reconstruction methods (Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Nie et al., 2020) use direct supervision to train an object representation and detector to infer an editable 3D scene from a single frame observation.

In this work, we demonstrate that a representation factorized into static and movable 3D regions can serve as a powerful backbone for object discovery.

In this section, we describe the process of inferring a neural ground plan given one or several image observations in a feed-forward manner, as well as subsequent novel view synthesis.

A neural groundplan is a 2D grid of features aligned with the ground plane of the 3D scene, which we define to be the \(xz-\)plane. A 3D point is decoded by projecting it onto the groundplan and retrieving the corresponding feature vector using bilinear interpolation. This feature is then concatenated with the vertical \(y\)-coordinate of the query point and decoded into radiance and density values via a fully connected network, enabling novel view synthesis using volume rendering (Mildenhall et al., 2020).

We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021).

**Reconstructing neural groundplans from images**. Inferring a neural groundplan from one or several images proceeds in three steps: (1) feature extraction, (2) feature unprojection, (3) pillar aggregation. Given a single image \(\mathbf{I}\), we first extract per-pixel features via a CNN encoder to yield a feature tensor \(\mathbf{F}\). We define the camera as the world origin and center the neural groundplan accordingly, approximately aligned with the ground level. The image features are unprojected to a 3D feature volume \(\mathbf{v}\) in contracted world space using the inverse of the contract function defined earlier. We extract the feature at a contracted 3D point \(\mathbf{x}^{\prime}\) in \(\mathbf{v}\) as \(\mathbf{v}(\mathbf{x}^{\prime})=\mathbf{F}[\pi(C^{-1}(\mathbf{x}^{\prime}))]\), where \(C^{-1}(\mathbf{x}^{\prime})\) first maps the contracted point to linear world space and \(\pi(\cdot)\) projects it onto the image plane of the context view using camera extrinsics and intrinsics.

We first use a coordinate-encoding MLP \(D(\cdot)\) to transform the volume as \(\mathbf{f}(\mathbf{x}^{\prime})=D(\mathbf{v}(\mathbf{x}^{\prime}),\mathbf{x}_ {\mathbf{c}},\mathbf{d})\), where \(\mathbf{x}_{\mathbf{c}}\) denotes the 3D point in linear camera coordinates of the context camera, and \(\mathbf{d}\) denotes the ray direction from the camera center to that point. Since all features along a camera ray are identical in \(\mathbf{v}\), coordinate encoding is used to add the depth information to the features. In the case of multi-view input images, the volumes corresponding to each input view are mean pooled. Associated to each 2D vertex of the groundplan is now a set of features \(\{\mathbf{f}_{i}\}_{i=1}^{N}\), where \(N\) is the number of samples along the \(y\)-dimension. We use a "pillar-aggregation" MLP to compute softmax scores as \(\alpha_{i}=P(\mathbf{f}_{i},\mathbf{x}_{i})\), where \(P(\cdot)\) denotes the MLP and \(\mathbf{x}_{i}\) is the linear coordinate of the \(i\)-th point on the pillar. Finally, the features are aggregated by computing the weighted sum of the features, \(\mathbf{g}=\sum_{i}\alpha_{i}\mathbf{f}_{i}\).

We can render images from novel camera views via differentiable volume rendering (DeVries et al., 2021; Lombardi et al., 2019; Mildenhall et al., 2020).

Furthermore, we describe a method for performing self-supervised 3D object discovery and 3D bounding box prediction using the geometry encoded in the dynamic groundplan representation.

We leverage the fact that objects move in the given multi-view videos as the training signal.

For each frame, we infer an _entangled_ neural groundplan as described in the previous section. Features in this entangled neural groundplan parameterize both static and dynamic features of the scene, for instance, a car as well as the road below it. We feed this groundplan into a fully convolutional 2D network, which disentangles it into two separate groundplans containing _static_ and _dynamic_ features. The per-frame static groundplans are mean-pooled to obtain a single, time-independent static groundplan.

To render a scene using the disentangled static and dynamic groundplans, we first decode query points using both groundplans, yielding _two_ sets of (density, color) values for each point. We use the compositing operation proposed by Yuan et al. (2021) to compose the contribution from static and dynamic components along the ray. Given the color and density for static \((\mathbf{c}^{S},\sigma^{S})\) and dynamic \((\mathbf{c}^{D},\sigma^{D})\) parts, the density of the combined scene is calculated as \(\sigma^{S}+\sigma^{D}\). The color at the sampled point is computed as a weighted linear combination \(w^{S}\mathbf{c}^{S}+w^{D}\mathbf{c}^{D}\), where \(w^{S}=(1-\exp(-\delta\sigma^{S}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), \(w^{D}=(1-\exp(-\delta\sigma^{D}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), and \(\delta\) is the distance between adjacent samples on the camera ray.

