Title: Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing
Venue: NeurIPS 2025
Accepted: yes
Keywords: neural fields

sdf

deformations

arap

geometry

implicit
Abstract: Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner -- particularly under spatial constraints -- remains an open challenge, as existing approaches struggle to balance surface quality, robustness, and efficiency. We address this by introducing a novel method for handle-guided neural field deformation, which leverages discrete local surface representations to optimize the As-Rigid-As-Possible deformation energy. To this end, we propose the local patch mesh representation, which discretizes level sets of a neural signed distance field by projecting and deforming flat mesh patches guided solely by the SDF and its gradient. We conduct a comprehensive evaluation showing that our method consistently outperforms baselines in deformation quality, robustness, and computational efficiency. We also present experiments that motivate our choice of discretization over marching cubes. By bridging classical geometry processing and neural representations through local patch meshing, our work enables scalable, high-quality deformation of neural fields and paves the way for extending other geometric tasks to neural domains.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a technique for handle-driven deformation of shapes represented as implicit surfaces. To enable plausible deformations, the authors propose a method for evaluating the widely used As-Rigid-As-Possible (ARAP) energy directly on implicit surfaces. Since ARAP traditionally relies on information such as edge lengths and surface connectivity—data that are not readily available in implicit representations—the paper introduces a strategy to approximate these quantities in the implicit domain. Specifically, the proposed method projects a set of planar meshes onto various level sets of the implicit function approximating the target surface. These projected meshes are then used to compute the ARAP regularization loss by leveraging the connectivity between their vertices. Combined with soft handle constraints, this regularization loss guides the optimization of a deformation field parameterized by a neural network.\n\nSTRENGTHS AND WEAKNESSES:\nThis paper presents a straightforward technique for estimating ARAP energy in the context of deforming implicit surfaces. The approach involves projecting a set of 2D mesh patches onto the target surface and leveraging their connectivity to approximate the ARAP energy.\n\nWhile the core idea is interesting, I have some concerns regarding its practical applicability and use cases. A rich set of tools for processing implicit surfaces—such as mesh extraction, topology optimization, and mesh-based deformation—has been extensively studied and is already well-established in the computer graphics literature. As a result, while the paper demonstrates that deformation in the implicit domain is feasible, it remains unclear whether this approach offers tangible practical benefits over existing methods. In particular, the requirement to train and store a separate neural network for each deformation step could lead to inefficiencies, especially in interactive design scenarios where multiple deformations are applied in sequence. Addressing this limitation or proposing ways to mitigate it would further strengthen the work.\n\nAlthough the paper targets a well-defined problem, the overall scope of the contribution feels relatively narrow—especially when compared to related efforts such as [1], which address a broader range of surface properties (e.g., normals, curvature) and additional applications like smoothing and sharpening.\n\nLastly, the experiment section feels somewhat unorganized. For example, acronyms such as “EL” and “FA” (Line 228) are used without prior introduction, and some results referenced in the text—such as those on the DFAUST dataset mentioned in Line 234—are not presented in the main paper. Clarifying these points would improve the clarity and completeness of the experimental evaluation.\n\n[1] Geometry processing with neural fields, Yang et al., NeurIPS 2021\n\nQUESTIONS:\n1. Have the authors considered using volumetric meshes when applying discretization-based deformation methods? Since the proposed method benefits from the volume preservation property of the NICE model, while many baselines operate solely on surface meshes, this comparison may seem somewhat unbalanced.\n2. Could the authors provide statistics (e.g., mean and standard deviation) for the vertex and face counts of the meshes used in the comparisons? This includes both the raw outputs from Marching Cubes and their re-meshed versions.\n3. While Table 1 reports that the proposed method achieves zero volume error, Figure 9 shows that all patch construction methods exhibit some degree of volume error. Could the authors clarify this discrepancy? Additionally, please provide dataset details—specifically, which shapes and how many were sourced from the Thingi10K and DFAUST datasets?\n4. In the “Data and baselines” paragraph, the authors describe three variants of the proposed method. Which variant corresponds to “Ours” in Table 1?\n\nLIMITATIONS:\nYes. The authors discussed the limitations of their work.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 1, "ORIGINALITY": 1, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a local patch meshing strategy as a bridge between neural implicit fields and mesh-based shape manipulation. Instead of relying on explicit iso-surface extraction (e.g., via Marching Cubes), the method projects and deforms predefined patch meshes using signed distance function (SDF) values and gradients. By randomly sampling patch meshes from various level sets of a neural SDF, the approach enables the use of mesh-based deformation priors such as ARAP loss for shape manipulation.\nThey show reliable and efficient mesh deformations, offering better computational efficiency compared to full-surface extraction and remeshing pipelines. In addition, the paper includes extensive ablation studies on hyper-parameters such as patch size, density, sampling strategies.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\nThe work is well-motivated and presents an interesting idea by introducing ARAP-based deformation constraints into neural field representations, without requiring explicit mesh extraction. The proposed local patch meshing strategy provides a flexible and generalizable way to represent local surface geometry across arbitrary level sets of the SDF. It also demonstrates robustness to variations in patch structure, patch density, and input mesh resolution.\nFigures 13 and 14 show that the method produces more plausible and stable mesh deformations on the TDF and DFAUST datasets compared to existing baselines, highlighting the practical advantages of the approach in real-world scenarios.\n\nWeaknesses:\n1)\tFrom the quantitative results in Tables 1 and 4, the method is inferior to some baselines regarding Area, EL, and FA.\n2)\tMissing comparison against two recent works:\nneural network optimization-based method -- NJF\nlearning-based shape manipulation method -- NSDP\nAigerman, et al. Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes. SIGGRPAH 2022\nTang, et al. Neural Shape Deformation Priors. NeurIPS 2022\n\nQUESTIONS:\nThe current mesh deformation evaluation primarily focuses on geometric preservation metrics such as edge length, volume, and face angle. However, it might be beneficial to include vertex-wise error metrics between the deformed and target mesh, especially if temporal mesh sequences are available. In such cases, a subset of vertex displacements could serve as handle movements to be used as input constraints for the deformation method.\nThe paper could be further strengthened by including comparisons against two more recent methods,  Neural Jacobian Fields (NJF) and Neural Shape Deformation Priors (NSDP), which addresses similar challenges in non-rigid deformation.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper address the existing challenge of deforming shapes represented by neural fields. It leverages local mesh representation to be deformed with guidance by the SDF and its gradient. Experimental comparison with baselines demonstrates the superiority in terms of deformation quality, robustness, and computational efficiency.

