PhyRecon: Physically Plausible Neural Scene Reconstruction

Authors: junfeng  ni
yixin  chen
⋆  bohan
nan  jiang
bin  wang
bo  dai
puhao  li
yixin  zhu
song-chun  zhu
siyuan  huang
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-14 17:33:49

Abstract: We address the issue of physical implausibility in multi-view neural reconstruction. While implicit representations have gained popularity in multi-view 3D reconstruction, previous work struggles to yield physically plausible results, limiting their utility in domains requiring rigorous physical accuracy. This lack of plausibility stems from the absence of physics modeling in existing methods and their inability to recover intricate geometrical structures. In this paper, we introduce PHYRECON, the first approach to leverage both differentiable rendering and differentiable physics simulation to learn implicit surface representations. PHYRECON features a novel differentiable particle-based physical simulator built on neural implicit representations. Central to this design is an efficient transformation between SDF-based implicit representations and explicit surface points via our proposed Surface Points Marching Cubes (SP-MC), enabling differentiable learning with both rendering and physical losses. Additionally, PHYRECON models both rendering and physical uncertainty to identify and compensate for inconsistent and inaccurate monocular geometric priors. The physical uncertainty further facilitates physics-guided pixel sampling to enhance the learning of slender structures. By integrating these techniques, our model supports differentiable joint modeling of appearance, geometry, and physics. Extensive experiments demonstrate that PHYRECON significantly improves the reconstruction quality. Our results also exhibit superior physical stability in physical simulators, with at least a 40% improvement across all datasets, paving the way for future physics-based applications.