We train our model on multi-view video, where multi-view information is used to learn the 3D structure, while motion is used to disentangle the static and dynamic components in the scene. During training, we sample two time-steps per video. For each time-step, we sample multiple images from different camera views; some of the views are used as input to the method while others are used to compute the loss function. We use the input images to infer static and dynamic groundplans, and use them to render out per-frame query views.

Our formulation yields a model that maps a single image to two radiance fields, parameterizing static and dynamic 3D regions respectively.

We now perform a search for connected components in the dynamic neural groundplan to perform 3D instance-level segmentation, monocular 3D bounding box prediction, and the extraction of object-centric 3D representations. Specifically, given a dynamic groundplan, we first sample points in a 3D grid around the groundplan origin and decode their densities. We now perform conventional connected-component labeling in the groundplan space using accumulated density values, identifying the disconnected dynamic objects. We perform 2D instance-level segmentation for a queried viewpoint using volume rendering based on the densities expressed by the dynamic groundplan and assigning a color to the points corresponding to each of the identified objects, see Fig. 1 for an example.

This approach is not limited to a fixed number of objects during training or at test time. As we will show, this simple method is at par with the state of the art on self-supervised learning of object-centric 3D representations, uORF (Yu et al., 2022). Note that our approach is compatible with prior work leveraging slot attention (Locatello et al., 2020; Kipf et al., 2021) and other inference modules, which can be run on the disentangled dynamic groundplan which, in contrast to image space, enables shift-equivariant processing free from perspective distortion and encodes 3D structure.

We demonstrate that our method infers a 3D scene representation from a single image while disentangling static and dynamic components of the scene into static and dynamic groundplans respectively.

Our method is trained on multi-view observations of dynamic scenes.

We present novel views rendered from groundplans inferred from a single image from CLEVR and CoSY. For single-shot 3D reconstruction and novel view synthesis, we compare against PixelNeRF (Yu et al., 2020), a state-of-the-art single-image 3D reconstruction method, and uORF (Yu et al., 2022), state-of-the-art unsupervised object-centric 3D reconstruction method.

Fig. 4 provides a qualitative comparison to PixelNeRF and uORF in terms of single-image 3D novel view synthesis on both CoSY and CLEVR. Note that our model produces novel views with plausible completions of parts of the scene that are unobserved in the context image such as the back-side of objects.

Given only a single image, our method computes separate static and dynamic groundplans that can be used to individually render the static and movable parts of the scene respectively. Fig. 5 shows results on single-image reconstruction of static and movable scene elements.

The separate reconstruction of movable scene components in the dynamic groundplan enables object detection via instance-level segmentation and bounding box prediction. Fig. 6 presents the instance-level segmentation and 3D bounding box prediction results of the proposed 3D object discovery via connected component discovery using the density inferred using the dynamic groundplan from the bird's-eye view.

As the dynamic groundplan does not encode static scene regions such as the street below cars, cars can easily be moved from one scene to another.

Our paper demonstrates self-supervised learning of 3D scene representations that are disentangled into movable and immovable scene elements. By leveraging multi-view video at training time, we can reconstruct disentangled 3D representations from a single image observation at test time. We show the potential of neural ground plans as a representation that may enable data-efficient solutions to downstream processing of the 3D scene, such as completion, instance-level segmentation, 3D bounding box prediction, and 3D scene editing. We hope that our paper will inspire future work on the use of self-supervised neural scene representations for general scene understanding tasks.

* Yu et al. (2020) Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one or few images. _Proc. CVPR_, 2020.

* Yu et al. (2022) Hong-Xing Yu, Leonidas J Guibas, and Jiajun Wu. Unsupervised discovery of object radiance fields.

* Yuan et al. (2021) Wentao Yuan, Zhaoyang Lv, Tanner Schmidt, and Steven Lovegrove. Star: Self-supervised tracking and reconstruction of rigid objects in motion with neural rendering. In _Proc. CVPR_, pp. 13144-13152, 2021.

We populate a coarse 3D feature volume of shape \(64\times 16\times 64\) with 128-dimensional latents for points in the camera frustum by bilinearly sampling the aggregated encoder feature tensor. This volume is processed as explained in the main paper: a coordinate encoding MLP transforms each feature into a new \(128\) dimensional feature vector.

