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:

By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region.

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:In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020).

The bird's-eye view is generated either directly without 3D inductive biases (Mani et al., 2020), or similar to our proposed approach, by using 3D geometry-driven inductive biases such as unprojection into a volume (Harley et al., 2022; Chen et al., 2022; Roddick et al., 2019), or by generating a 3D point cloud (Philion and Fidler, 2020; Hu et al., 2021).

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).

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 definition, however, it is only possible to decode 3D points that lie within the boundaries of the neural groundplan, which precludes reconstruction and representation of unbounded scenes. We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021). Points \(\mathbf{x}\) within a radius \(r_{\text{inner}}\) around the groundplan origin remain unaffected, but points outside this radius are contracted. For any 3D point \(\mathbf{x}\), the contracted 3D coordinate can be computed as \(\mathbf{x}^{\prime}=C(\mathbf{x})=((1+k)-k/||\mathbf{u}||)(\mathbf{u}/|| \mathbf{u}||)r_{\text{inner}}\), where \(\mathbf{u}=\mathbf{x}/r_{\text{inner}}\), and \(k\) is a hyperparameter which controls the size of the contracted region. Note that \(C\) is invertible, such that \(\mathbf{x}=C^{-1}(\mathbf{x}^{\prime})\) is a function that takes a 3D point in contracted space \(\mathbf{x}^{\prime}\) to the original 3D point \(\mathbf{x}\) in linear space.

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.

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.

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. We then show that connected components analysis suffices to leverage the densities in the dynamic groundplan for instance-level segmentation, bounding box prediction, and scene editing.

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.

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.

This results, like in the monocular case, in a 3D volume of \(128\times 64\times 16\times 64\) (\(CH\times X\times Y\times Z\)).

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.

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 \(\mathbf{x}\).

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 the claim: "By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region."

Summary of evaluation:
The evidence strongly supports this claim. The paper explicitly details the compactification process using a non-linear coordinate re-mapping from Barron et al. (2021), providing the mathematical formulation showing how points outside an inner radius are contracted while maintaining invertibility. The technical implementation details and mathematical foundations are thoroughly described, and the evidence demonstrates practical implementation in their architecture. The claim is well-stated and accurately reflects what the method achieves without exaggeration.

<score>1</score>

Justification:
1. The evidence directly substantiates the claim with detailed mathematical formulation: "Points within a radius r_inner around the groundplan origin remain unaffected, but points outside this radius are contracted."

2. The invertibility is explicitly proven: "C is invertible, such that x=C^-1(x') is a function that takes a 3D point in contracted space x' to the original 3D point x in linear space."

3. Implementation details validate practical application with specific dimensions and architecture choices (128×64×16×64 volume, 256×256×256 groundplan).

4. The review comments don't raise any concerns about this specific aspect of the work, suggesting this particular claim is well-supported.


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:

By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region.

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:In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020).

The bird's-eye view is generated either directly without 3D inductive biases (Mani et al., 2020), or similar to our proposed approach, by using 3D geometry-driven inductive biases such as unprojection into a volume (Harley et al., 2022; Chen et al., 2022; Roddick et al., 2019), or by generating a 3D point cloud (Philion and Fidler, 2020; Hu et al., 2021).

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).

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 definition, however, it is only possible to decode 3D points that lie within the boundaries of the neural groundplan, which precludes reconstruction and representation of unbounded scenes. We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021). Points \(\mathbf{x}\) within a radius \(r_{\text{inner}}\) around the groundplan origin remain unaffected, but points outside this radius are contracted. For any 3D point \(\mathbf{x}\), the contracted 3D coordinate can be computed as \(\mathbf{x}^{\prime}=C(\mathbf{x})=((1+k)-k/||\mathbf{u}||)(\mathbf{u}/|| \mathbf{u}||)r_{\text{inner}}\), where \(\mathbf{u}=\mathbf{x}/r_{\text{inner}}\), and \(k\) is a hyperparameter which controls the size of the contracted region. Note that \(C\) is invertible, such that \(\mathbf{x}=C^{-1}(\mathbf{x}^{\prime})\) is a function that takes a 3D point in contracted space \(\mathbf{x}^{\prime}\) to the original 3D point \(\mathbf{x}\) in linear space.

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.

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.

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. We then show that connected components analysis suffices to leverage the densities in the dynamic groundplan for instance-level segmentation, bounding box prediction, and scene editing.

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.

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.

This results, like in the monocular case, in a 3D volume of \(128\times 64\times 16\times 64\) (\(CH\times X\times Y\times Z\)).

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.

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 \(\mathbf{x}\).

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 the claim: "By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region."