Main paper: 
 introduction: 
 3D scene reconstruction is fundamental in computer vision, with applications spanning graphics, robotics, and more. Building on neural implicit representations [45] , previous methods [18, 63, 77] have utilized multi-view images and monocular cues to recover fine-grained 3D geometry via volume rendering [10] . However, these approaches have overlooked physical plausibility, limiting their applicability in physics-intensive tasks such as embodied AI [17, 1, 30] and robotics [15, 26, 60] .The inability to achieve physically plausible reconstruction arises primarily from the lack of physics modeling. Existing methods based on neural implicit representation rely solely on rendering supervision, lacking explicit incorporation of physical constraints, such as those from physical simulators. This oversight compromises their ability to optimize 3D shapes for stability, as the models are not informed by the physics that would ensure realistic and stable structures in the real world.Additionally, these methods often ignore thin structures, focusing instead on optimizing the substantial parts of objects within images. This limitation is due to overly-smoothed and averaged optimization In Isaac Gym In Isaac Gym Figure 1 : Illustration of PHYRECON. We leverage both differentiable physics simulation and differentiable rendering to learn implicit surface representation. Results from previous methods [32] fail to remain stable in physical simulators or recover intricate geometries, while PHYRECON achieves significant improvements in both reconstruction quality and physical plausibility. results from problematic geometric priors, including multi-modal inconsistency (e.g., depth-normal), multi-view inconsistency, and inaccurate predictions deviating from the true underlying 3D geometry. As a result, they struggle to capture the slender structures crucial for object stability, leading to reconstructions that lack the fine details necessary for accurate physical simulation.To address these limitations, we present PHYRECON, the first effort to integrate differentiable rendering and differentiable physical simulations for learning implicit surface representations. Specifically, we propose a differentiable particle-based physical simulator and an efficient algorithm, Surface Points Marching Cubes (SP-MC), for differentiable transformation between SDF-based implicit representations and explicit surface points. The simulator facilitates accurate computation of 3D rigid body dynamics subjected to forces of gravity, contact, and friction, providing intricate details about the current shapes of the objects. Our differentiable pipeline efficiently implements and optimizes the implicit surface representation by coherently integrating feedback from rendering and physical losses. Moreover, to enhance the reconstruction of intricate structures and address geometric prior inconsistencies, we propose a joint uncertainty model describing both rendering and physical uncertainty. The rendering uncertainty identifies and mitigates inconsistencies arising from multi-view geometric priors, while the physical uncertainty reflects the dynamic trajectory of 3D contact points in the physical simulator, offering precise and interpretable monitoring of regions lacking physical support. Utilizing these uncertainties, we adaptively adjust the per-pixel depth, normal, and instance mask losses to avoid erroneous priors in surface reconstruction. Observing that intricate geometries occupying fewer pixels are less likely to be sampled, we propose a physics-guided pixel sampling based on physical uncertainty to help recover slender structures.We conduct extensive experiments on real datasets including ScanNet [9] and ScanNet++ [76] , and the synthetic dataset Replica [62] . Results demonstrate that our method significantly surpasses all state-of-the-art methods in both reconstruction quality and physical plausibility. Through ablative studies, we highlight the effectiveness of physical loss and uncertainty modeling. Remarkably, our approach achieves significant advancements in stability, registering at least a 40% improvement across all examined datasets, as assessed using the physical simulator Isaac Gym [39] .In summary, our main contributions are three-fold:1. We introduce the first method that seamlessly bridges neural scene reconstruction and physics simulation through a differentiable particle-based physical simulator and the proposed SP-MC that efficiently transforms implicit representations into explicit surface points. Our method enables differentiable optimization with both rendering and physical losses.2. We propose a novel method that jointly models rendering and physical uncertainties for 3D reconstruction. By dynamically adjusting the per-pixel rendering loss and physics-guided pixel sampling, our model significantly improves the reconstruction of thin structures.Extensive experiments demonstrate that our model significantly enhances reconstruction quality and physical plausibility, outperforming state-of-the-art methods. Our results exhibit substantial stability improvements, signaling broader potential for physics-demanding applications.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: Our abstract and introduction accurately reflect the paper's contributions and scope.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
related work: 
 Neural Implicit Surface Reconstruction With the increasing popularity of neural implicit representations [48, 79, 35, 6, 49, 7, 40] in 3D reconstruction, recent studies [50, 64, 75] have bridged the volume density in Neural Radiance Fields (NeRF) [45, 80] with the iso-surface representation, e.g., occupancy [42] or signed distance function (SDF) [52] to enable reconstruction from 2D images. Furthermore, advanced methods [68, 29, 69, 32] achieve compositional scene reconstruction by decomposing the latent 3D representation into the background and foreground objects. Despite achieving plausible object disentanglement, these methods fail to yield physically plausible reconstruction results, primarily due to the absence of physics constraints in existing neural implicit reconstruction pipelines. This paper addresses this limitation by incorporating both appearance and physical cues, thereby enabling surface learning with both rendering and physical losses.Incorporating Priors into Neural Surface Reconstruction Various priors, such as Manhattanworld assumptions [20, 18] , monocular geometric priors (i.e., normal [63] and depth [77] from off-theshelf model [55, 12, 2] ) and diffusion priors [70, 34] , have been employed to improve optimization and robustness in surface reconstruction, especially in texture-less regions of indoor scenes. However, these priors primarily involve geometry and appearance, neglecting physics priors despite their critical role in assessing object shapes and achieving stability. This paper proposes to incorporate physical priors through a differentiable simulator, with physical loss to penalize object movement and a joint uncertainty modeling of both rendering and physics. Rendering uncertainty filters multi-view inconsistencies in the monocular geometric priors, akin to prior work [41, 73, 51, 71] . The physical uncertainty employs the 3D contact points from the simulator to offer accurate insights into areas lacking physical support, which helps modulate the rendering losses and guides pixel sampling.Physics in Scene Understanding There has been an increasing interest in incorporating physics commonsense in the scene understanding community, spanning various topics such as object generation [47, 14, 61, 44, 43] , object decomposition [36, 82, 5] , material simulation [23, 31, 72, 81] , scene synthesis [54, 74] , and human motion generation [57, 59, 22, 78, 66, 21, 4, 8, 25, 65, 24] . In the context of scene reconstruction, previous work primarily focuses on applying collision loss on 3D bounding boxes to adjust their translations and rotations [11, 3] , and penalize the penetration between objects [79, 69] . Ma et al. [38] controls objects within a differentiable physical environment and integrates differentiable rendering to improve the generalizability of object control in unknown rendering configurations. In this paper, we propose to incorporate physics information into the neural implicit surface representation through a differentiable simulator, significantly enhancing both the richness of the physical information and the granularity of the optimization. The simulator not only furnishes detailed object trajectories but also yields detailed information about the object shapes in the form of 3D contact points. With physical loss directly backpropagated to the implicit shape representation, our approach leads to a refined optimization of object shapes and physical stability.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes] Justification: We discuss the limitations of our work and potential negative impact in the supplementary materials Appx. E and Appx. F, respectively.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
method: 