To construct an entangled groundplan, we aggregate the 3D feature volume into a 2D groundplan using a pillar aggregation MLP. Consider a pillar of features orthogonal to the groundplan for a particular point \((x,z)\), in our case that is \(128\times 16\). The MLP takes in each latent with its corresponding 3D coordinate in the world coordinate system. It outputs the softmax scores for each of these latents which can be used to sum these latents along the pillar into a single 128-dimensional latent, as explained in the main paper.

We use a shallow CNN with 4 hidden convolutional layers to disentangle the entangled groundplan of shape \(128\times 64\times 64\).

This shallow CNN outputs groundplan of shape \(256\times 256\times 256\), in which the first 128 channels of the feature tensor are attributed as the static groundplan and the rest of the 128 channels are used as the dynamic groundplan for that timestep.

Our method performs project of a 3D point on the image plane to get the corresponding feature tensor. This is performed using the intrinsic matrix of the camera. For a given 3D point in camera coordinates \(\mathbf{x_{c}}\) and intrinsic matrix \(\mathbf{K}\), the resulting 2D point on the image plane is computed as \(\mathbf{Kx}\). For projecting a 3D query point \(\mathbf{x}\) on the groundplan, we use grid sample using \((x,z)\)-coordinates of the 3D query points \(\mathbf{x}\).

Our model supports multi-view, as well as monocular reconstruction. We start our training only using multi-view reconstruction with 5 input views for the first 200 epochs, and then switch to a variable mode where the model is given a varying number of input views ranging between 1-5 views. Thiscurriculum approach helps the network to first learn the relevant scene priors, before learning to complete the 3D structure of the scene. For localization of objects, we consider the dynamic groundplan and render it from an orthographic bird's-eye view. Along with the bird's-eye view RGB image, we also generate the occupancy map (per-pixel accumulated alpha) as shown in the manuscript in Fig. 5.

Given the localization in the orthographic bird's-eye view, we can find the height of the objects by computing the depth within each region. This information gives us a 3D bounding box around each of the localized object. The instance level segmentation is produced via volume rendering, by overriding the RGB values within the detected region to a chosen color for the object.

Scene editing is performed by editing the dynamic groundplan.

Our method successfully integrates information across observations into a single, multi-view consistent representation.

First, our method is in the regime of prior-based reconstruction from a few images. This is in contrast to the regime of single-scene overfitting (e.g. NeRF) in which prior work has demonstrated photo-realistic results. In our task setup of prior based reconstruction, a certain degree of uncertainty exists. For instance, there is uncertainty about the exact depth and geometry of the 3D scene given the input images. In these cases, the model will learn to blur proportionate to the amount of uncertainty.

We outperform pixelNeRF, a strong baseline in this regime of 3D reconstruction from few images, both quantitatively and qualitatively.

In contrast to single-scene methods, our method needs to fit not only the differentiable rendering in GPU memory, but also the whole inference pipeline - CNNs, 3D lifting, groundplans, etc.

Fig. 11 provides rendered images from edited groundplans where the cars are rotated at different angles. Note that the representation only allows for rotations in the \(xz\)-plane. The dynamic groundplan can be further used to perform motion interpolation in 3D, using optical flow for groundplan interpolation prediction using off-the-shelf, state-of-the-art optical flow and frame interpolation methods.

We first trained our model on the GQN dataset and used the output dynamic groundplans to train the frame interpolation method.

Firstly, we extracted dynamic groundplan for the samples over different timesteps by passing the multi-view observation through our groundplan generation pipeline. Two dynamic groundplans at different timesteps were given as input to RIFE, and an intermediate timestep was queried.

The proposed method succeeds at inferring the correct object motion, and enables novel view synthesis through space and time.

Input: Figure 1: Given a single image, our model infers separate 3D representations for static and dynamic scene elements, enabling high-quality novel view synthesis with plausible completion, unsupervised instance-level segmentation, 3D bounding box prediction, 3D scene editing, and extraction of objectcentric 3D representations. Our model is trained self-supervised using unlabeled multi-view videos.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 4: Qualitative comparisons. Comparison for novel-view synthesis given a single context view with PixelNeRF (Yu et al., 2020) and uORF (Yu et al., 2022).

Input: Figure 5: Single-image reconstruction, disentanglement of static and dynamic objects, and novel view synthesis. Given a single input image, our method can disentangle the observed scene into static and object components based on what the model observed as not-moving and moving in the training data. In these examples, the cars are isolated in the object component as the model was training on video data of cars moving on the road.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 6: Object Localization. Given a single input image, we can use our inferred 3D representation of the scene to compute (a) bird’s-eye view rendering, (b) object localization in the bird’s-eye view space, (c) instance-level segmentation, and (d) 3D bounding box prediction.