Summary:
The evidence strongly supports this claim. The paper explicitly describes the compactification process using a non-linear coordinate re-mapping from Barron et al. (2021), providing precise mathematical details of how points within and outside a radius r_inner are handled. The invertible mapping C(x) is well-defined, and the paper demonstrates practical implementation with specific volume dimensions (128×64×16×64). The claim is modest in scope, focusing on the technical capability without overstating its implications.

<score>1</score>

Justification:
1. The claim is directly supported by mathematical evidence:
- Clear description of the compactification function C(x) and its inverse C^-1(x')
- Explicit formulation: "x'=C(x)=((1+k)-k/||u||)(u/||u||)r_inner"
- Proof of invertibility is mentioned

2. Implementation details validate practicality:
- Specific volume dimensions are provided (128×64×16×64)
- Concrete technical details about feature handling and coordinate systems

3. No overstatement:
- Claim focuses purely on the technical capability
- Doesn't make broader claims about performance or applications
- Matches the reviewer's technical assessment, who doesn't dispute this specific aspect

The only minor criticism in the review related to coordinate system clarity, but this doesn't affect the fundamental truth of the compactification claim itself.


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:

By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region.

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:In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020).

The bird's-eye view is generated either directly without 3D inductive biases (Mani et al., 2020), or similar to our proposed approach, by using 3D geometry-driven inductive biases such as unprojection into a volume (Harley et al., 2022; Chen et al., 2022; Roddick et al., 2019), or by generating a 3D point cloud (Philion and Fidler, 2020; Hu et al., 2021).

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).

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 definition, however, it is only possible to decode 3D points that lie within the boundaries of the neural groundplan, which precludes reconstruction and representation of unbounded scenes. We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021). Points \(\mathbf{x}\) within a radius \(r_{\text{inner}}\) around the groundplan origin remain unaffected, but points outside this radius are contracted. For any 3D point \(\mathbf{x}\), the contracted 3D coordinate can be computed as \(\mathbf{x}^{\prime}=C(\mathbf{x})=((1+k)-k/||\mathbf{u}||)(\mathbf{u}/|| \mathbf{u}||)r_{\text{inner}}\), where \(\mathbf{u}=\mathbf{x}/r_{\text{inner}}\), and \(k\) is a hyperparameter which controls the size of the contracted region. Note that \(C\) is invertible, such that \(\mathbf{x}=C^{-1}(\mathbf{x}^{\prime})\) is a function that takes a 3D point in contracted space \(\mathbf{x}^{\prime}\) to the original 3D point \(\mathbf{x}\) in linear space.

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.

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.

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. We then show that connected components analysis suffices to leverage the densities in the dynamic groundplan for instance-level segmentation, bounding box prediction, and scene editing.

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.

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.

This results, like in the monocular case, in a 3D volume of \(128\times 64\times 16\times 64\) (\(CH\times X\times Y\times Z\)).

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.

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 \(\mathbf{x}\).

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 the claim "By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region."

1. Summary of evaluation:
The evidence strongly supports this claim with concrete mathematical details. The paper clearly describes the compactification process using a non-linear coordinate re-mapping function C(x), which contracts points outside an inner radius while preserving those within it. The function is proven to be invertible, allowing reconstruction of original 3D coordinates. The technical implementation details, including specific formulas and the mathematical framework, are well documented. The claim is precise and accurately reflects what the evidence demonstrates without overstatement.

2. Final score:
<score>1</score>

Justification:
- The evidence provides explicit mathematical formulation of the compactification process: "Points within a radius r_inner around the groundplan origin remain unaffected, but points outside this radius are contracted."
- The invertibility is proven: "C is invertible, such that x=C^-1(x') is a function that takes a 3D point in contracted space x' to the original 3D point x in linear space."
- The review comments do not dispute this specific technical claim about the compactification approach.
- The claim avoids overstating capabilities and precisely describes what the mathematical framework achieves.


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:

By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region.

The review comment to be evaluated is:

Strength：
1. The conditional neural groundplans proposed are intriguing. This allows efficient processing of scene appearance and geometry directly in 3D, through the self-supervised learning of conditional neural groundplans, a hybrid discrete continuous representation of 3D neural scenes.
2. The proposed disentanglement of static background and movable foreground objects is novel. This approach uses object motion for training an encoder-based system that can reconstruct scenes from a single image instead of decomposing video frames based on scene specifics.
3. The proposed method is promising for understanding 3D from a single image. The dynamic groundplan encodes 3D geometry, allowing us to segment and animate objects in 3D using single images and 3D bounding boxes.