STRENGTHS AND WEAKNESSES:
Strengths

- The technique is well developed. It leverages the ARAP in an elegant way to solve the deformation of SDF. The deformed shape can be represented as a invertible MLP of the deformation along with the original sign function.
- Experimental results study the robustness of the technique to the samples local patch. 
- The comparison against baselines shows superiority.

Weaknesses
- The Fig.5 is challenging to look at, especially for the layers, although it delivers the information that the proposed method is better.

QUESTIONS:
- is it possible to approximate the deformed SDF with a new SDF, rather than composing the R and f with two separated models?

LIMITATIONS:
There is paragraph discussing limitations in the conclusion.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a local patch based meshing technique for the purpose of neural field deformation. It is positioned in contrast to Geometry Processing for Neural Fields (GPNF) paper in the sense that it is solving a more specific problem of handle guided neural deformation -- which is does in a fraction of time (and with higher quality) compared to GPNF. The local patch based meshing avoids the need for repeated marching cubes steps that make optimization very costly. Moreover the local mesh structure naturally provides the topology information to apply ARAP which is not possible in a pure neural field setting. Experiments are conducted large scale datasets such as Thingi10K and DeFAUST which corroborate the paper claims. Ablations are provided for various design choices made in the method which help in understanding contributions of individual components.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n\n1. For the task of ARAP, the approach taken by the paper makes total sense as local patching provides a natural means to apply ARAP loss. I am also hopeful that this approach can be explored in future works for other geometry processing/ graphics tasks like UV mapping, etc. \n\n2. The performance gains achieved viz time saved and improved accuracy (especially in volume preservation) are noteworthy. I find the ablations quite useful. \n\nWeakness:\n\n1. The difference in method is not very clear with respect to GPNF. I find several similarities -- GPNF too seems to not require MC for its optimization. It looks like the use of an invertible neural network model for approximating the deformation field is also present in GPNF. So what are key differentiations other than the fact that a local mesh structure allows for ARAP like losses to be applied? \n\n2. I don't get why GFNP's volume loss is also not zero given that it too uses an invertible network which in theory should also be volume preserving as is the case in this paper?\n\n3. I am also not very clear about the reason for ARAP (mesh based) to have such artefacts as shown in Figure 4. Why is the paper theoretically superior in approximating deformations? Is this supposed to do with the discretisation of ARAP? \n\n4. I believe the paper would benefit from giving a more gentle introduction to ARAP, and the baselines considered while highlighting the key differences.\n\nQUESTIONS:\n1. Given that the paper is solving a specific part of the larger geometry processing problems handled by GPNF, I am curious to know what prevents the local patch based meshing to handle tasks other than ARAP? Perhaps a detailed discussion on this would be helpful to the reader. \n\n2. Can you throw some clarity on why GPNF takes 14hrs?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}