Input: Figure 2: Groundplan inference. Given a context image, we first extract a set of CNN features. We unproject the features into 3D and re-sample them at “pillars” on top of the location of groundplan vertices. Pillars are aggregated into groundplan features using a softmax-weighted sum. The resulting 2D grid of features is decomposed into separate dynamic and static groundplans by a 2D CNN. The coordinate-encoding MLP is not visualized in this figure. Please refer to Sec. 3 for details.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 9: Visual quality of views for a given input image.

Input: Figure 8: Object-centric representations and scene editing. The proposed static-dynamic neural groundplans enables object discovery using connected components labeling on the density of objects encoded in the dynamic groundplan (left). This enables straight-forward scene editing such as deletion, addition, or rigid-body transformation via directly editing the neural groundplan (right).

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 3: Learning Static-Dynamic Disentanglement. Given multiple frames of a video, we extract per-frame, compactified, static and dynamic groundplans according to Fig. 2. Static groundplans are pooled into a time-invariant groundplan. We then composite per-frame dynamic and static time-invariant groundplans via differentiable volume rendering. Our model is supervised only via a re-rendering loss on video frames. We encourage the model to explain as much of the scene density as possible with the static groundplan via a sparsity loss on per-frame dynamic volume rendering densities. The surface loss is not visualized here.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. The claim appears reasonably well-stated based on the extensive evidence provided. The paper demonstrates:
- Successful implementation of neural groundplans for single-image 3D reconstruction (shown in multiple figures)
- Self-supervised training approach using multi-view videos (detailed methodology in Section 3)
- Effective disentanglement of static and dynamic components (validated in Figures 5, 6)
- Processing in 3D space through the groundplan representation (demonstrated through experiments)

While some technical details could be clearer (as noted in review comments), the core contributions are substantiated by comprehensive methodology descriptions and experimental results. The claim avoids hyperbole and accurately reflects what the method achieves.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

In summary, our contributions are:* We introduce self-supervised training of conditional neural groundplans, a hybrid discrete-continuous 3D neural scene representation that can be reconstructed from a single image, enabling efficient processing of scene appearance and geometry directly in 3D.

The review comment to be evaluated is:

Strengths include:
* The self-supervised training removes the need for GT annotation, e.g., object bounding boxes, for the supported downstream tasks.
* The decomposition of static and movable object feature spaces looks like quite an elegant solution to utilize the inductive bias in multi-view videos while enabling capabilities such as segmentation and object-level scene editing.
* The results overall look promising. Single-view/few-view novel view synthesis is a very challenging task, and the comparisons with PixelNeRF and uORF clearly demonstrated the advantages in synthesis quality. The analysis of adding more views (Fig.10) is strong evidence that the learned 3D representation can figure out how 2D views are related to, and hence help improve, 3D reconstruction.

Weaknesses include:
* There is no study of the generalization capability of the model. It seems likely that the learned models can overfit the limited appearances in the dataset (a few types of shapes/objects with mostly uniform colors).
* Related to the last point, the evaluation is completely done on synthesized datasets, and it's not clear how well the model can learn real-world data with much more diverse appearances. Since the method does not require GT annotations, some evaluation on real-world data does not seem too difficult.
* The are some quality issues with the presented view synthesis results. For example, while unobserved regions are understandably blurry, why are observed regions also not sharp? We can see from Fig.10 that adding more views does not help the quality of observed regions any further.
* Training requires multi-view videos. I can't find clarification on whether these need to be from static cameras. Nothing in the model appears to have such a requirement, but if so, that's a strong limitation. Moreover, why can't the model be trained on frames from a single moving camera?
* It's not clearly described how scene editing is done. It says that's enabled by "directly editing the neural groundplan". Does that mean editing the (movable object) feature space? The feature space is not sparse (i.e. locations without objects have non-zero features), so how does cropping in such space work, and why can that make sense?

The evidence to be evaluated is:Emerging neural scene representations enable reconstruction of geometry and appearance from images as well as high-quality novel view synthesis via differentiable rendering. A large part of recent work focuses on the case of reconstructing a _single_ 3D scene given dense observations (Cheng et al., 2018; Tung et al., 2019; Sitzmann et al., 2019; Lombardi et al., 2019; Mildenhall et al., 2020; Yariv et al., 2020; Tewari et al., 2021). Alternatively, differentiable rendering may be used to supervise encoders to reconstruct scenes from a single or few images in a feedforward manner. Pixel-aligned conditioning enables reconstruction of compositional scenes (Yu et al., 2020; Trevithick and Yang, 2021), but does not infer a compact 3D representation.