 Given an input set of N posed RGB images I = {I 1 , . . . , I N } and corresponding instance masks S = {S 1 , . . . , S N }, our objective is to reconstruct each object and the background in the scene. Fig. 2 presents an overview of our proposed PHYRECON.Volume Rendering of SDF-based Implicit Surfaces We utilize neural implicit surfaces with SDF to represent 3D geometry for implicit reconstruction. The SDF provides a continuous function that yields the distance s(p) to the closest surface for a given point p, with the sign indicating whether the point lies inside (negative) or outside (positive) the surface. We implement the SDF function as a multi-layer perceptron (MLP) network f (•), and similarly, the appearance function as g(•).For each camera ray r = (o, v) with o as the ray origin and v as the viewing direction, n points{p i = o + t i v | i = 0, 1, . . . , n -1} are sampled, where t i is the distance from the sample point to the camera center. We predict the signed distance s(p i ) and the color c i for each point along the ray, and the normal n i is the analytical gradient of the s(p i ). The predicted color Ĉ(r), depth D(r), and normal N (r) for the ray r are computed with the unbiased rendering method following NeuS [64] :EQUATIONwhere T i is the discrete accumulated transmittance and α i is the discrete opacity value, defined as:EQUATIONwhere Φ u (x) = (1 + e -ux ) -1 and u is a learnable parameter.Object-compositional Scene Reconstruction Following previous work [68, 69, 32] , we consider the compositional reconstruction of k objects utilizing their corresponding masks, and we treat the background as an object. More specifically, for a scene with k objects, we predict k SDFs at each point p, and the j-th (1 ≤ j ≤ k) SDF represents the geometry of the j-th object. Without loss of generality, we set j = 1 as the background object and others as the foreground objects. In subsequent sections of the paper, we denote the j-th object SDF at point p as s j (p). The scene SDF s(p) is the minimum of the object SDFs, i.e., s(p) = min s j (p), j = 1, 2, . . . , k, which is used for sampling points along the ray and volume rendering in Eqs. (1) and (2) . See more details in the Appx. A.To jointly optimize the neural implicit representations with rendering and physical losses, we propose a particle-based physical simulator and a highly efficient method to transition implicit SDF, which is adept at modeling visual appearances, to explicit representations conducive to physics simulation.Surface Points Marching Cubes (SP-MC) Existing methods [13, 43] fall short of attaining a satisfactory balance between efficiency and precision in extracting surface points from the SDF-based implicit representation. Thus, we develop a novel algorithm, SP-MC, with differentiable and efficient parallel operations and surface point refinement leveraging the SDF network f (•).x axis Fig. 3 illustrates the SP-MC algorithm. Formally, let S ∈ R N ×N ×N denote a signed distance grid of size N obtained using f (•), where S(p) ∈ R denotes the signed distance of the vertex p to its closest surface. SP-MC first locates the zero-crossing vertices V , where a sign change occurs from the neighboring vertices in signed distances, by shifting the SDF grid along the x, y, and z axis, respectively. For example, shifting along the x axis means S x (i, j, k) = S(i + 1, j, k). Then each vertex p ∈ V can be found through the element-wise multiplication of S and the shifted grids S d∈{x,y,z} , together with its sign-flipping neighbor vertex denoted as p shift . The coarse surface points P coarse are determined along the grid edge via linear interpolation:EQUATIONFinally, P coarse are refined using their surface normals and signed distances by querying f (•):EQUATIONBenefiting from all operations that are friendly for parallel computation, SP-MC is capable of extracting object surface points faster than the Kaolin [13] algorithm with less GPU memory consumption.In the meantime, it also achieves unbiased estimation of the surface points compared with direct thresholding the signed distance field [43] , which is crucial for learning fine structures. For detailed algorithm and quantitative computational comparisons, please refer to the Appx. B.To incorporate physics constraints into the neural implicit reconstruction, we develop a fully differentiable particle-based simulator implemented with Diff-Taichi [19] . Our simulator is designed for realistic simulations between rigid bodies, which are depicted as a collection of spherical particles of uniform size. The simulator captures the body's dynamics through translation and rotation, anchored to a reference coordinate system. The body state at any time is given by its position, orientation, linear and angular velocities. The total mass and the moment of inertia are intrinsic physical properties of the rigid body, reflecting its resistance to external forces and torques. During forward dynamics, the states are updated through time using explicit Euler time integration. Besides gravity, the changes in the rigid body state are induced by contact and friction forces, which are resolved using an impulse-based method. For more implementation details, please refer to the Appx. C.The simulator is used to track the trajectory and contact state of the object's surface points P fine until reaching stability or maximum simulation steps. Utilizing the trajectories and contact states, we present our simple yet effective physical loss: L phy = p∈Pcontact p ′ -p 0 2 , where the initial position of each point p is denoted as p 0 and its first contact position with the supporting plane as p ′ . Our physical loss intuitively penalizes the object's movement and is only applied to the contact points P contact instead of all the surface points. If the physical loss is homogeneously applied to all the surface points, it will contradict the rendering cues when the object is unstable, leading to degenerated results. The contact points P contact , on the other hand, indicate the areas of object instability. As shown in the experiment section, our design leads to stable 3D geometry under the coordination between the appearance and physics constraints.Apart from incorporating explicit physical constraints, we propose a joint uncertainty modeling approach, encompassing both rendering and physical uncertainty, to mitigate the inconsistencies and improve the reconstruction of thin structures, which is crucial for object stability.The rendering uncertainty is designed to address the issue of multi-view and multi-modal inconsistencies in monocular geometry priors, including depth uncertainty and normal uncertainty. We model the depth uncertainty u d and normal uncertainty u n of a 3D point as view-dependent representations [51, 58, 71] , which we utilize the appearance network g(•) to predict along with the color c for a 3D point p:EQUATIONwhere n is the normal at p, v is the viewing direction, and f is a geometry latent feature output from the SDF network f (•).The depth uncertainty Ûd (r) and normal uncertainty Ûn (r) of ray r are computed using u d and u n through volume rendering, similar to Eq. ( 1). Subsequently, we modulate the L 2 depth loss L D (r) and L 1 normal loss L N (r) based on the rendering uncertainty:EQUATIONIntuitively, the uncertainty-aware rendering loss can assign higher uncertainty to the pixels with larger loss, thus filtering the inconsistent monocular priors when the prediction from one viewpoint differs from others. Fig. 6 depicts how higher uncertainty precisely localizes inconsistent monocular priors.We introduce physical uncertainty to capture object instability from physics simulations. Specifically, we represent the physical uncertainty field with a dense grid G u-phy ∈ R N ×N ×N . The physical uncertainty u phy (p) ∈ R for any 3D point p is obtained through trilinear interpolation. G u-phy is initialized to zero and updated after each simulation trial using the 3D contact points P contact . For each contact point, we track its trajectory from p 0 to p ′ , forming the uncertain point set P u . We design a loss function L u-phy to update G u-phy :EQUATIONwhere ξ > 0 represents the increasing rate for G u-phy . Thus, areas with high physical uncertainty indicate that the object lacks support and requires the development of supporting structures. The physical uncertainty Ûphy (r) of the pixel corresponding to ray r is computed via volume rendering.Finally, we present the rendering losses re-weighted by both rendering and physical uncertainty:EQUATIONThe segmentation loss L S (r) is weighted by physical uncertainty only since we use view-consistent instance masks following prior work [68, 69, 32] . We detach Ûphy (r) in the above losses, ensuring the physical uncertainty field G u-phy reflects accurate physical information from the simulator.Physics-Guided Pixel Sampling A critical observation is that intricate object structures occupy only a minor portion of the image, leading to a lower probability of being sampled despite their significance in preserving object stability. Effectively pinpointing these fine geometries is perceptually challenging, yet physical uncertainty precisely outlines the areas where the object lacks support and requires special attention for optimization. Hence, we introduce a physics-guided pixel sampling strategy to enhance the learning of detailed 3D structures. Using physical uncertainty, we calculate the sampling probability of each pixel in the entire image by: p(r) = Ûphy (r)r∈R Ûphy (r) .In summary, our overall loss function is:L = L RGB + L D + L N + L S + L phy + L u-phy + L reg ,where the loss weights are omitted for simplicity. Following prior work [16, 77, 32] , we introduce ScanNet [9] , and Replica [62] demonstrate that our model produces higher quality reconstructions compared to the baselines. Our results contain finer details for slender structures (e.g., chair legs and objects on the table) and plausible support relations, which are highlighted in the zoom-in boxes.L reg to regularize the unobservable regions for background and foreground objects, as well as the implicit shapes through an eikonal term.To ensure robust optimization and coordination among various components, we empirically divide the training into three stages. In the first stage, we exclusively leverage the rendering losses with rendering uncertainties. In the second stage, we introduce our physical simulator to incorporate physical uncertainty into rendering losses and enable physics-guided pixel sampling. Finally, we integrate the physical loss using a learning curriculum that gradually increases the physical loss weight. The staged training allows the simulator to pinpoint more accurate contact points, essential for effective optimization of shape through the physical loss. For further details about the loss, training, and implementation details, please refer to Appx. A.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [Yes]Justification: The code will be released at the project page.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
experiments: 