Weaknesses：
1. The biggest weakness is that only results on simple synthetic data are presented. Currently, there are a number of well-annotated 3D driving scenes available. An example is KITTI 360 (https://www.cvlibs.net/datasets/kitti-360/). Could the authors explain why results on the real datasets are not presented? Is it because of some specific annotation (such as BEV correspondence or the number of views) needed by the method? Otherwise, the generalizability on natural scenes and the practical value of the method are questioned.
2. I think there are some ambiguity behind the proposed Static-Dynamic Disentanglement. A definition of Static and Dynamic should be made clear in the proposed framework. A car remaining still in the sequence will be considered as Static. Considering a situation when two moving and static cars looks similar or exactly the same, how can we distinguish from a single image if a car is static or dynamic? The method should mention the above cases as an assumption, or making a clear definition of being Static and Dynamic.
3. Groundplans implicitly assume that objects are aligned on a plane. However, in real life, it is common that scenes/objects are not placed on a flat ground plane (e.g., a curved plane). The ability of persistent 3D scene representation is a little overclaimed, if we consider the implicit assumption behind groundplans.

The evidence to be evaluated is:In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020).

The bird's-eye view is generated either directly without 3D inductive biases (Mani et al., 2020), or similar to our proposed approach, by using 3D geometry-driven inductive biases such as unprojection into a volume (Harley et al., 2022; Chen et al., 2022; Roddick et al., 2019), or by generating a 3D point cloud (Philion and Fidler, 2020; Hu et al., 2021).

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).

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 definition, however, it is only possible to decode 3D points that lie within the boundaries of the neural groundplan, which precludes reconstruction and representation of unbounded scenes. We thus compactify \(\mathbb{R}^{3}\) by implementing a non-linear coordinate re-mapping as proposed by Barron et al. (2021). Points \(\mathbf{x}\) within a radius \(r_{\text{inner}}\) around the groundplan origin remain unaffected, but points outside this radius are contracted. For any 3D point \(\mathbf{x}\), the contracted 3D coordinate can be computed as \(\mathbf{x}^{\prime}=C(\mathbf{x})=((1+k)-k/||\mathbf{u}||)(\mathbf{u}/|| \mathbf{u}||)r_{\text{inner}}\), where \(\mathbf{u}=\mathbf{x}/r_{\text{inner}}\), and \(k\) is a hyperparameter which controls the size of the contracted region. Note that \(C\) is invertible, such that \(\mathbf{x}=C^{-1}(\mathbf{x}^{\prime})\) is a function that takes a 3D point in contracted space \(\mathbf{x}^{\prime}\) to the original 3D point \(\mathbf{x}\) in linear space.

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.

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.

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. We then show that connected components analysis suffices to leverage the densities in the dynamic groundplan for instance-level segmentation, bounding box prediction, and scene editing.

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.

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.

This results, like in the monocular case, in a 3D volume of \(128\times 64\times 16\times 64\) (\(CH\times X\times Y\times Z\)).

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.

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 \(\mathbf{x}\).

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 the claim "By compactifying 3D space with a nonlinear mapping, neural groundplans can encode unbounded 3D scenes in a bounded region."

Summary:
The evidence strongly supports this claim. The paper explicitly describes the compactification process using a non-linear coordinate re-mapping method from Barron et al. (2021), providing the mathematical formulation C(x) for contracting points outside an inner radius. The mapping is shown to be invertible (C^(-1)), allowing reconstruction of original 3D points. The technical details are well-documented, including specific implementation details about the coordinate encoding and volume transformation. The claim is precise and accurately reflects the mathematical foundation presented without exaggeration.

<score>1</score>

Justification:
1. The claim directly aligns with the detailed mathematical evidence showing how the compactification works: "Points x within a radius r_inner around the groundplan origin remain unaffected, but points outside this radius are contracted."

2. The invertibility is explicitly proven: "C is invertible, such that x=C^(-1)(x') is a function that takes a 3D point in contracted space x' to the original 3D point x in linear space."

3. Even reviewer criticism regarding limitations (e.g., synthetic data, ground plane assumptions) don't challenge this specific technical claim about the compactification capability.

4. The implementation details provided (128×64×16×64 volume dimensions, precise mathematical formulations) demonstrate practical realization of the claimed capability.


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:

We further propose to reconstruct separate neural groundplans for 3D regions of a scene that are movable and 3D regions of a scene that are static given a single input image.

The evidence to be evaluated is: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). In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020). 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 work is related to prior work on learning to disentangle dynamic objects and static background. Some prior work leverages object motion across video frames to learn separate representations for movable foreground and static background in 2D (Kasten et al., 2021; Ye et al., 2022; Bao et al., 2022), while other recent work can also learn 3D representations (Yuan et al., 2021; Tschernezki et al., 2021). 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.