Hybrid discrete-continuous neural scene representations offer a compromise by factorizing a dense 3D field into several lower-dimensional representations that are used to condition an MLP (Chan et al., 2022; Chen et al., 2022).

We similarly use axis-aligned 2D grids of features for self-supervised scene representation via neural rendering, but reconstruct them directly from few or a single 2D image observations.

In contrast, we present a self-supervised conditional groundplan representation, learned only from images via neural rendering.

Our approach is similar in using object motion as cue for disentanglement and multi-view as cue for 3D reconstruction, but uses it as supervision to train an encoder-based approach that enables reconstruction from a _single_ image instead of scene-specific disentanglement from multiple video frames.

Prior work has aimed to infer object-centric representations directly from images, with objects either represented as localized object-centric patches (Lin et al., 2020; Eslami et al., 2016; Crawford and Pineau, 2019; Kosiorek et al., 2018; Jiang et al., 2019) or scene mixture components (Engelcke et al., 2020; Burgess et al., 2019; Greff et al., 2019, 2016; 2017; Du et al., 2021), with the slot attention module (Locatello et al., 2020) increasingly driving object-centric inference. Resulting object representations may be decoded into object-centric 3D representations and composed for novel view synthesis (Yu et al., 2022; Smith et al., 2022; Elich et al., 2022; Chen et al., 2021; Bear et al., 2020; Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Du et al., 2021).

Several scene reconstruction methods (Zakharov et al., 2020; Zekharov et al., 2020; Beker et al., 2020; Nie et al., 2020) use direct supervision to train an object representation and detector to infer an editable 3D scene from a single frame observation.

In this work, we demonstrate that a representation factorized into static and movable 3D regions can serve as a powerful backbone for object discovery.

In this section, we describe the process of inferring a neural ground plan given one or several image observations in a feed-forward manner, as well as subsequent novel view synthesis.

A neural groundplan is a 2D grid of features aligned with the ground plane of the 3D scene, which we define to be the \(xz-\)plane. A 3D point is decoded by projecting it onto the groundplan and retrieving the corresponding feature vector using bilinear interpolation. This feature is then concatenated with the vertical \(y\)-coordinate of the query point and decoded into radiance and density values via a fully connected network, enabling novel view synthesis using volume rendering (Mildenhall et al., 2020).

We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021).

**Reconstructing neural groundplans from images**. Inferring a neural groundplan from one or several images proceeds in three steps: (1) feature extraction, (2) feature unprojection, (3) pillar aggregation. Given a single image \(\mathbf{I}\), we first extract per-pixel features via a CNN encoder to yield a feature tensor \(\mathbf{F}\). We define the camera as the world origin and center the neural groundplan accordingly, approximately aligned with the ground level. The image features are unprojected to a 3D feature volume \(\mathbf{v}\) in contracted world space using the inverse of the contract function defined earlier. We extract the feature at a contracted 3D point \(\mathbf{x}^{\prime}\) in \(\mathbf{v}\) as \(\mathbf{v}(\mathbf{x}^{\prime})=\mathbf{F}[\pi(C^{-1}(\mathbf{x}^{\prime}))]\), where \(C^{-1}(\mathbf{x}^{\prime})\) first maps the contracted point to linear world space and \(\pi(\cdot)\) projects it onto the image plane of the context view using camera extrinsics and intrinsics.

We first use a coordinate-encoding MLP \(D(\cdot)\) to transform the volume as \(\mathbf{f}(\mathbf{x}^{\prime})=D(\mathbf{v}(\mathbf{x}^{\prime}),\mathbf{x}_ {\mathbf{c}},\mathbf{d})\), where \(\mathbf{x}_{\mathbf{c}}\) denotes the 3D point in linear camera coordinates of the context camera, and \(\mathbf{d}\) denotes the ray direction from the camera center to that point. Since all features along a camera ray are identical in \(\mathbf{v}\), coordinate encoding is used to add the depth information to the features. In the case of multi-view input images, the volumes corresponding to each input view are mean pooled. Associated to each 2D vertex of the groundplan is now a set of features \(\{\mathbf{f}_{i}\}_{i=1}^{N}\), where \(N\) is the number of samples along the \(y\)-dimension. We use a "pillar-aggregation" MLP to compute softmax scores as \(\alpha_{i}=P(\mathbf{f}_{i},\mathbf{x}_{i})\), where \(P(\cdot)\) denotes the MLP and \(\mathbf{x}_{i}\) is the linear coordinate of the \(i\)-th point on the pillar. Finally, the features are aggregated by computing the weighted sum of the features, \(\mathbf{g}=\sum_{i}\alpha_{i}\mathbf{f}_{i}\).