 We assess the effectiveness of PHYRECON by evaluating scene and object reconstruction quality, as well as object stability. We present additional results in Appx. D and limitations in Appx. E.Datasets We conduct experiments on both the synthetic dataset Replica [62] and real datasets Scan-Net [9] and ScanNet++ [76] . We use 8 scenes from Replica following the setting of MonoSDF [77] and ObjectSDF++ [69] . For ScanNet, we use the 7 scenes following RICO [32] . Additionally, we conduct experiments on 7 scenes from the more recent real-world dataset ScanNet++ with higher-quality images and more accurate camera poses. More data preparation details are in Appx. D.1.We choose MonoSDF [77] , RICO [32] , and ObjectSDF++ [69] as the baseline models. For reconstruction, we measure the Chamfer Distance (CD), the F-score (F-score), and Normal Consistency (NC) following MonoSDF [77] . These metrics are evaluated for both scene and object reconstruction across all datasets. As MonoSDF is designed to reconstruct the whole scene, we only evaluate its scene reconstruction quality. To evaluate the physical plausibility of the reconstructed objects, we report the Stability Ratio (SR), defined as the ratio of the number of physically stable objects against the total number of objects in the scene. The assessment is conducted using dropping simulation via the Isaac Gym simulator [39] to avoid bias in favor of our method. We provide more details on our evaluation procedure in Appx. D.2.Tab. 1 and Fig. 4 present the quantitative and qualitative results of the neural scene reconstruction. In Fig. 5 , we visualize the trajectory for the reconstructed object during dropping simulation in Isaac Gym [39] . Fig. 6 showcases visualizations of several critical components in our methods, including the sampling strategy, volume renderings of the geometric cues, and the uncertainty maps. Our method significantly outperforms all baselines, and we summarize the key observations as follows.Physical Stability From the results in Tab. 1, our method realizes significant improvements in object stability, outperforming all baselines by at least 40% across all datasets. This signifies a significant [32] and ObjectSDF++ [69] in Fig. 5 fail to capture all the chair legs, leading to inherent instability.Reconstruction Quality Note that the improvement of the physical plausibility does not come under the sacrifice of reconstruction quality. From the results in Tab. 1, our method surpasses all the state-of-the-art methods across three datasets in all the reconstruction metrics. As also shown in Fig. 4 , while the baseline methods are capable of reconstructing substantial parts of objects, e.g., sofa or tabletop, they struggle with the intricate structures of objects. In contrast, our model achieves much more detailed reconstruction, e.g., the vase and lamp on the tables, shown in the zoom-in views.Joint Uncertainty Modeling Lastly, we discuss the intermediate results of our joint uncertainty modeling exemplified on the ScanNet dataset. As shown in Fig. 6 , the physical uncertainty adeptly pinpoints the regions critical for remaining stability, such as the chair legs and table base. The physicsguided pixel sampling, informed by the physical uncertainty map, prioritizes intricate structures over the random sampling strategy. Moreover, it modulates rendering losses, particularly useful for instance mask loss where chair legs are absent in the ground-truth instance mask. Meanwhile, the depth and normal uncertainty maps identify inconsistencies in the geometric prior, e.g., miss detections in the normal prior and the overly sharp depth prior. Collectively, they contribute to the physically plausible and detailed reconstructed mesh, surpassing the ground truth. We conduct ablative studies on the physical loss (P L), rendering uncertainty (RU ), physical uncertainty (P U ), and physics-guided pixel sampling (P S). Tab. 2 and Fig. 7 illustrate quantitative and qualitative comparisons, respectively. Key findings are as follows: 1. Physical loss significantly improves 3D object stability. However, due to the insufficient regularization of thin structures and imprecise contact points in the simulation, adding physical loss alone will overshadow the rendering losses, leading to degenerated object shapes to sustain stability. 2. Rendering uncertainty, physical uncertainty, and physic-guided pixel sampling collectively contribute to enhancing the reconstruction quality, particularly on thin structures. However, despite the advancements, the reconstructed results still struggle to maintain physical plausibility without direct physical supervision during the optimization. 3. When all components are introduced, the enhanced reconstruction of thin structures leads to more meaningful contact points in simulation, thus enabling effective joint optimization with physical loss. This not only improves the objects' stability but also preserves their reasonable shapes, leading to robust reconstruction with both physical plausibility and fine details simultaneously.We present and diagnose representative failure examples. Fig. 8 (a) demonstrates that in regions scarcely observed in the input images, optimizing with the physical loss may lead to degenerated object shapes, e.g., bulges, to maintain physical stability. This is due to insufficient supervision from the rendering losses. Fig. 8 (b) illustrates that objects may be divided into several disconnected parts, which also appear stable in the simulation. This is a common limitation of the current neural reconstruction pipeline and may be addressed by incorporating topological regularization to penalize disconnected parts of the object or further enhance the physical simulator. 
conclusion: 
 In conclusion, this paper introduces PHYRECON as the first approach to leverage both differentiable rendering and differentiable physics simulation for learning implicit surface representations. Our framework features a novel differentiable particle-based physical simulator and joint uncertainty modeling, facilitating efficient optimization with both rendering and physical losses. Extensive experiments validate the effectiveness of PHYRECON, showcasing its significant outperformance of all state-of-the-art methods in terms of both reconstruction quality and physics stability, underscoring its potential for future physics-demanding applications. Depth Consistency Loss Monocular depth and normal cues [77] can greatly benefit indoor scene reconstruction. For the depth consistency, we minimize the difference between rendered depth D(r) and the depth estimation D(r) from the Marigold model [27] :EQUATION)where w and q are the scale and shift values to match the different scales. We solve w and q with a least-squares criterion, which has the closed-form solution. Please refer to the supplementary material of [77] for a detailed computation process.Normal Consistency Loss We utilize the normal cues N (r) from Omnidata model [12] to supervise the rendered normal through the normal consistency loss, which comprises L1 and angular losses:L N = r∈R || N (r) -N (r)|| 1 + ||1 -N (r) T N (r)|| 1 . (A4)The volume-rendered normal and normal estimation will be transformed into the same coordinate system by the camera pose.Semantic Loss Building on previous work [68, 32] , we transform each point's SDFs into instance logits h(p) = [h 1 (p), h 2 (p), . . . , h k (p)], whereh j (p) = γ/(1 + exp(γ • s j (p))). (A5)Here, γ is a fixed parameter. Subsequently, we can obtain the instance logits Ĥ(r) ∈ R k of pixel corresponds to the ray r using volume rendering as:Ĥ(r) = n-1 i=0 T i α i h i . (A6)We minimize the semantic loss between volume-rendered semantic logits of each pixel and the ground-truth pixel semantic class. The semantic objective is implemented as a cross-entropy loss:L S = r∈R k j=1 -hj (r) log h j (r). (A7)The hj (r) is the ground-truth semantic probability for j-th object, which is 1 or 0.Eikonal Loss Following common practice, we also add an Eikonal term on the sampled points to regularize the SDF learning by:L Eikonal = n i (||∇ min 1≤j≤k s j (p i )|| 2 -1). (A8)The Eikonal loss is applied to the gradient of the scene SDF, which is the minimum of all the SDFs.Background Smoothness Loss Building upon RICO [32] , we use background smoothness loss to regularize the geometry of the occluded background to be smooth. Specifically, we randomly sample a P × P size patch every T P iterations within the given image and compute semantic map Ĥ(r) and a patch mask M (r):EQUATIONA9) wherein the mask value is 1 if the rendered class is not the background, thereby ensuring only the occluded background is regulated. Subsequently, we calculate the background depth map D(r) and background normal map N (r) using the background SDF exclusively. The patch-based background smoothness loss is then computed as:L( D) = 3 d=0 P-1-2 d m,n=0 M (r m,n ) ⊙ (| D(r m,n ) -D(r m,n+2 d )| + | D(r m,n ) -D(r m+2 d ,n )|), L( N ) = 3 d=0 P-1-2 d m,n=0 M (r m,n ) ⊙ (| N (r m,n ) -N (r m,n+2 d )| + | N (r m,n ) -N (r m+2 d ,n )|), (A10) L bs = L( D) + L( N ) (A11)Object Point-SDF Loss and Reversed Depth Loss To regularize SDFs of the object and the background, we further employ an object point-SDF loss to regulate objects within the room L op and a reversed depth loss L rd , following previous work [32] .Specifically, for the sampled points along the rays, we initially apply a root-finding algorithm among the background SDF of these points to determine the zero-SDF ray depth t ′ . Then, the object point-SDF loss can be expressed as:EQUATIONwhich pushes the objects' SDFs at points behind the surface to be greater than a positive threshold ϵ.Moreover, L rd optimizes the entire ray's SDF distribution rather than focusing solely on discrete points. Specifically, the ray depths {t i |i = 0, 1, . . . , n -1} are transformed into the reversed ray depths, denoted as { ti |i = 0, 1, . . . , n -1}, whereti = (t 0 + t n-1 ) -t n-1-i . (A13)The reversed depth d o of the hitting object is determined by the pixel's rendered semantic and d b of the background. The reversed depth loss is computed as:EQUATIONFinally, the regularization loss in our main paper L reg is computed as follows:L reg = L bs + L op + L rd + L Eikonal (A15) 
experimental setting/details: 
 Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes] Justification: We provide detailed descriptions of the experimental details in the main text Sec. 3.4 and supplementary materials Appx. A and Appx. D.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [No] Justification: Our experiments fixed the random seed following the previous works.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).• Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)? Answer: [NA] Justification: The paper poses no such risks. Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort. 12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [Yes] Justification:The paper uses open-source datasets, and all sources have been properly cited. Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. 
 