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).

In this work, we demonstrate that a representation factorized into static and movable 3D regions can serve as a powerful backbone for object discovery. While not explored in this work, slot attention and related object-centric algorithms could be run on our already sparse groundplan of movable 3D regions, faced with a dramatically easier task than when run on images directly.

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.

**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. At any vertex of the groundplan, the discretized \(y\)-coordinates of the volume form a "pillar".

**Disentangling static and dynamic neural groundplans**. We leverage the fact that objects move in the given multi-view videos as the training signal. We pick two random frames of a video. 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.

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.

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. Furthermore, we compute the smallest box that contains the connected component to get a 3D bounding box for each identified object.

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.

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.

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.

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.

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.

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.

Scene editing is performed by editing the dynamic groundplan.

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. This limits the resolution of the groundplans (a car is expressed by \(\sim 6\) latents) as well as the number of volume rendering samples.

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.

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 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 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 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 claim and evidence, I find that the claim is accurate but slightly understated in conveying the full scope of what the evidence demonstrates. The evidence shows not just reconstruction of separate neural groundplans for movable and static regions, but also demonstrates:
- Successful disentanglement using motion cues from video frames
- Ability to perform this from a single input image at test time
- Practical applications like object segmentation, 3D bounding boxes, and scene editing
- Validation through extensive experiments and visualizations

The claim is well-stated and conservatively worded, focusing on a core capability while not overstating the results.

<score>1</score>

Justification:
1. The claim aligns precisely with the evidence presented in multiple sections, particularly in "Disentangling static and dynamic neural groundplans" where they detail the technical approach
2. Figures 1, 5, and 8 provide visual evidence demonstrating successful separation of static and dynamic elements
3. The results are thoroughly validated through experiments and applications
4. The authors acknowledge limitations (e.g., resolution constraints, ground plane rotations only)
5. The claim uses careful language ("propose to reconstruct") rather than making absolute statements about performance


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:

We further propose to reconstruct separate neural groundplans for 3D regions of a scene that are movable and 3D regions of a scene that are static given a single input image.

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: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). In particular, neural groundplans and axis-aligned 2D grids enable high-quality unconditional generation of 3D scenes (DeVries et al., 2021; Chan et al., 2022) as well as reconstruction of 3D geometry from pointclouds (Peng et al., 2020). 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 work is related to prior work on learning to disentangle dynamic objects and static background. Some prior work leverages object motion across video frames to learn separate representations for movable foreground and static background in 2D (Kasten et al., 2021; Ye et al., 2022; Bao et al., 2022), while other recent work can also learn 3D representations (Yuan et al., 2021; Tschernezki et al., 2021). 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.

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).

In this work, we demonstrate that a representation factorized into static and movable 3D regions can serve as a powerful backbone for object discovery. While not explored in this work, slot attention and related object-centric algorithms could be run on our already sparse groundplan of movable 3D regions, faced with a dramatically easier task than when run on images directly.

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.

**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. At any vertex of the groundplan, the discretized \(y\)-coordinates of the volume form a "pillar".

**Disentangling static and dynamic neural groundplans**. We leverage the fact that objects move in the given multi-view videos as the training signal. We pick two random frames of a video. 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.

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.

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. Furthermore, we compute the smallest box that contains the connected component to get a 3D bounding box for each identified object.

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.

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.

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.

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.

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.

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.

Scene editing is performed by editing the dynamic groundplan.

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. This limits the resolution of the groundplans (a car is expressed by \(\sim 6\) latents) as well as the number of volume rendering samples.

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.

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 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 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 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 about reconstructing separate neural groundplans for movable and static 3D regions from a single image appears to be well-stated and accurately reflects the capabilities demonstrated in the paper. The evidence shows:

1. Clear methodology for disentangling static and dynamic components using neural groundplans
2. Extensive visual results showing successful separation of movable objects (cars) from static backgrounds
3. Demonstrated applications including novel view synthesis, instance segmentation, and scene editing
4. Transparent discussion of limitations (e.g., resolution constraints, ground plane rotations only)
5. Reviewer feedback confirms the technical achievement while noting some limitations

The claim conservatively describes the core capability without overstating the results or hiding limitations.

<score>1</score>

Justification:
- The claim simply states they "propose to reconstruct separate neural groundplans" - a modest framing supported by extensive technical details and results
- Evidence shows working implementation with clear visual examples
- Authors acknowledge limitations openly rather than making grandiose claims
- Reviewer feedback validates the core technical achievement while noting reasonable limitations
- Language is precise and measured, focusing on the fundamental capability rather than downstream applications