We can render images from novel camera views via differentiable volume rendering (DeVries et al., 2021; Lombardi et al., 2019; Mildenhall et al., 2020).

Furthermore, we describe a method for performing self-supervised 3D object discovery and 3D bounding box prediction using the geometry encoded in the dynamic groundplan representation.

We leverage the fact that objects move in the given multi-view videos as the training signal.

For each frame, we infer an _entangled_ neural groundplan as described in the previous section. Features in this entangled neural groundplan parameterize both static and dynamic features of the scene, for instance, a car as well as the road below it. We feed this groundplan into a fully convolutional 2D network, which disentangles it into two separate groundplans containing _static_ and _dynamic_ features. The per-frame static groundplans are mean-pooled to obtain a single, time-independent static groundplan.

To render a scene using the disentangled static and dynamic groundplans, we first decode query points using both groundplans, yielding _two_ sets of (density, color) values for each point. We use the compositing operation proposed by Yuan et al. (2021) to compose the contribution from static and dynamic components along the ray. Given the color and density for static \((\mathbf{c}^{S},\sigma^{S})\) and dynamic \((\mathbf{c}^{D},\sigma^{D})\) parts, the density of the combined scene is calculated as \(\sigma^{S}+\sigma^{D}\). The color at the sampled point is computed as a weighted linear combination \(w^{S}\mathbf{c}^{S}+w^{D}\mathbf{c}^{D}\), where \(w^{S}=(1-\exp(-\delta\sigma^{S}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), \(w^{D}=(1-\exp(-\delta\sigma^{D}))/(1-\exp(-\delta(\sigma^{S}+\sigma^{D}))\), and \(\delta\) is the distance between adjacent samples on the camera ray.

We train our model on multi-view video, where multi-view information is used to learn the 3D structure, while motion is used to disentangle the static and dynamic components in the scene. During training, we sample two time-steps per video. For each time-step, we sample multiple images from different camera views; some of the views are used as input to the method while others are used to compute the loss function. We use the input images to infer static and dynamic groundplans, and use them to render out per-frame query views.

Our formulation yields a model that maps a single image to two radiance fields, parameterizing static and dynamic 3D regions respectively.

We now perform a search for connected components in the dynamic neural groundplan to perform 3D instance-level segmentation, monocular 3D bounding box prediction, and the extraction of object-centric 3D representations. Specifically, given a dynamic groundplan, we first sample points in a 3D grid around the groundplan origin and decode their densities. We now perform conventional connected-component labeling in the groundplan space using accumulated density values, identifying the disconnected dynamic objects. We perform 2D instance-level segmentation for a queried viewpoint using volume rendering based on the densities expressed by the dynamic groundplan and assigning a color to the points corresponding to each of the identified objects, see Fig. 1 for an example.

This approach is not limited to a fixed number of objects during training or at test time. As we will show, this simple method is at par with the state of the art on self-supervised learning of object-centric 3D representations, uORF (Yu et al., 2022). Note that our approach is compatible with prior work leveraging slot attention (Locatello et al., 2020; Kipf et al., 2021) and other inference modules, which can be run on the disentangled dynamic groundplan which, in contrast to image space, enables shift-equivariant processing free from perspective distortion and encodes 3D structure.

We demonstrate that our method infers a 3D scene representation from a single image while disentangling static and dynamic components of the scene into static and dynamic groundplans respectively.

Our method is trained on multi-view observations of dynamic scenes.

We present novel views rendered from groundplans inferred from a single image from CLEVR and CoSY. For single-shot 3D reconstruction and novel view synthesis, we compare against PixelNeRF (Yu et al., 2020), a state-of-the-art single-image 3D reconstruction method, and uORF (Yu et al., 2022), state-of-the-art unsupervised object-centric 3D reconstruction method.

Fig. 4 provides a qualitative comparison to PixelNeRF and uORF in terms of single-image 3D novel view synthesis on both CoSY and CLEVR. Note that our model produces novel views with plausible completions of parts of the scene that are unobserved in the context image such as the back-side of objects.