 Appendix: We implement our model in PyTorch [53] and utilize the Adam optimizer [28] with an initial learning rate of 5e -4. We sample 1024 rays per iteration. When incorporating physics-guided pixel sampling, we allocate 768 rays for physics-guided pixel sampling and the remaining 256 rays for random sampling. Our model is trained for 450 epochs on ScanNet [9] and ScanNet++ [76] datasets, and 2000 epochs on Replica [62] dataset. As introduced in Sec. 3.4, training is divided into three stages. For the ScanNet [9] and ScanNet++ [76] datasets, the second and final stages begin at the 360 th and 430 th epochs, respectively, while for the Replica [62] dataset, these stages start at 1700 th and 1980 th epochs. All experiments are conducted on a single NVIDIA-A100 GPU.Following previous work [77, 32] , we set 1, 0.1, 0.05, 0.04, 0.05, 0.1, 0.1 and 0.1 as loss weights for L RGB , L D , L N , L S , L Eikonal , L bs , L op , L rd , respectively. Additionally, we set ξ = 100 for updating G u-phy , initialize the loss weight for L phy as 60, and increase it by 30 per epoch.Integrating a physical simulator into the learning of the SDF-based implicit representation demands highly efficient and accurate extraction of surface points. The SP-MC algorithm is inspired by the marching cube algorithm [37] which estimates the topology (i.e., the vertices and connectivity of triangles) in each cell of the volumetric grid. Since surface points are only required for simulation, we improve the operation efficiency and combine the implicit SDF network f (•) to create fine-grained surface points.The Surface Points Marching Cubes (SP-MC) is divided into three steps for extracting surface points from SDF-based implicit surface representation. First, the object is voxelized to obtain a discretized signed distance field S ∈ R N ×N ×N with grid vertices denoted as P . Second, we shift the SDF grid S along the x, y, and z axis, respectively, to locate zero-crossing vertices. For example, shifting along the x axis results in S x (i, j, k) = S(i + 1, j, k). We then obtain coarse surface points P coarse through linear interpolation. We refer to this step as the Shift-Interpolation operation in Alg. 2. Third, P coarse is refined to yield P fine using their surface normals and signed distances. For a detailed algorithm, please refer to Alg. 2.In this algorithm, the background's boundary remains the boundary of the entire scene. For the foreground object, its boundary starts as the boundary of the entire scene and is expanded by δ = 0.1 around its current surface points' boundary after each SP-MC iteration. The updated boundary is more accurate than the entire scene, leading to improved precision in SP-MC.Finally, we emphasize the importance of the refinement step, which not only enhances the accuracy of P coarse , but also ensures reliable backpropagation of the gradient in the physical loss from an explicit physical simulator to the implicit SDF-based surface representation. Directly converting the SDF into a triangle mesh, as done in Marching Cubes [37] , does not support stable and effective backpropagation in case of topological change, as observed in the works by Liao et al. [33] and Remelli et al. [56] . Thus, we detach the gradient in the steps involving the extraction of coarse surface points and rely on the refinement step for backpropagation.To quantitatively compare with existing methods in efficiency, we assess SP-MC alongside Kaolin [13] , which converts the SDF field into a triangle mesh and surface points. The assessment of time and memory involves the transformation from SDF to surface points, which are prepared P fine = {p -f (p) • ∇f (p) | p ∈ P coarse } 8: return P fineand ready for use in both simulation and the computational graph for gradient backpropagation in both methods. We compared Kaolin and SP-MC at a grid resolution of 96 on a single A100 80GB machine, testing the average running time and GPU memory for all objects in all scenes of ScanNet++ [76] . From the results presented in Tab. A1, SP-MC consumes considerably less running time and GPU memory compared to Kaolin. The performance improvement of SP-MC primarily stems from its direct pursuit of surface points through simplified operations like grid-shifting and optimized parallel computation. This eliminates the need for face search in Kaolin's marching cubes, which consumes significant time and GPU memory. Furthermore, we also note that Mezghanni et al. [43] propose a method for extracting surface points through direct thresholding of the SDF in the discretized signed distance field S, defined as:P coarse = {p | |s(p)| < δ, p ∈ S} . (A16)Although this method is conceptually simpler, it introduces a surface bias δ, leading to an inevitable discrepancy between the extracted points and the actual surface points. It additionally requires a higher resolution of the SDF grid to capture fine structures, since the formulation puts higher requirements on the surface points, i.e., from SDF sign flipping to SDF < δ. Higher resolutions will decrease computational speed and consume more GPU memory.We use the supporting plane to provide contact and friction for object surface points in the physics simulation. More specifically, we use SP-MC to obtain the surface points of both the object to be simulated and the supporting plane (e.g., background for objects on the floor) before each simulation. We only include the background surface points within proximity under the object surface points for the simulation to reduce the computational load. Note that our physical simulator and physical loss both support more general contacts, e.g., the box on the cabinet and the monitor on the table ∥p a i -p b j ∥ < 2r ∥p a i -p b j ∥ < 2r ∥p a i -p b j ∥ < 2r vc • Nc < -ϵ ∥vc • Nc∥ < ϵ vc • Nc > ϵ 36:compute required impulse: J ← Eq. (A28a) For each rigid body do 52:compute historical motion information v up ← Eq. (A32), rwa ← Eq. (A30)53:if rwa < ∥g∥ • ∆t then Monocular Cues We utilize a pre-trained Marigold model [27] to generate a depth map D for each input RGB image. It's important to note that estimating the absolute scale in general scenes is challenging, thus D should be regarded as a relative depth cue. Furthermore, we employ another pre-trained Omnidata model [12] to obtain normal maps N for each RGB image. While depth cues offer semi-local relative information, normal cues are local and capture geometric intricacies. Consequently, we anticipate that surface normals and depth complement each other effectively.GT Instance Mask For the ScanNet++ [76] dataset, we utilize the provided GT mesh and per-vertex 3D instance annotations, along with their rendering engine to generate instance masks for each image. For the ScanNet [9] and Relica [62] datasets, we observed discrepancies in the masks provided by RICO [32] and ObjectSDF++ [69] . To ensure a fair comparison with the baselines, we merged their instance masks into consistent ones. In our experiments, we focused solely on object-ground support for simplicity and training efficiency, leaving the determination of more general support relationships for future work.Stability Ratio To evaluate the physical stability of a reconstructed object mesh shape, we employ the Isaac Gym [39] simulator. This involves conducting a dropping simulation to determine if the shape remains stable within 5 • in rotation and 5cm translation after the simulation, under the influence of gravity, contact forces, and friction provided by the ground. Next, we define the stability ratio of the scene as the proportion of the number of stable objects to the total object number in the scene. More specifically, we import the object shape and the reconstructed background into the simulator using URDFs that include parameters such as the center of mass, mass, and inertia matrix, where the relative positions of the object shape and background are preserved in the scene. Subsequently, we simulate for T = 200 steps with a time step of ∆t = 0.016s (i.e. 60Hz).Reconstruction Metrics To evaluate 3D scene and object reconstruction, we use the CD in cm, F-score with a threshold of 5cm and NC following prior research [77, 32, 69] . In detail, CD comes from Accuracy and Completeness, F-score is derived from Precision and Recall, and NC is computed using both Normal-Accuracy and Normal-Completeness. We follow previous work [18, 77, 32, 69] to evaluate reconstruction only on the visible areas. These metrics are defined in Tab. A3. Table A3 : Evaluation metrics. We show the evaluation metrics with their definitions that we use to measure reconstruction quality. P and P * are the point clouds sampled from the predicted and the ground truth mesh. n p is the normal vector at point p.Chamfer Distance (CD) In Fig. A2 , we present the reconstruction results of the intermediate states across different stages.Epochs 360 and 430 mark the beginning of the 2 nd and 3 rd training stages. In the 1 st stage, the reconstruction quality of the object's visible structure is continuously improved. In the 2 nd stage, the object areas crucial for stability are optimized with the physical uncertainty. In the 3 rd stage, the reconstructed object reaches stability when the physical loss is introduced. We conduct additional experiments on example scenes from the ScanNet++ dataset to assess the time consumption of the rendering and physical simulation. On average, it takes approximately 0.23 seconds (5.13% in total time consumption) for rendering and 4.25 seconds (94.87% in total time consumption) for physical simulation (including automatic gradient calculation) during one single forward pass. Note that the time required for physical simulation is related to the number of particle points involved, it will vary across different scenes and objects. The above experiments involve around 8000 object surface points and 6000 background surface points (i.e. the supporting plane) on average physical simulation.Additionally, we compare the total training time between our method, RICO, and ObjectSDF++ as shown in Tab. A4 on ScanNet++. Integrating physical simulation has significantly enhanced the stability of the reconstruction results, although it has also increased time consumption. Performance vs. Max Simulation Steps in a Forward Simulation In our framework, the physics forward simulation continues until the object reaches a stable state or the maximum simulation steps are reached. Therefore, the choice of maximum simulation steps affects both simulation time and performance. We conducted a sensitivity analysis of performance versus maximum simulation steps in a forward simulation. The results are evaluated on example scenes in ScanNet++, shown in Tab. A5. The results illustrate that increasing the maximum simulation steps generally improves the final stability of the objects. This trend becomes negligible once the maximum simulation steps exceed 100, as most objects achieve a stable state within 100 simulation steps. This also explains why increasing the maximum simulation steps leads to longer simulation time, though this increase is not linear to the number of steps. Consequently, in the experiments for our main paper, we chose 100 as the maximum simulation steps. Representative failure examples in Fig. 8 present that optimizing with the physical loss may lead to degenerated object shapes, e.g., bulges, to maintain physical stability. This is due to insufficient supervision from the rendering losses. The disconnected parts in the reconstruction results are another common limitation of the current neural implicit surface representation and reconstruction pipeline. This may be addressed by incorporating topological regularization to penalize disconnected parts of the object or further enhancing the simulator. Plus, our particle-based simulator treats all surface points from an object as a rigid body, thus it cannot handle soft bodies (which deform after collision) or dynamic scenes.In addition, our current framework requires additional object-supporting information for the simulation. While determining ground-object support is straightforward, identifying more complex relationships remains challenging. The implicit representation is optimized through per-object physical simulation with the background, for the sake of efficient computation in the current neural scene understanding settings. However, our SP-MC, physical simulator and loss are designed to be compatible with multi-object scenarios, enabling seamless extension to joint optimization for the whole scene, ensuring versatility without loss of generality.3D scene reconstruction in general, while offering various benefits in fields like AR/VR, robotic and Embodied AI, also raises concerns about potential negative social impacts. Some of these impacts include potential privacy concerns in public areas, surveillance and security risks. Addressing these concerns requires careful consideration of ethical guidelines, regulatory frameworks, and responsible development practices to ensure that 3D scene reconstruction is deployed in a manner that respects privacy, security, and societal well-being.NeurIPS Paper Checklist 