Given only a single image, our method computes separate static and dynamic groundplans that can be used to individually render the static and movable parts of the scene respectively. Fig. 5 shows results on single-image reconstruction of static and movable scene elements.

The separate reconstruction of movable scene components in the dynamic groundplan enables object detection via instance-level segmentation and bounding box prediction. Fig. 6 presents the instance-level segmentation and 3D bounding box prediction results of the proposed 3D object discovery via connected component discovery using the density inferred using the dynamic groundplan from the bird's-eye view.

As the dynamic groundplan does not encode static scene regions such as the street below cars, cars can easily be moved from one scene to another.

Our paper demonstrates self-supervised learning of 3D scene representations that are disentangled into movable and immovable scene elements. By leveraging multi-view video at training time, we can reconstruct disentangled 3D representations from a single image observation at test time. We show the potential of neural ground plans as a representation that may enable data-efficient solutions to downstream processing of the 3D scene, such as completion, instance-level segmentation, 3D bounding box prediction, and 3D scene editing. We hope that our paper will inspire future work on the use of self-supervised neural scene representations for general scene understanding tasks.

* Yu et al. (2020) Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one or few images. _Proc. CVPR_, 2020.

* Yu et al. (2022) Hong-Xing Yu, Leonidas J Guibas, and Jiajun Wu. Unsupervised discovery of object radiance fields.

* Yuan et al. (2021) Wentao Yuan, Zhaoyang Lv, Tanner Schmidt, and Steven Lovegrove. Star: Self-supervised tracking and reconstruction of rigid objects in motion with neural rendering. In _Proc. CVPR_, pp. 13144-13152, 2021.

We populate a coarse 3D feature volume of shape \(64\times 16\times 64\) with 128-dimensional latents for points in the camera frustum by bilinearly sampling the aggregated encoder feature tensor. This volume is processed as explained in the main paper: a coordinate encoding MLP transforms each feature into a new \(128\) dimensional feature vector.

To construct an entangled groundplan, we aggregate the 3D feature volume into a 2D groundplan using a pillar aggregation MLP. Consider a pillar of features orthogonal to the groundplan for a particular point \((x,z)\), in our case that is \(128\times 16\). The MLP takes in each latent with its corresponding 3D coordinate in the world coordinate system. It outputs the softmax scores for each of these latents which can be used to sum these latents along the pillar into a single 128-dimensional latent, as explained in the main paper.

We use a shallow CNN with 4 hidden convolutional layers to disentangle the entangled groundplan of shape \(128\times 64\times 64\).

This shallow CNN outputs groundplan of shape \(256\times 256\times 256\), in which the first 128 channels of the feature tensor are attributed as the static groundplan and the rest of the 128 channels are used as the dynamic groundplan for that timestep.

Our method performs project of a 3D point on the image plane to get the corresponding feature tensor. This is performed using the intrinsic matrix of the camera. For a given 3D point in camera coordinates \(\mathbf{x_{c}}\) and intrinsic matrix \(\mathbf{K}\), the resulting 2D point on the image plane is computed as \(\mathbf{Kx}\). For projecting a 3D query point \(\mathbf{x}\) on the groundplan, we use grid sample using \((x,z)\)-coordinates of the 3D query points \(\mathbf{x}\).

Our model supports multi-view, as well as monocular reconstruction. We start our training only using multi-view reconstruction with 5 input views for the first 200 epochs, and then switch to a variable mode where the model is given a varying number of input views ranging between 1-5 views. Thiscurriculum approach helps the network to first learn the relevant scene priors, before learning to complete the 3D structure of the scene. For localization of objects, we consider the dynamic groundplan and render it from an orthographic bird's-eye view. Along with the bird's-eye view RGB image, we also generate the occupancy map (per-pixel accumulated alpha) as shown in the manuscript in Fig. 5.

Given the localization in the orthographic bird's-eye view, we can find the height of the objects by computing the depth within each region. This information gives us a 3D bounding box around each of the localized object. The instance level segmentation is produced via volume rendering, by overriding the RGB values within the detected region to a chosen color for the object.

Scene editing is performed by editing the dynamic groundplan.

Our method successfully integrates information across observations into a single, multi-view consistent representation.

First, our method is in the regime of prior-based reconstruction from a few images. This is in contrast to the regime of single-scene overfitting (e.g. NeRF) in which prior work has demonstrated photo-realistic results. In our task setup of prior based reconstruction, a certain degree of uncertainty exists. For instance, there is uncertainty about the exact depth and geometry of the 3D scene given the input images. In these cases, the model will learn to blur proportionate to the amount of uncertainty.