Decision: The paper presents PhyRecon, a method combining differentiable rendering and physics simulation to improve 3D reconstruction using neural implicit representations. It introduces Surface Points Marching Cubes (SP-MC) to enhance surface detail and accounts for uncertainties to improve realism and stability. This approach integrates physics simulation with rendering for better 3D reconstruction and significantly improves reconstruction quality and stability. The reviews have concerns on the approach might be too complex, and focuses only on static, rigid objects. After carefully reading the paper, reviews, and rebuttals, the AC recommends to accept the paper.

Reviews: review: paper_summary: paper_summary: This paper proposes a framework for scene reconstruction using neural implicit function with an emphasis on physical plausibility. The key idea is to integrate differentiable physical simulation into the neural scene reconstruction such that the reconstructed shape is stable under gravity. A surface points marching cube method is proposed to convert the neural surface into particles, which is differentiable, enabling the back propagation of gradients from simulation. The authors further propose rendering and physical uncertainty to identify the regions that are not consistent across multiview images and unstable under physical simulation. These uncertainties are beneficial to capture the thin structures of the reconstructed object. Experimental results on various datasets including ScanNet, ScanNet++,  and Replica are conducted to demonstrate the effectiveness of the proposed method.
strength_weakness: strength_weakness: - My major concern of the paper is its novelty. Though the authors position their paper as scene reconstruction, the examples shown in the paper are actually object-centric. In this sense, there are actually a series of works that have explored the physical stability of the generated objects represented as neural functions. Specifically, [37] handles the robustness of slender structure in shape generation, and [38] deals with stability of the generated shape. Especially the second work, it has a very similar problem setting to this paper, as they also first converted the SDF into surface points followed by a differentiable simulator. Somehow I feel the method in [38] is neater since the gradient is propagated to the shape latent code rather than a dense voxel grid as proposed in this paper. Neither [37] or [38] is compared in the experiments. This undermines the motivation and technical novelty of the proposed approach, since compared to shape generation, addressing scene reconstruction exclusively does not pose additional challenges for physical plausibility.