We outperform pixelNeRF, a strong baseline in this regime of 3D reconstruction from few images, both quantitatively and qualitatively.

In contrast to single-scene methods, our method needs to fit not only the differentiable rendering in GPU memory, but also the whole inference pipeline - CNNs, 3D lifting, groundplans, etc.

Fig. 11 provides rendered images from edited groundplans where the cars are rotated at different angles. Note that the representation only allows for rotations in the \(xz\)-plane. The dynamic groundplan can be further used to perform motion interpolation in 3D, using optical flow for groundplan interpolation prediction using off-the-shelf, state-of-the-art optical flow and frame interpolation methods.

We first trained our model on the GQN dataset and used the output dynamic groundplans to train the frame interpolation method.

Firstly, we extracted dynamic groundplan for the samples over different timesteps by passing the multi-view observation through our groundplan generation pipeline. Two dynamic groundplans at different timesteps were given as input to RIFE, and an intermediate timestep was queried.

The proposed method succeeds at inferring the correct object motion, and enables novel view synthesis through space and time.

Input: Figure 1: Given a single image, our model infers separate 3D representations for static and dynamic scene elements, enabling high-quality novel view synthesis with plausible completion, unsupervised instance-level segmentation, 3D bounding box prediction, 3D scene editing, and extraction of objectcentric 3D representations. Our model is trained self-supervised using unlabeled multi-view videos.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 4: Qualitative comparisons. Comparison for novel-view synthesis given a single context view with PixelNeRF (Yu et al., 2020) and uORF (Yu et al., 2022).

Input: Figure 5: Single-image reconstruction, disentanglement of static and dynamic objects, and novel view synthesis. Given a single input image, our method can disentangle the observed scene into static and object components based on what the model observed as not-moving and moving in the training data. In these examples, the cars are isolated in the object component as the model was training on video data of cars moving on the road.

Input: Figure 10: Resolving uncertainty with increasing number of context views Our model can take a variable number of viewpoints of a scene as input. We find that the model gets a good prior on the object from a single view but struggles to reconstruct high-quality details in the unobserved regions of the background. This uncertainty gets resolved with more input views.

Input: Figure 6: Object Localization. Given a single input image, we can use our inferred 3D representation of the scene to compute (a) bird’s-eye view rendering, (b) object localization in the bird’s-eye view space, (c) instance-level segmentation, and (d) 3D bounding box prediction.

Input: Figure 2: Groundplan inference. Given a context image, we first extract a set of CNN features. We unproject the features into 3D and re-sample them at “pillars” on top of the location of groundplan vertices. Pillars are aggregated into groundplan features using a softmax-weighted sum. The resulting 2D grid of features is decomposed into separate dynamic and static groundplans by a 2D CNN. The coordinate-encoding MLP is not visualized in this figure. Please refer to Sec. 3 for details.

Input: Figure 11: Scene editing with rotated objects. We present images of scenes with edited groundplans where cars are rotated at various angles in the ground plane.

Input: Figure 9: Visual quality of views for a given input image.

Input: Figure 8: Object-centric representations and scene editing. The proposed static-dynamic neural groundplans enables object discovery using connected components labeling on the density of objects encoded in the dynamic groundplan (left). This enables straight-forward scene editing such as deletion, addition, or rigid-body transformation via directly editing the neural groundplan (right).

Input: Figure 12: Temporal 3D scene interpolation for novel view synthesis in space and time.

Input: Figure 3: Learning Static-Dynamic Disentanglement. Given multiple frames of a video, we extract per-frame, compactified, static and dynamic groundplans according to Fig. 2. Static groundplans are pooled into a time-invariant groundplan. We then composite per-frame dynamic and static time-invariant groundplans via differentiable volume rendering. Our model is supervised only via a re-rendering loss on video frames. We encourage the model to explain as much of the scene density as possible with the static groundplan via a sparsity loss on per-frame dynamic volume rendering densities. The surface loss is not visualized here.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, the claim appears to be fairly well-supported but modestly overstated in a few aspects. The evidence demonstrates that the authors successfully implemented a self-supervised neural groundplan system capable of single-image 3D reconstruction and scene representation. However, some limitations exist:

1. The claim doesn't acknowledge that training requires multi-view videos (not just single images)
2. The term "efficient processing" isn't fully substantiated in the evidence
3. Performance is only demonstrated on synthetic datasets with limited object diversity
4. Some quality issues exist in observed regions of reconstructions

While the core technical contribution is valid, the broad framing without acknowledging key constraints makes this slightly overstated.

<score>2</score>