- With the above being said, I think the technical novelty lies in the uncertainty model. However, what confuses me is whether this modeling on the whole voxel grid is necessary. From the qualitative results in Fig. 7, the rendering uncertainty models are mainly helping to grow the shape regions that are "sparsely" covered by the multi-view images. I guess simple post-processing methods such as region growing would be sufficient for dealing with these cases. The physical uncertainty may also be unnecessary: from Fig. 7 and the failure cases in the appendix, physical uncertainty and physical losses are nothing more than changing the geometric shape so that its center of mass lies on the supporting plane of the shape's points connected to the ground. The proposed approach, especially the part of "physical uncertainty",  to me is an overkill to problem. I am also not a big fan of using the term "uncertainty" here since there is really no probability estimation/inference. A better wording could be "heuristics".
questions: questions: See Weaknesses.
limitations: limitations: The authors have provided sufficient limitations and failure cases of the proposed method.
paper_summary: paper_summary: This paper proposes to improve implicit surface representations by considering object dynamics (physics) in their resting state. It made a clever observation that the objects should be stable with respect to their supporting planes if the surface representation is correct. This observation leads to utilizing object surface points in the physical simulator to decide if the objects are stable, by penalizing any instability, the solution encourages more plausible surface reconstruction.

Physical loss and physical uncertainty were introduced, assisted by the proposed SP-MC (Surface Points Marching Cubes) to improve surface point sampling efficiency for deriving the losses in simulations.

Tests on ScanNet and ScanNet++ demonstrated superior results compared to existing works.
strength_weakness: strength_weakness: 1. Applying this idea would require an object mask, and also knowledge of the ground. This is not a constraint in the existing work MonoSDF.
2. The construction of Physical uncertainty (equation 7), based on the trajectory of the point before it makes contact, is not actually the same as the supporting structure of the object. To be more specific, such a trajectory is often a curve unless the object is falling without any rotation. Such a loss would lead to bulkiness in the supporting structure during reconstruction (as seen in Figure 7e).
3. The author mentioned a couple of times about the supporting plane or ground, where is that information from?
4. In general, this physical loss is only applicable to contact the the supporting plane, and not applicable to other contacts (such as a cup on a table).
questions: questions: 1. What is the ground plane, and how is it calculated/retrieved from the dataset?
2. In the losses the author used (as shown in the appendix), a combination of losses from many existing works is used, what would be the performance if the baseline is a version that combined all of the existing losses?
3. Section 3.3 mentioned the physical uncertainty $U_{phy}(r)$, which the author didn’t give a clear definition.
limitations: limitations: The author discussed certain limitations in the Appendix. See the above comments for additional concerns.
paper_summary: paper_summary: The paper introduces a novel method for physically plausible 3D scene reconstruction. It enforces the reconstructions to be in a static equilibrium state, which is achieved by minimizing the displacement of 3D points over time in a differentiable rigid body simulator. The experiments are conducted on scannet/replica/scannet++, showing quite significant improvement over prior methods.
strength_weakness: strength_weakness: - It only deals with static scenes with rigid objects. The physical loss presented is not applicable to complex contact interactions, dynamic scenes or soft materials. But I don't think this is a major issue as the method works well for the indoor scene reconstruction task being considered.
- More explanation on SP-MC is needed. Since the gradient only comes from the refinement step, I would imagine the gradient to be fairly local and noisy. How does it work when the initial shape is far from being physically plausible?
- I'd like to suggest moving appendix C to the main text, since the physical simulator plays an important part in the overall story.
questions: questions: - How expensive is the simulation compared to rendering? e.g., in a forward pass, how much time is consumed by simulation? Does the use of simulation introduce significant compute overhead? Relatedly, I'd like to see a sensitivity analysis of performance vs number of simulation steps.
- How is the ground-plane computed for physical simulation? Does the method handle complex terrian (e.g., with a carpet on the floor, or outdoor scenes)?
- Since the optimization is multi-staged, it will be good to show result after each stage.
- Showing more intermediate results along the axis of optimization would help. For instance, how does the shape change from iteration 0 to final iteration?
limitations: limitations: The paper discussed the limitations and social impact.
paper_summary: paper_summary: This paper addresses scene surface reconstruction in an object-compositional format. Unlike previous work that only considered rendering constraints, the proposed PhyRecon framework incorporates physical constraints into the model training. To identify interaction points, the paper introduces a differentiable transformation between the SDF field and explicit surface points. Using these points, the authors integrate physical constraints into previous approaches to ensure reasonable interactions between objects. To further enhance model performance, they introduce a joint uncertainty modeling design for depth, normal, and physical constraints, which increases the stability of the final reconstruction results. The experimental results demonstrate the effectiveness of the framework and its components, proving beneficial for various downstream tasks.
strength_weakness: strength_weakness: 1. The overall solution is based on ObjectSDF++ and RICO, which requires hours of optimization for training. The introduction of additional constraints in PhyRecon further increases the total training time. Improving efficiency could be a focus for future work.
2. The training process involves three stages: initially applying rendering loss for initialization, then incorporating a physical simulator, and finally introducing a physical loss to stabilize object contact. This multi-stage optimization and the complexity of the loss functions make the entire system intricate.
questions: questions: 1. The method relies on ground-truth instance labels. It would be interesting to explore whether the proposed physical solution can handle noise in the ground-truth 2D instance mask, such as erosion and dilation. While uncertainty training might help mitigate this issue, it is crucial to understand how much the physical constraint can aid in overcoming label noise.
2. In the particle simulator, how does the system perform when the points are sparse and non-uniformly distributed? Understanding the simulator's effectiveness in such cases would be beneficial.
limitations: limitations: The author mentioned their limitation and potential societal impact in the appendix.

Comments: title: More discussion (Cont.)
More discussion
Reply to the rebuttal
comment: **4. Comparison between heuristic region growing and proposed method**

While the goal of reconstruction is to recover the 3D geometry according to the image inputs, we believe existing methods are far from "strictly adhering to image observations in all cases," especially for the less observed ones. In our work, we have made efforts to incorporate uncertainties into the rendering losses to mitigate this gap. On the other hand, how to perform "heuristic region growing" is not trivial (see our discussion in Question 2), and its integration with rendering losses remains unexplored. We consider this comparison to be beyond the scope of the current paper, but we will include this discussion in the revision if additional suggestions arise.


[1] RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation.  
[2] PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification.  
[3] NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis.  
[38] Physically-aware generative network for 3d shape modeling.
Thank you for the suggestions. We have provided further clarification below and will incorporate the discussions in the revision.

**1. Use of MLPs for SDF fields and dense voxel grids**

Thanks for further clarifying your primary concern, which suggests that the shape latent code could be used to further achieve physically plausible object reconstruction for each individual object, similarly to the auto-decoder in [38]. However, we believe that this method may present the following three issues:
* The optimization for the shape code in [38] does not allow for the incorporation of image conditions, and directly integrating rendering loss remains unexplored. In contrast, our method can seamlessly incorporate the rendering losses.
* The above method using shape latent codes requires querying two representations for rendering images or exporting a mesh. In contrast, our method only learns a single representation through NeRF MLPs, which is the sole representation queried during inference, making it more streamlined. The dense voxel grid is only used during training to adjust the loss and guide pixel sampling, without affecting SDF calculation.
* The 3D geometry obtained using the shape latent code is constrained by the generalizability of the pre-trained auto-decoder, which converts the code into an object's SDF. Our method, on the other hand, can effectively overfit the scene without the need for extra data priors.

Thanks again for your comments, we will add more clarification in the revision.

**2. Clarification on rendering uncertainty**

Thanks for further clarifying your original concern. We believe that the simple strategy, e.g., 'growing sparsely covered regions', may struggle to effectively address the issues in reconstructing the thin structures, primarily due to two key challenges:

* **How to locate the less reconstructed regions (e.g., sparsely covered)?** Generally it's non-trivial to identify the 3D regions that require further attention. For example, determining the 3D points visible from images is error-pruning (considering the error in the up-to-scale depth estimation and camera poses),  computationally intensive (enumeration over the 3D space for all input views), and there is no intuitive method to quantify their sparsity. On the other hand, the rendering uncertainties have been proposed to implicitly achieve this goal from the rendering losses perspective. The physical uncertainty also provides explicit and efficient knowledge of where potentially lacks structure from the external knowledge in the simulation. 
* **How to grow these sparsely covered regions?** Designing a heuristic region-growing mechanism within the context of implicit representation can also be challenging, as it may easily lead to degenerated results. This is also the reason why we rely on modulating the rendering loesses to recover the 3D geometry, and only apply physical losses on the contact points. How to effectively grow the region under the image constraints may be a separate problem by itself.

In summary, we believe that the solution to effectively leverage 'simple strategy' is not as intuitive as it may look, and its extension may require extra design choices and hyper-parameter search, which are out of the scope of this paper. However, we will be more than happy to add this discussion to the revision if you have other effective strategies to solve this problem in mind.

**3. Claim of integrating differentiable rendering with differentiable physical simulations**

We clarify our method is distinguished by optimizing the geometry shape using both differentiable rendering and differentiable physical simulations. In contrast, RISP[1] does not optimize object geometry at all, instead, it focuses on controlling given objects within a differentiable physical environment and integrates differentiable rendering into the simulation to improve the generalizability of object control in unknown rendering configurations. PAC-NeRF[2], like vanilla NeRF[3], uses only differentiable rendering to optimize object geometry shape. They employ a physical simulator to optimize the physical properties (such as elastic materials, plasticine, sand, and Newtonian/non-Newtonian fluids) of objects rather than the geometry.

While there are existing works that leverage both differentiable rendering and simulation, our submission and rebuttal describe our work as "the first method to integrate differentiable rendering with differentiable physical simulation *for neural surface reconstruction*." We will add these discussions in the related work section in the revision.
Thank you for the authors’ rebuttal. Unfortunately, many of my initial concerns remain unaddressed. I would like to emphasize that the review and rebuttal process aims to improve the paper and make it compelling to a broader audience. If the paper is accepted, it should clearly convey the technical aspects of the proposed method: what is novel, what is comparable, and in which scenarios the method may fail. Therefore, I encourage the authors to consider my comments as potential questions that any general reader might ask. While these comments do not necessarily lead to the rejection of the paper, addressing them can significantly enhance the paper’s impact and solidity.

Detailed responses to the authors’ rebuttal:

**1. Use of MLPs for SDF fields and dense voxel grids** 

The authors state that their method employs MLPs to model SDF fields and rendering uncertainty, while a dense voxel grid is used solely for modeling physical uncertainty, reflecting accurate 3D physical information from the simulator. However, using MLPs for SDF does not inherently preclude the use of a dense voxel grid, as querying dense voxel positions is necessary for rendering images. My primary concern was whether the “dense voxel grid” is truly necessary, particularly when compared to the shape latent code used in [38]. I would be convinced if the authors provided results or compelling arguments demonstrating the advantages of the dense voxel grid over shape latent code, such as better reconstruction quality, faster convergence, or reduced computational resources.

**2. Clarification on rendering uncertainty**

The authors assert that my review implied that their method was “growing the shape regions that are sparsely covered by the multi-view images,” which was not true. My original concern was whether a simpler strategy, such as growing sparsely covered regions, might be sufficient to address the issue, rather than employing a complex model for “rendering uncertainty.”

**3. Claim of integrating differentiable rendering with differentiable physical simulations**

The authors claim that their work is the first to integrate differentiable rendering with differentiable physical simulations for learning implicit surface representation. I find this claim invalid, as there are already published works [1, 2] that achieve similar integration. Additionally, positive comments from other reviewers do not necessarily resolve the concerns I raised.

[1] RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation, ICLR 2022.
[2] PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification, ICLR 2023.

**4. Comparison between heuristic region growing and proposed method**

The authors argue that heuristic region growing could lead to degenerated results deviating from the image observations. While this is true, it does not imply that the proposed method strictly adheres to image observations in all cases. A comparison between the two approaches would be necessary to substantiate this point.

The remainder of the rebuttal has adequately addressed my concerns.
Thanks for the rebuttal, which addressed my questions. I'd like to keep my rating and recommend for accpetance.
**5. "Uncertainty" or "heuristics".**

Although the uncertainty mentioned in this paper is not the same as the uncertainty in Bayesian learning, we use "uncertainty" in accordance with prior work [2, 3, 4] in NeRF and neural scene reconstruction.

[1] DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation

[2] Activenerf: Learning where to see with uncertainty estimation

[3] Conditional-flow nerf: Accurate 3d modelling with reliable uncertainty quantification

[4] Debsdf: Delving into the details and bias of neural indoor scene reconstruction

[37] Physical simulation layer for accurate 3d modeling

[38] Physically-aware generative network for 3d shape modeling
**6. How is the ground-plane computed for physical simulation? Does the method handle complex terrian (e.g., with a carpet on the floor, or outdoor scenes)?**

We use the supporting plane (i.e. the ground-plane in reviewer question) to provide contact and friction for object surface points in the physics simulation. For objects on the floor, we use SP-MC to obtain the surface points of both the object to be simulated and the background before each simulation. Additionally, we only include the background surface points located within proximity under the object surface points in the simulation to reduce computational load.

This means our method is capable of handling more complex terrian, e.g., the carpet or outdoor scenes, if the corresponding SDFs are adequately trained.

**7. The physical loss presented is not applicable to complex contact interactions, dynamic scenes or soft materials.**

Yes, the current design of the physical loss and physical simulator in the paper is based on the assumption that rigid bodies move under the forces of gravity, contact, and friction. Thus, it cannot handle soft bodies (which deform after collision) or dynamic scenes. Extending the physical loss for broader applications and enhancing the physical simulator to support soft body collisions would be an interesting direction for future research. We will add this as an limitation and future potential in the revision.

**8. Moving appendix C to the main text.**

Due to the length limitation of the paper, we placed the implementation of the differentiable particle simulator in the appendix. Thank you for your suggestion, we will add relevant content to the main text in a future revision.


[1] DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation