PartSDF: Part-Based Implicit Neural Representation for Composite 3D Shape Parametrization and Optimization
Authors: Nicolas Talabot
Olivier Clerc
Arda Cinar Demirtas
Hieu Le
Doruk Oner
Pascal Fua
Venue: Accepted by TMLR ()

Abstract: Accurate 3D shape representation is essential in engineering applications such as design, optimization, and simulation. In practice, engineering workflows require structured, part-based representations, as objects are inherently designed as assemblies of distinct components. However, most existing methods either model shapes holistically or decompose them without predefined part structures, limiting their applicability in real-world design tasks. We propose PartSDF, a supervised implicit representation framework that explicitly models composite shapes with independent, controllable parts while maintaining shape consistency. Thanks to its simple but innovative architecture, PartSDF outperforms both supervised and unsupervised baselines in reconstruction and generation tasks. We further demonstrate its effectiveness as a structured shape prior for engineering applications, enabling precise control over individual components while preserving overall coherence.

Published in Transactions on Machine Learning Research (10/2025)
PartSDF: Part-Based Implicit Neural Representation for Composite 3D Shape Parametrization and Optimization
Nicolas Talabot EPFL
Sicobas.talbbott@ep...cc
Olivier Clerc
EPFL
Arda Cinar Demirtas Bilkent University
Alexis Goujon
Neural Concept
Hieu Le EPFL, University of North Carolina at Charlotte
hle40@ccarlltte..de edu
Doruk Oner
Caruk..nerrBbilent..ccci
Bilkent University
Pascal Fua EPFL
fascal.fua@effe
Reviewed on OpenReview:
https: // openreview. net/ forum? id= #143C1yBKo
Abstract
Accurate 3D shape representation is essential in engineering applications such as design, optimization, and simulation. In practice, engineering workflows require structured, part- based representations, as objects are inherently designed as assemblies of distinct compo- nents. However, most existing methods either model shapes holistically or decompose them without predefined part structures, limiting their applicability in real-world design tasks. We propose PartSDF, supervised implicit representation framework that explicitly models composite shapes with independent, controllable parts while maintaining shape consistency. Thanks to its simple but innovative architecture, PartSDF outperforms both supervised and unsupervised baselines in reconstruction and generation tasks. We further demonstrate its effectiveness as a structured shape prior for engineering applications, enabling precise control over individual components while preserving overall coherence. Code available at https://github... wttp:/twwwb.occ.aaaaoooooe.e cttp///labbbpff//aartt
1 Introduction
Engineering design is fundamentally part-driven. Whether it's car with distinct wheels, a chair with adaptable legs, or an industrial mixer with a removable helix, objects are designed and reasoned about in terms of their components. These parts are not just geometric regions-thl carry semantics and functional roles and must satisfy number of constraints. In real workflows, enginoers rarely optimize or modify shape as whole. Instead, they manipulate individual parts, often under precise constraints, while expecting the overall assembly to remain coherent and valid.

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O
(b)
Figure 1: Part-based implicit representation. PartSDF is a simple and modular approach to represent- ing composite 3D shapes for many different purposes: (a) Shape generation, possibly conditioned on a part layout. (b) Part-based manipulation. (c) Part-aware optimization. In this examplc, the car body, shown in red, is optimized to reduce aerodynamic drag while maintaining the shape and position of the wheels fixed.
Despite this, most 3D shape modeling methods relying on machine learning treat objects as indivisible units holistic fields, point clouds, or meshes with no modular structure. particular, Implicit Neural Representations (INRs), first introduced in (Park al. 2019 Mescheder et al.] 2019 Chen & Zhang, 2019)
and then refined in works such Zhang et al. (2022 2023 yield impressive fidelity and flexibility but often encode shapes global functions with no built-in notion of parts. This makes tasks like part-specific manipulation, targeted optimization, or structured shape generation surprisingly difficult, often requiring cumbersome post-processing or bespoke architectures.
Although introducing parts into INRs might seem straightforward, it is, in fact, far from trivial. Modeling parts isolation can easily break the continuity and alignment of the overall shape (Wu et al., 2020 Deng ett a 2022). Training such models often assumes clean, watertight geometries for each part an assumption rarely met in real-world data. And even if each part is modeled successfully, how can ensure that they remain responsive to one another so that modilying one component, like enlarging the wheel of car, naturally causes other parts, such as the car body, to adapt in response?
In this work, we introduce PartSDF, a simple yet effective framework for learning part-aware shape represen- tations using signed distance functions. Each part is represented by a latent vector and a pose capturing its geometry and spatial configuration- by taking the minimum across part SDFs, producing seamless composite. This formulation is modular, supports precise part control, and naturally composes into globally coherent shapes.
decoded by a novel shared implicit model. The full shape emerges
To make part-based modeling practical and robust, we develop decoder architecture that enables dynamic interaction between parts during inference. This decoder involves multiple lightweight convolutions that operate within each part and across parts respectively, enabling part-wise information exchange into a shared intermediate representation and allowing each part to adapt itself based on the geometry of others. This yields consistent dcformations, without heavy computations and without resorting to complex hicrarchical assemblies or atlention-based systems (Deng al. 2022 Hertz al. 2022 Li et al.) 2024). Complementing this, propose novel supervision scheme that bypasses the need for clean, watertight part meshes. Instead of requiring explicit SDF supervision for each part, derive supervisory signals from the global shape's SDF, applied only within regions of space closest to each part. This strategy aligns with the natural spatial semantics of parts and allows effective training even when part segmentations are not watertight, broadening the method's applicability without compromising geometric fidelity.
This results in a versatile and fully differentiable multi-part representation that is both compact and expres- sive. It can be applied across tasks-inchuding shape reconstruction, part-aware generation, and constrained optimization without modifying the core auto-decoder architecture, illustrated in Figure [ Even though its architecture is simpler than that of other state-of-the-ai metsods, PartSDF not only improves perfor- mance on traditional benchmarks but also opens up practical capabilities that are hard to achieve with existing methods, such as optimizing a car body for drag while keeping its wheels fixed or generating diverse furniture layouts with interchangeable components.
This combination of simplicity and effectiveness is made possible by the following innovations.
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We introduce supervised, part-aware implicit representation that models each component indepen- dently, ensuring both expressi veness and part consistency for composite objects, key component of which is an innovative decoder that enforces consistency without undue complexity.
We demonstrate that our approach serves as a versatile basis for various tasks such as shape recon- struction, manipulation, and optimization, all with the same core decoder network.
We propose novel part supervision technique relying on the full shape's SDF and inter-part losses, applicable to both watertight and non- won-watert segmentations.
Through comprchensive evaluations, we show that PartSDF effectively captures the structure of composite shapes, making it well-suited for engineering applications requiring part-aware representation and control.
2 Related Work
Over the last several decades, the evolution of traditional CAD systems has reflected fundamental tension between simplicity and expressiveness. Early approaches relied on basic geometric primitives such as spheres, cylinders, and NURBS surfaces [Peeg] 1991). offering mathematical precision but limited representational power. Recent years have witnessed a shift toward more sophisticated primitives, from simple cuboids (Tul- siani et al. 2017 Niu et al. 2018 Sun et al. 2019 Kluger et al. 2021] to learned deep representation, which we briefly review here. We start with generic 3D shape representations learned from data and continue with more flexible part-based approaches.
2.1 Learned 3D Shape Representation
Learning-based methods for 3D shape representation have evolved significantly. beginning with explicit ones such as voxel grids, point clouds, and meshes. Voxel methods (Wu et al. 2015 2016 Choy et al. 2016b Dai et al.] 2017) partition 3D space into grids but are memory-intensivee at finer resolutions, which can be mitigated using octrees (Riegler et al. 20177 Tatarchenko al.) 2017), but only up to a point. Point clouds roduce memory costs by representing shapes
set of points but ignore connectivity, which can compromisc
topological consistency (Fan et al.
2017 Yang el al.
2018 Achliopias el al.
2018
Peng el. al. 2021 Zeng
et al. 2022 Meshes, though well-suited for detailed surface representation, impose rigid topology that is
difficult to modify (Groueix et al.
2018 Kanazawa et al. 2018 Wang et al.
2018 Pan & Jia
2019
Implicit Neural Representations (INRs) offer a. flexible alternative, defining shapes as continuous functions
of the 3D space that encode the surface implicitly (Park al. 2019 Meschoder al. 2019: Chen & Zhang,
Xu et al.) 2019). It can then be recovered explicitly using meshing algorithms (Lorensen & Cline Lewiner et al. 2003 Ju et al. 2002). Even though these meshing algorithms may not be themselves differentiable, differentiability can be preserved by relying on the implicit function theorem (Guillard et al. 2024), enabling pock-propagation from the explicit surface, for example, when optimizing a shape to maximize its aerodynamic performance (Baqué et al.] 2018). Extensions enable shape manipulation (Hao el. al.) 2020). point-cloud reconstruction (Peng et al.] 20200,, and training directly from point data (Atzmon & Lipman 2020 Gropp al.) 2020). Newer works (Sizzmann et al., 2020 Takikawa al. (021) improve the accuracy Turther with new latent struetures, such grids (ann 2022 Mittal al.] 2022), irregular grids (Zhang)
2019
1987
et al. 2022 or unordered sets (Zhang et al. 2023). and using generative models within these latent spaces.
2.2 Part Based Models
As effective as they are, the INRs described above model 3D shapes as single entities, limiting their capacity represent structured, part-based composite objects. This requires decomposing the shapes into their component parts, which can be done in a supervised or unsupervised manner.
Unsupervised Part Decomposition. Early unsupervised approaches learn shape abstractions using local primitives such as cuboids (Tulsiani al. 2017 Zou et al. 2017 Sun et al.) 2019 Smirnov et al.) 2020 Yang & Chen 2021), superquadrics (Paschalidou et al. 2019 2020). anisotropic Gaussians (Genova et al. 2019), convexes (Deng et al. 2020), approximating complex shapes combinations of simpler parts.
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More recently, complex objects are better represented by predicting and deforming primitives (aaschalidou 2021 Shuai et al. 2023). creating deformable part templates (Hui et al.) 2022), or performing part-
et al.
based co-segmentation, which consistently divides shapes into parts across a dataset without relying on
labeled boundarics (Chen ct al. 2023 or does so for only a subset of the data (Chen et al.) 2019). Instead.
RIM-Net (Niu et al. 2022) learns hierarchical structure of INRs, while PartNeRT (Tertikas et al. 2023)
proposes a rendering-baae based approach for generating part-aware editable 3D shapes. SPAGHETTI (Hertz
et al. 2022) predicts Gaussian parts from a global latent vector and reconstructs them into a single cohesive
object, supporting interactive editing of user-defined parts. It can be combined with SALAD (Koo et al. 2023), which employs a cascaded diffusion model for part generation.
However, the parts learned by these methods are typically arbitrary and lack semantic meaning, making them unsuitable for tasks requiring specific, predefined part structures.
Supervised Part Representation. Supervised methods leverage known part decompositions to create explicit, structured representations of composite shapes. SDM-Net (Gao et al.
2019
proposes VA at the
part and shape levels to learn deformable meshes. HybridSDF (Vasu al.) 2022
mixes INRs with geometric
primitives to represent and manipulate shapes, while ANTSF (Petrov et al. 2023 learns to assemble implicit
parts for reconstruction from images and point clouds. Recently, DiffFacto Nakayama et al. 2023 proposes
cross-diffusion (o generale and control part-based point clouds, which are, however, not suited to engineering needs such as simulations. Instead, PQ-NET (Wu et al.) 2020), ProGRIP (Deng et al. 2022), and PASTA (Li focus on implicit composite shape generation. PQ-NET uses a recurrent neural network (Cho
itt al. ct al. generation, while ProGRIP relies on shape programs to produce composite INR shapes. PASTA employs an autoregressive transformer to predict part bounding boxes that are decoded into a single global shape.
2024)
2014] as an auto-encoder for sequences of parts, using a latentGAN (Achlioptas et al. 2018 for
While effective for shape generation, these methods typically forgo part consistency across shapes, thus continuous parametrizat and the representation of individual parts. Thus, there is need for an approach that leverages part supervision to produce modular, flexible representations that can output composite shapes by parts and act as a prior in backward tasks such as optimization. PartSDF aims to fulfill that need.
Part-Aware Generation from Images. In addition to methods trained with 3D part supervision, several recent works explore part- or object-aware 3D generation, typically from images. Part123 (Liu et al. 2024 and PartGen (Chen al. 2024) both begin by generating multi-view renderings with associated 2D part segmentations. Part123 then employs NeuS (Wang et al.) (021) to recover part geometries, while PartGen predicts completed part images to fill occlusions before reconstructing their 3D geometry; it can also operate from text prompts in addition to images. Concurrently, MIDI (Huang et al., 2025), addresses single-view scene reconstruction by segmenting objects and conditioning a 3D diffusion model on each object instance, with cross-object attention, while CAST (Yao et al.) 2025) performs open-vocabulary scene reconstruction from an RGB image using largo-scale pro-trained foundation models, diffusion, and physics-aware post- processing.
Unlike PartSDF, these approaches primarily focus on image-to-3D pipelines and emphasize image reconstruc- tion, as opposed to geometric accuracy case of manipulation. In contrast, PartSDF learns supervised, part-aware implicit representations with explicit latent parametrization, enabling coherent part manipulation and constrained optimization, which are crucial in engineering and design scenarios.
3 Method
We introduce PartSDF, modular and structured composite shape representation built on signed distance fields (SDFs). As shown in Figure a), cach object is represented by a set of parts, each one being param- eterized by a latent code capturing its geometry, along with pose parameters defining its spatial placement (Section 3.1.. These per-part representations are decoded into SDFs using a cross-part decoder (Section 3.2 which supports both independent part modcling and inter-part coordination. It is trained in an auto-dccoding fashion (Park et al. 2019) in which the latent vectors and the decoder's weights are learned simultancously, with supervision applied at both the global and part levels (Section 3.3
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Part latents
Part SDFs
Global SDF
Part latents
Cross-Part Decoder fo
Zp
min
Zp
Meshing
Meshing
Encoder, Diffusion,
9p, 1p $p
T
4p tp Sp
Part poses
Part poses
Point cloud,
Query position
noise,
(a) Composite shape auto-decoding
(b) Part encoding generation
Figure PartSDF pipeline. (a) Our model's core a part auto-decoder Sa that takes as input part latents Zp and poses expressed in terms of quaternion qp, translation ty, and scale Sp, along with the query position RR3 It outputs signed distances 8p for all parts at the queried position, which may be combined into the global signed distance. (b) A secondary model may be used based the task at hand, such encoders to map a given modality, e.g., point clouds, to part latents and poses, diffusion model to generate them from noise.
As shown in Figure b), our architecture supports secondary models for part encoding or generation, allowing further adaptation of part latents and poses for tasks such as shape reconstruction or generation, while maintaining the same core part decoder for efficient inference and manipulation (Section 3.4.
3.1 SDF Computation
In our composite shape representation, each part is described by a latent vector 2p E TR22 and a pose Pp E 1R consisting of rotation quaternion qa E IR,, translation tp E IR3, and scale Sp R3. Given query point x R3, it is mapped into each part's canonical space via inverse transformation T-1, resulting in the transformed query points
x T (x. Pp) = (x - tpp/sp. Vp.
(1)
where Rp is the rotation matrix obtained from 9p- Our cross-part decoder fe, with 0 containing all trainable parameters, operates on all parts' latents Z and transformed query points X to output the part SDFs
$ = Z
(2)
The SDFs for all parts can then be combined to recover the full shape representation as & = min, 8p.
3.2
Cross-Part Auto-Decoder
To represent complex shapes in a modular yet coherent manner, we introduce an innovative decoder that explicitly handles multiple interacting parts. At each layer, the decoder maintains a multi-part feature matrix x' E x'ERPxx PxD:: where each row corresponds to a part and each column to a shared feature dimension. This structure maintained throughout the network, preserving an explicit notion of parts across all layers. As a result, the decoder's output naturally yields one part per row- enabling direct, part-specific SDF predictions.
To achieve this, we design the network to alternate between two types of layers: single-part layers that updale parts independently and cross-part layers that enable controlled feature sharing across parts.
Single-part layer. The first type of layer processes each part separately, allowing the network to learn the shape distribution of individual parts, denoted as hap:
1+1 -i/p (Mpp x²) = (W +b' + W +b,)
(3)
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H
Ryp
Pep
Pap
non Brear
PxD
Figure 3: Cross-part adaptation in PartSDF. Our decoder alternates between updating each part independently and sharing information across parts, allowing them to adapt to one another while pre- serving modularity. This is implemented through sequence of lightweight convolutions applied along rows and columns of the part feature matrix.
(a)
(b)
(c)
Figure 4: Supervision for non-watertight parts. (a) Semantic parts of a chair, (b) a 2D slice of its signed distances (red/blue) with parts high- lighted in color, and (c) the specific regions of space where cach part is supervised. This enables training without requiring parts to be watertight.
where a is an activation function, x denotes the p-th row of X i.e., the features of part p at layer L, (W',bl are the layer's parameters, W is the parameters of a latent modulation (Dupont et al. 2022). and by, the lcarnable bias of part p at layer l.
Cross-port layer. The second type of layer enables feature aggregation across parts, denoted as hep. For each feature dimension d, we write
X = -0
=
(4)
where x denotes the d-th column of X i.e., the d-th feature dimension across all parts, and (Wi, bb) are the layer's parameters. This layer enables the decoder to capture inter-part dependencies and improve adaptability during part manipulation with as little as p2 + P added trainable parameters per such layer, with P the number of parts, as shown in our ablation study of Section 4.5 We also add a skip connection to ensure these layers don't mix part identities.
By stacking alternating hap and hep layers (sce Figure 3), which can be efficiently implemented using convo- lutions, the decoder enables each part to specialize while remaining aware of its context producing modular, adaptive, and coherent shape representations. We provide network details in Appendix B.1
3.3 Learning from Global Shape Supervision
Let us consider dataset D where each shape S is decomposed into up to P parts, given as the segmentation of its surface, as commonly found in online databases. To establish initial poses for each part, we fit simple primitives cuboids or cylinders- to the segmented parts and use these primitives' poses as the part poses, Therefore, cach clement of the dataset becomes tuple D {S, (Pp). {Pp]),) of the shape, its parts, and their poses Py = (qp= hp: Sp).
Training the Decoder. For watertight shapes S, PartSDF's decoder is then trained in auto-decoding fashion (Park et al. 2019), where model parameters 0 and part latent vectors Zp are optimized jointly. Note that we can directly use the parts poses from D during training. When a part is missing from a specific shape, we assign it the average pose of that part over the dataset, allowing the model to naturally learn to output SDF > 0 for nonexistent parts, without having to predict existence scores, as Petrov et al. (0023)
Some parts Pp, however, may not be watertight they correspond to open surface fragments rather than closed volumes common characteristic of online part-based CAD models. This makes it difficult to compute reliable per-part signed distance fields, especially near part boundarics or in regions where parts overlap. While one option is to repair or approximate each part's volume (Wu et al. 2020: Petrov el al., 2023), this often introduces artifacts and scaling issues. Instead, we take advantage of a key observation: when reconstructing the global shape as the minimum across all part SDFs, only the part whose surface is closest a given point affects the output. We therefore supervise each part using the global shape's SDF, but only in regions of space where that part is closest to the surface.
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Formally, part Pp is supervised only at points
x x R2 Ip= arg mind(())))
(5)
where (x) the projection distance of to part i, depicted by Figure This region-based supervision ensures that each part learns only the portion of space it is responsible for and avoids penalizing it in regions where it is occluded irrelevant. Crucially, it allows us to train directly from surface-based part annotations, without requiring watertight meshes or explicitly constructing per-part SDFs.
To further encourage modularity, we introduce a non-intersection loss that penalizes overlapping negative SDF predictions across parts. This promotes clean spatial separation, ensuring that each part occupies a distinct region of space-cruchs for enabling localized editing, part replacement, and consistent composition under the minimum-SDF fusion.
Loss Function. For any shape from D, minimize
[ Ladt + Cpart + Linter Σ
1zpl13
(6)
where À is a hyperparameter controlling the latent. 122regularization and the loss terms are defined below. For the whole shape, we minimize
Laat
Σ
18-8.1
X
(xx,9:)EX'
where X' is a set of sampled points in 3D and around S, with their ground truth SDF 8; from the full shape S. is the predicted SDF at those points. For notational simplicity, we omit the dependency on and the Zp along with the clamping of SDF values (Park et al. 2019).
For individual parts, we minimize
Carr
Σ
1pp. - -s,,
(8)
X
with an additional index p: of the part closest to x,, re-using X' as slight abuse of notation to explicitly state that we compute these losses on the same 3D samples. 8p, is the predicted part SDF at those points.
Finally, we introduce a non-intersoction loss that pushes the SDF of parts to be positive at cach position x; where at least two parts have SDF< 0. Using & as the subset of such 3D points, the loss written
Linter
Σ X.E
kww.sp/
where & is the vector of predicted part SDF at point x; and w, = softmax (S:), defining 8; as 8; with all posilive values replaced by -oo. This pushes towards more strongly the SDFs that are closer to
3.4 Part Encoding and Generation
Once PartSDF's decoder is trained, is frozen to be used reamstream tasks, optionally in conjunction with separate specialized networks. While this requires training two networks independently, makes the training of each one easier. Furthermore, the decoder need only be trained once and used again and again for the different tasks.
Encoding To reconstruct a shape from a given modality, e.g., point clouds or images, encoders can be trained to directly predict part latents and poses, to then be decoded with PartSDF: With input data I corresponding to the shape our training data D, encoders are trained to map this new modality to the part latents and poses of our pre-trained decoder. As an example, we show how to reconstruct unseen shapes for which part decomposition is unknown in Section 4.1 We do this by training point cloud encoder to predict part latents and poses, which then refined in auto-decoding strategy and part-agnostic manner.

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Generation For shape generation with coherent part set, generative models can be trained to map random noise to the parts parametrization. Generative Adversarial Networks (GAN) (Goodfellow et al. 2014) have been used to generate shape latents, often dubbed latentGANs in related work (Achiioptas ct al. 2018 Chen & Zhang 2019) such as PQ-NET (Wu et al., 2020p. Recently, diffusion models (Sohl- Dickstein et al. 2015 Ho et al. 2020) have gained a lot of traction for their generative performances, even shape (Zhang et al.) [022)] or part-based generation (Koo et al. 2023). Generating new shapes with PartSDF can be achieved by training such generative models on the part poses and latents of our pre-trained decoder
and, even if not shown here, could be conditioned on images texts (Zhang et al. 2023 Koo et al. 2023)
4 Experiments
We demonstrate our method on several tasks and compare it to multiple part-based baselines. Additional implementation details and results are given in Appendices B and G
Datasets Public shape datasets like ShapeNet (Chang et al. 2015 and PartNet (Mo et al. 2019 often suffer from ser--eegmentttinn or inconsistent part definitions. To address this, we use three curated datasets with clean, consistent part decompositions: (1) Car, a hand-processed ShapeNet subset with separated wheels; (2) Mizer, liquid mixers with a helix, tube, and two attach points (Vasu et al. 2022); and (3) Chair, cleaned PartNet-based set with individually segmented legs and arms. These datasets contain 1046, 1949, and 1332 shapes with 5, 4, and 8 parts, respectively. We use 80% for training and 20% for testing.
Baselines. We compare against part-based methods across different supervision levels to evaluate their ability to represent composite shapes: DAE-NET (Chen et al., 2023) (unsupervised deformable parts), BAE-NET (Chen et al.
2019) (weakly supervised with 8 labeled shapes), PQ-NET (Wu et al.) (0200) and PASTA Li et al., 2024) (fully supervised, though PASTA does not. output parts). We also evalu- ate 3DShapc2VocSet (Zhang et al. 2023), a ttate-of-the-art, non-part-based method that, while unsuitable for composile shapes, provides an upper bound on achievable accuracy without enforcing part structure.
Metrics. Reconstruction accuracy is assessed using three different metrics: surface accuracy, Intersection over Union (IoU) for volume, and Image Consistency (IC) (Guillard et al. 2022) for shape appearance and normals. Part reconstruction is evaluated by averaging the per-part lol and we do not make the assumption that parts must be watertight, we compute part occupancies using the same strategy as for our training losses in Section 3.3 For generation, we report Minimum Matching Distance (MMD) and Coverage Score (COV) (Achlioptas et al. 2018), using CD as the distance metric.
(CD) for
4.1 Shape and Part Reconstruction
We evaluate the accuracy of shape and part reconstruction across all datasets and methods. At inference, our model uses auto-decoding: the decoder remains frozen while latent vectors are optimized to minimize reconstruction loss. We also report results for PartSDF using single part and refer to it as Ours-1P. Meshes are reconstructed using Marching Cubes (Lewiner et al. 2003) at a resolution of 256. We report quantitative results in Table 1 with qualitative ones shown in Figure 5 Across all metrics, our method achieves the best results on cars and chairs and equivalent results on mixers to Ours-1P, which does not reconstruct individual parts. Notably, 3DShape2VecSet struggles with the mixer's helical structures, likely due to its positional encoding's s difficulty with periodic geometry. Other part-based methods perform significantly worse on both surface and volume metrics.
One thing that handicaps DAE-NET, BAE-NET, and PQ-NET is their reliance on voxelized data despite being INR-based: For speed and memory, the data is binarized and voxelized at 643, which delivers efficient and fast models but greatly limits accuracy. This is particularly visible in the case of the thin helix of the mixers or the equally thin chair parts: they lend to either disappear or be inflated. Instead, PartSDF is trained with samples directly obtained from the original shape S and yields superior accuracy, capturing detailed part-specific gcometry and structure. While the more recent PASTA also trained with these samples and improves on the other works, it still performs less well than our approach. Because it only uses the part bounding boxes as input, it may fail to capture the correct local details and, thus, fail to properly
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Shape reconstruction. We compute the average Chanfer-Distance CD (x10"), Intersection over Union loU (%), and Image Consistency IC between reconstructions and corresponding test shapes. We also report average per-part Intersection over Union ploU (%) for part-based methods. Ours-1P uses a single part reconstruct the full shape and Ours-PC uses a point cloud encoder to get initial part latents and poses that refined in part-agnostic manner.
Table 1:
CD (4)
LoU (%, f)
IC (1)
ploU (%, f)
Car
Mixer
Chair
Car
Mixer
Chair
Car
Mixer
Chair
Car
Mixer
Chair
3DShape2
2.73
5.19
3.35
92.03
68.82
92.13
0.887
0.851
0.909
Ours-1P
1.37
1.44
3.74
97.41
95.16
93.78
0.924
0.978
0.913
DAE-NET
28.38
15.93
100.49
81.91
70.14
56.37
0.797
0.918
0.662
34.71
31.83
52.80
BAE-NET
33.43
13.68
106.60
75.17
33.38
40.79
0.771
0.818
0.594
21.83
31.14
38.72
PQ-NET
30.20
17.75
38.90
72.00
26.71
49.09
0.754
0.739
0.690
36.27
25.67
51.48
PASTA
12.15
6.27
40.89
83.88
50.83
60.36
0.855
0.942
0.750
Ours
1.27
1.60
1.30
98.02
94.43
97.17
0.931
0.978
0.942
94.89
90.42
93.67
Ours-PC
1.28
1.73
1.57
97.95
83.38
97.09
0.930
0.966
0.942
94.25
78.61
88.13
3DS2VS
Ours-1P
DAE-NET
BAE-NET
PQ-NET
PASTA
Ours
GT
Figure 5: Shape reconstruction. Reconstruction of test shapes with all models. For part-based methods, we color each part with different color and translate the helix outside of the mixers for visualization.
reconstruct some shapes, as in the chairs of Figure It is also unable represent individual parts, despite being part-aware.
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Table 2: Shape generation. We compute the Minimum Matching Distance MMD (x10*) and Coverage Score (COV) (%), using the Chamfer Distance (CD), between generated and test shapes.
MMD-CD (4)
COV-CD (%, 1)
Car
Mixer
Chair
Car
Mixer
Chair
VeeSete2Veceet
20.57
13.59
54.96
83.81
39.23
88.39
PQ-NET
30.61
25.25
70.68
43.81
50.26
74.91
PASTA
27.72
16.31
118.35
40.95
51.03
23.97
Ours
20.67
11.97
55.46
85.71
86.67
83.90
LDSShape2ecSSe
PQ-NET
PASTA
Ours
Ours 1
Figure 6: Shape generation. We generate shapes on all datascts, and we also provide examples of posc- conditioned generation (Ours!) where part latents are generated based on the poses' coarse description of the shape (left image for each pair). When possible, we translate the helix outside of the mixer for visualization.
Additionally, to illustrate that part encoder models can be used in conjunction with PartSDF, we also reconstruct test shapes using part-agnostic point clouds: We use point cloud encoder based on a simplified 3DShape2VeeSet without final cross-attention. It predicts initial part latents and poscs, refined via auto- decoding without Cpart. As shown in the last row of Table [ this approach successfully recovers both global shape and parts, though very thin features remain more challenging.
4.2 Shape Generation
We compare PartSDF's shape generation abilities against those of 3DShape2VecSet, which relies dif- fusion model to generate its set of latent vectors, PQ-NET, which trains latentGAN (Achlioptas et al. 2018) to yield global latent vector, and PASTA, which uses an autoregressive transformer to generate part bounding boxes. For PartSDF, we leverage SALAD (Koo et al. 2023), a cascaded diffusion model that first generates part poses and then part latents conditioned on these poses. This also enables us to generate shapes fitting specified pose decompositions, something that PQ-NET cannot do with its single latent space, and generate various geometries for a given pose decomposition, which PASTA cannot do as it only relies part poses for reconstruction. We report. MMD and COV metrics in Table 2 and show generated examples
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Figure 7: Part manipulation. We manipulate two shapes per dataset, first by changing the latent of specific parts (car body, mixer helix, and chair backrest) and second by editing part poses (car wheels, mixer width, chair width and height). In all cases, the parts adapt to the modifications and to each other, maintaining coherent whole with the new parts.
Initial car
Ours
Ours-1P
0.635
0.413
0.383
0.466
0.361
0.348
0.497
0.473
0.308
Figure 8: Part-hased optimization. We refine the car bodies to reduce aerodynamic drag while preserving the size and position of the wheels. (Ours) Our part-based representation enables this. (Ours-1P) In contrast when using a single-part, everything changes, including the wheels. We highlight individual parts on the left, the surface pressure on the right (from blue to red), and give the drag coefficient Ca as an inset.
in Figure 6. PartSDF achieves consistently better results than the part-aware baselines, with more detailed composite shapes. We note that despite significant integration effort on our side, the PASTA- -este-egeeeteed poses exhibit low diversity and occasional pose errors. Our results are also better than, or on par with, those of 3DShape22ecSee in addition that our models are part-aware, whereas those of 3eeSe are not, and therefore not usable for engineering design. Furthermore, it requires training different auto-encoder models between shape reconstruction and generation, while PartSDF uses the same decoder for both.
4.3 Part Manipulation
We evaluate our model's ability to perform part-specific shape manipulation by editing part latent vectors and poses in Figure 7 Both latents and poses can be edited conjointly PartSDF; we do so separately here for visualization purposes. When modifying part latents, the appearance of the corresponding parts is changed, but the shape's structure and parts layout remain fixed. On the other hand, when changing poses, the part layout adapts, and their general appearance is unchanged. In all cases, the resulting composite shape preserves its overall consistency while fitting the editions. These qualitative results emphasize the flexibility of our bast- representation, showing that our model can adapt individual parts independently while preserving overall shape integrity.
4.4 Part Optimization
To demonstrate the effectiveness of PartSDF a part-aware shape prior for downstream tasks, we address key engineering problem: Refining the shape of to reduce the drag induced by air flowing over its
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Table 3: Ablation on PartSDF components. We ablate the use of part poses, latent modulation (latMod), and cross-part layers (hep) the Car datasct. Best performance is achieved with poses and latent modulation, though note that hep layers decrease slightly the part accuracy of our model. However, this is counterbalanced by enabling inter-part adaptability; see Figure g
CD (4)
IoU (%, 1)
IC (f)
ploU (%, f)
w/o poses
1.43
97.81
0.928
91.71
w latMod
1.39
97.37
0.923
92.33
w w/o Pep
1.27
98.02
0.932
96.37
PartSDF
1.27
98.02
0.931
94.89
surface S, without editing the wheels. Drag be computed the surface integral of the air pressure:
drag, (S) = - (x) p(x) dS(x),
(10)
where p(x) is the pressure and n(x) the surface normal at point x, with ne its component along the a axis, which is directed along the car from front to back. This value is then normalized to get the drag coefficient C2 (Munson et al. 2013). For simplicity, we ignore the friction drag that tends to be negligible for cars. To compute a differentiable estimate of the surface pressure f(x) and resulting drag, we use a GCNN surrogate model (Baqué et al. 2018). More specifically, we use a GraphSage Convolution GNN (Hamilton) eet al. 2017 Bonnet et al.] 2022 predict f(x) on the mesh's s surface, using simulation data obtained with
Open OAM [OpenCFD].
Shape optimization can then be achieved by minimizing
Lárag Ca (MC(f,, + Lreg (Z,P)
(11)
with respect to (Z, P), where Ligg are optional regularization terms and MC is the Marching Cubes algo- rithm (Lewiner et al. 2003). Importantly, gradients can be computed through the meshing step (Remelli ct al. 2020). In practice, we minimize Ldrag over the PartSDF latents Z and pose parameters P, starting from their values for an existing car. In the example of Fig. g we optimize the shapes of several cars while keeping their wheels unchanged, which is something that our part-based approach allows and can not be done with a global representation such as the one of Ours-1P or 3DShape2 VecSet (Zhang et al. 2023 While they may yield a lower final drag, the shapes do not respect design constraints, which is undesirable. For instance, in the second and last row of Figure g results with Ours-1P tend to converge to average car, ignoring the specificity of the initial cars and their wheels. We provide more details and results in Appendix D
4.5 Ablation Study
We conduct an ablation study to evaluate the impact of cross-part layers hep: the use of pose parameters, and latent modulation in PartSDF, and report metrics the Car dataset in Table 3l Pose parameters allow independent control of part transformations, which improves the shape reconstruction performance but also allows more precise part manipulation. Latent modulation, é.e., injecting the part latent vectors Zp at every hap layer, is a simple modification that improves surface and part reconstruction, as mcasured by Chamfer- Distance and part. loU. On the other hand, cross-part layers hep cause a slight decrease in part accuracy, largely counterbalanced by the inter-part adaptability it enables. In Figure 9 we show that adding these layers PartSDF maintains the consistency between parts when doing part manipulation. We also show the necessity of the con-intersection loss Cinter: without it, the losses do not prevent the parts from bleeding into one another, causing the model to learn incorrect part decomposition with overlapping parts.
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T
w/o hep
w/ hep
GT
w/o Linter
w/ Linter
(a) Cross-part layers
(b) Non-intersection loss
Figure 9: Ablation study of PartSDF. (a) Without the cross-part layers hep (Section 3.2). manipulating part would not affect the others: The translated and scaled wheels incorrectly collide with the car. With these layers, manipulating some parts correctly affects the others, and the car adapts to the new wheels without intersection. (b) Without the non-intersection loss Linter, the parts incorrectly overlap. With it, the correct decomposition is learned. We visualize an exploded view of the predicted parts to see the overlaps.
Figure 10: Failures cases of PartSDF. (Left) Interpolation between shapes where a part exists in one but not the other may produce floating artifacts for intermediate shapes (e-g., chair armrests). (Middle) Tn rare test cases, parts that should be absent can persist as small surface fragments, such as the green armrest patches, which affects Chamfer-Distance. (Right) Very thin structures, such as the helix of some mixers, remain challenging to represent and mesh accurately using an SDF-based approach.
5 Limitations
The main limitation of PartSDF is its reliance on part labels during training. For our intended application, computer-aided design, this not a major issue because shapes are typically constructed from individual parts; hence, the decomposition of shapes into parts is known a priori. Thus, PartSDF is particularly relevant in scenarios where objects are naturally created with part-aware structures. While this limits PartSDF's ap- plicability to datasets without predefined decompositions such as most of those available online it better matches with practical engineering requirements. Nonetheless, if generalization to unlabeled data is de- sired, PartSDF could be combined with co-segmentation methods to generate pseudo-labels for its training. PartSDF also has few typical failure modes that are illustrated in Fig. 10 These include occasional artifacts when interpolating between shapes with different part existences, residual small surfaccs for absent parts, and difficulties representing very thin structures. Such issues occur infrequently and can often be mitigated by discarding known-absent parts or by using higher-resolution meshing for thin geometries. Additionally, because the computational and memory costs scale with the number of parts, extending PartSDF shapes with high part counts might require strategies to improve efficiency, such sparse cross-part interactions. Finally, while we devised strategy to handle non-watertight parts, it still assumes that they are volumetric and can be represented by an SDF. Thus, parts that are pure surfaces, such as car hoods, would not be naturally handled without inflating them by wrapping a volume around them. An interesting direction for future work is to use unsigned distance functions to solve this.
6 Conclusion
In this work, we introduced PartSDF, a modular and supervised approach specifically designed for composite shape representation. PartSDF enables flexible, part-based shape modeling, supporting independent part
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manipulation and optimization while maintaining overall shape coherence. Our method leverages simple architecture, achieving strong performance across tasks such as shape reconstruction, manipulation, and generation. Experimental results demonstrate that PartSDF consistently outperforms baseline methods in part-level accuracy and can be adapted to a wide range of tasks, highlighting its effectiveness as a robust shape prior for composite structures. This flexibility makes PartSDF particularly suited for applications fields like engincering design, where precise control over individual components is essential for customization and optimization. While PartSDF achieves promising results, future work will explore enhancing part inter- actions to further support applications involving highly dynamic shapes complex inter-part peee-pprttoe dependencies. Furthermore, developing more advanced topological supervision for each part should also be investigated to help prevent topologically inconsistent predictions, further improving its robustness and applicability.
Acknowledgements
This work was funded in part by the Swiss National Science Foundation.
References
P. Achlioptas, O. Diamanti, I. Mitliagkas, and L. Guibas. Learning Representations and Generative Models for 3D Point Clouds. In International Conference on Machine Learning, pp. 40-49, 2018.
G. Allaire. A Review of Adjoint Methods for Sensitivity Analysis, Uncertainty Quantification and Optimiza- tion in Numerical Codes. Ingénieurs de l'Aulomobile, 836:33 36, July 2015.
M. Atzmon and Y. Lipman. SAL: Sign Agnostic Learning of Shapes from Raw Data. In Conference on Computer Vision and Pattern Recognition, 2020.
P. Baqué, E. Remelli, F. Fleuret, and P. Fua. Geodesic Convolutional Shape Optimization. In International Conference on Machine Learning, 2018.
F. Bonnet, J. A. Mazari, P. Cinnella, and P. Gallinari. AirIRANS: High fidelity computational fluid dynamics dataset for approximating reynolds-avern averaged mavier-stokes solutions. In Thirty-sizte Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2022.
A. Chang, T. Funkhouser, L. G., Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, J. Xiao, L. Yi, and F. Yu. Shapenel: An Information-Ren 3D Model Repository. In arXiv Preprind, 2015.
M. Chen, R. Shapovalov, I. Laina, T. Monnier, J. Wang, D. Novotny, and A. Vedaldi. PartGen: Part-level 3D Generation and Reconstruction with Vieti-View Diffusion Models. arXie Preprint, 2024.
Z. Chen and H. Zhang, Learning Implicit Fields for Generative Shape Modeling, In Conference on Computer Vision and Pattern Recognition, 2019.
Z. Chen, K. Yin, M. Fisher, S. Chaudhuri, and Zhang. BAE-NET: Branched Autoencoder for Shape
Co-Segmentation. In International Conference on Computer Vision, 2019.
Z. Chen, Q. Chen, H. Zhou, and H. Zhang. Dae-Net: Deforming Auto-Encoder for Fine-Grained Shape Co Co-Segmentation. ACM SIGGRAPH, 2023.
K. Cho, B. Van Merriënboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio. Learn- ing Phrase Representations Using RNN Encoder-Decodes for Statistical Machine Translation. In arXiv Preprint, 2014.
C. Choy, D. Xu, J. Gwak, K. Chen, and Savarese. 3DR2N2: A Unified Approach for Single and Multi- View 3D Object Reconstruction. In European Conference on Computer Vision, 2016a.
C. Choy, D. Xu, J. Gwak, K. Chen, and Savarese. 3D-R2n2: A Unified Approach for Single and Multi- View 3D Object Reconstruction. In Earopean Conference on Computer Vision, pp. 228-644, 2016b.
14

---

Published in Transactions on Machine Learning Research (10/2025)
A. Dai, C. Qi, and M. Nießner. Shape Completion Using AD-Encoder-Prediee CNNs and Shape Synthesis. In Conference Computer Vision and Pallern Recognition, 2017.
B. Deng, K. Genova, S. Yazdani, S. Bouaziz, G. Hinton, and A. Tagliasacchi. Cvxnel: Learnable Convex Decomposition. In Conference Computer Vision and Pattern Recognition, pp. 31 31-44, 2020,
B. Deng, S. Kulal, Z. Deng, C. Deng, Y. Tian, and J. Wu. Unsupervised Learning of Shape Programs with Repeatable Implicit Parts. In Advances in Neurol Information Processing Systems, 2022.
E. Dupont, H. Kim, S. M. A. Eslami, D. J. Rezende, and D. Rosenbaum. From data to functa: Your data point function and you can treat it like one. In International Conference on Machine Learning, 2022.
M. Elrefaie, F. Morar, A. Dai, and F. Ahmed. Ariw Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks. Advances in Neural Information Processing Systems, 2024.
H. Fan, H. Su, and L. Guibas. A Point Set Generation Network for 3D Object Reconstruction from a Single Image. In Conference on Computer Vision and Pattern Recognition, 2017.
L. Gao, J. Yang, T. Wu, Y.-J. Yuan, H. Fu, Y.-K. Lai, and H. Zhang. SDM-NET: Deep Generative Network for Structured Deformable Mesh. ACM Transactions on Gruphics, 2019.
K. Genova, F. Cole, D. Vlasic, A. Sarna, W. T. Freeman, and T. Funkhouser. Learning Shape Templates with Structured Implicit Functions. In International Conference on Compuler Vision, pp. 7154-7164, 2019.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio. Generative Adversarial Nets. In Advances in Neural Information Processing Systems, 2014.
A. Gropp, Yariv, N. Haim, M. Atzmon, and Y. Lipman. Implicit Geometric Regularization for Learning Shapos. In International Conference Machine Learning, 2020.
T. Groueix, M. Fisher, V. Kim, B. Russell, and M. Aubry. Atlasnet: A Papier-Mâché Approach to Learning 3D Surface Generation. In Conference on Computer Vision and Pattern Recognition, 2018
B. Guillard, F. Stella, and P. Fua. Meshudf: Fast and Differentiable Meshing of Unsigned Distance Field Networks. In Europeun Conference on Computer Vision, pp. 576 592, 2022.
В. Guillard, E. Remelli, A. Lukoianov, S. Richterr T. Bagautdinov, P. Baque, and P. Fua. Deepmesh: Differentiable Iso-Surface Extraction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(11):707 (007)))77777777 2024.
W. L. Hamilton, R. Ying, and J. Leskovec. Inductive representation learning on large graphs. In Proceedings of the 31st Indernational Conference on Neural Information Processing Systems, 2017.
Z. Hao, H. Averbuch-Elor, N. Snavely, and S. Belongie. Dualsdf: Semantic Shape Manipulation Using a LeveL Representation. In Conference on Computer Vision and Pottern Recognition, pp. 7631-7641, 2020.
A. Hertz, O. Perel, R. Giryes, O. Sorning and D. Cohen-Or. SPAGHETTI: Editing Implicit Shapes through Part Aware Generation. ACM Transactions on Graphics, 2022.
J. Ho, A. Jain, and P. Abbeel. Denoising Diffusion Probabilistic Models. In Advances in Neural Information Processing Systems, 2020.
Z. Huang, Y.C. Guo, X. An, Y. Yang, Y. Li, Z.-X. Zou, D. Liang, X. Liu, Y.-P. Cao, and L. Sheng. MIDI: Multi-instance diffusion for single image to 3d scene generation. In Conference on Computer Vision and Pattern Recognition, 2025.
K.-H. Hui, R. Li, J. Hu, and C.-W. Fu. Neural Template: Topology-Awen Aware Reconstruction and Disentangled Generation of 3D Meshes. In Conference on Computer Vision and Pattern Recognátion, 2022.
15

---

Published in Transactions on Machine Learning Research (10/2025)
A. Jacobson, D. Panozzo, et al. libigl: A Simple C++
Geometry Processing Library, 2018.
T. Ju, F. Losasso, S. Schaefer, and Warren. Dual Contouring of Hermite Data. In ACM SIGGRAPH, 2002.
A. Kanazawa, S. Tulsiani, A. Efros, and J. Malik. Learning Category-Specific Mesh Reconstruction from Image Collections. In Conference on Computer Vision and Pattern Recognition, 2018.
D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimisation. In International Conference on Learning Representations, 2015.
F. Kluger, H. Ackermann, E. Brachmann, M. Yang, and B. Rosenhahn. Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Images. In Conference on Computer Vision and Pattern Recognition, pp. 13070-133 13079, 2021.
J. Koo, S. Yoo, M. H. Nguyen, and M. Sung. SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation. In International Conference Computer Vision, 2023.
T. Lewiner, H. Lopes, A. W. Vieira, and G. Tavares. Efficient Implementation of Marching Cubes' Cases with Topological Guarantees. In Journal of Graphies Tools, 2003.
S. Li, D. Paschalidou, and L. Guibas. PASTA: Controllable Pwrt-Aware Shape Generation with Autoregres- sive Transformers. arXiv Preprint, 2024.
A. Liu, C. Lin, Y. Liu, X. Long, Z. Dou, H.-X. Guo, P. Luo, and W. W.Wang, Part123: Part-aware 3D Reconstruction from a Single-view Image. In ACM SIGGRAPH, 2024.
W.E. Lorensen and H.E. Cline. Marching Cubes: A High Resolution 3D Surface Construction Algorithm.
In ACM SIGGRAPH, pp. 163-169, 1987.
L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin, and A. Geiger. Occupancy Networks: Learning 3D Reconstruction in Function Space. In Conference Computer Vision and Pattern Recognition, pp. 4460- 4470, 2019.
P. Mittal, Y.-C. Cheng, M. Singh, and S. Tulsiani. AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation. In Conference on Computer Vision and Pattern Recognition, 2022.
Mo, S. Zhu A. X., Chang, L. Yi, S. Tripathi, L. Guibas, and H. Su. PartNet: A Large-Scale Benchmark for Fine-Grained and Hierarchical Part-Level 3D Object Understanding. In Conference on Computer Vision and Pattern Recognétion, 2019.
B.R. Munson, T.H. Okiishi, W. W. Huebsch, and A.P. Rothmayer. Fluid Mechanics. Wiley Singapore, 2013.
K. Nakayama, M. A. Uy, J. Huang, S.-M. Hu, K. Li, and L. Guibas. DiffFacto: Controllable Part-Based 3D Point Cloud Generation with Cross Diffusion. In International Conference Computer Vision, 2023.
C. Niu, J. Li, and K. Xu. Im2struct: Recovering 3D Shape Structure from a Single RGB Image. In Conference on Computer Vision and Pattern Recognition, pp. 4521 4529, 2018
C. Niu, M. Li, K. Xu, and H. Zhang. RIM-Nct: Recursive Implicit Fields for Unsupervised Learning of Hierarchical Shape Structures. In Conference on Computer Vision and Pattern Recognition, 2022.
Ltd OpenCFD. OpenFoam.
J. Pan and K. Jia. Deep Mesh Reconstruction from Single RGB Images via Topology Modification Networks. In International Conference on Computer Vision, 2019.
J. Park, Florence, J. Straub, R. A. Newcombe, and S. Lovegrove. Deepsdf: Learning Continuous Signed Distance Functions for Shape Representation. In Conference on Computer Vision and Pattern Recognition, 2019.
16

---

Published in Transactions on Machine Learning Research (10/2025)
R. Pascanu, T. Mikolov, and Y. Bengio. On the Difficulty of Training Recurrent Neural Networks. In International Conference on Machine Learning, pp. 1310-1318, 2013.
D. Paschalidou, O. Ulsso, and A. Geiger. Superquadrics Revisited: Learning 3D Shape Parsing Beyond Cuboids. In Conference on Computer Vision and Pattern Recognition, pp. 10344 10353, 2019.
D. Paschalidou, L. V. Gool, and A. Geiger. Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single Rgb Image. In Conference on Computer Vision and Pattern Recognition, pp. 1060 1070, 2020.
D. Paschalidou, A. Katharopoulos, A. Geiger, and S. Fidler. Neural Parts: Learning Expressive 3D Shape A Abstractions with Invertible Neural Networks. In Conference on Computer Vision and Pollern Recognition, pp. 3204 3215, 2021.
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. Devito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer. Automatic Diffcrentiation in Pytorch. In Advances in Neural Information Processing Systems, 2017.
S. Peng, M. Niemeyer, L. Mescheder, M. Pollefeys, and A. Geiger. Convolutional Occupancy Networks. European Conference on Computer Vision, pp. 523-5-43- 540, 2020.
S. Peng, C. Jiang, Y. Liao, M. Niemeyer, M. Pollefeys, and A. Geiger. Shape as Points: A Differentiable Poisson Solver. In Advances in Neural Information Processing Systems, 2021.
D. Petrov, M. Gadelha, R. Měch, and E. Kalogerakis. ANISE: Assembly-Based Neural Implicit Surface Reconstruction. In IEEE Transactions Visualization and Computer Graphics, 2023.
L. Piegl. On NURBS: A Survey. Computer Graphics and Applications, 11:55-71, 1991.
E. Remelli, A. Lukoianov, S. Richter, B. Guillard, T. Bagautdinov, P. Baque, and P. Fua. Meshsdf: Differ- entiable Iso-Surface Extraction. In Advances in Neural Information Processing Systems, 2020.
G. Riegler, A. O. Ulusoy, and A. Geiger. Octnet: Learning Deep 3D Representations at High Resolutions. Conference on Computer Vision and Pallern Recognition, 2017.
T. Salimans and D.P. Kingma. Weight Normalization A Simple Reparameterivation to Accelerate Training of Deep Neural Networks. In Advances in Neural Information Processing Systems, 2016.
Q. Shuai, C. Zhang, K. Yang, and X. Chen. Dpf-Net: Combining Explicit Shape Priors in Deformable Primitive Field for Unsupervised Structural Reconstruction of 3D Objects. In International Conference on Computer Vision, 2023.
Sitzmann, J. Martel, A. Bergman, D. Lindell, and G. Wetzstein. Implicit Neural Representations with Periodic Activation Functions. In Advances in Neural Information Processing Systems, 2020.
D. Smirnov, M. Fisher, V. G. Kim, R. Zhang, and J. Solomon. Deep Parametric Shape Predictions Using Distance Fields. In Conference on Computer Vision and Pattern Recognátion, 2020.
J. Sohl-Dickstein, E. A. Weiss, N. Maheswaranathan, and S. Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learning, 2015.
D. Stutz and A.Geiger. Learning 3D Shape Completion from Laser Scan Data with Weak Supervision. Conference on Computer Vision and Pattern Recognition, 2018.
C. Sun, Q. Zou, X. Tong, and Y. Liu. Learning Adaptive Hierarchical Cuboid Abstractions of 3D Shape Collections. ACM Transactions on Graphics, 386):11-13, 2019.
T. Takikawa, J. Litalien, K. Yin, K. Kreis, C. Loop, D. Nowrouzezahrai, A. Jacobson, M. McGuire, and
S. Fidler. Neural Geometric Level of Detail: Real-Time Rendering with Implicit 3D Shapes. In Conference on Computer Vision and Pattern Recognition, 2021.
17

---

Published in Transactions on Machine Learning Research (10/2025)
M. Tatarchenko, A. Dosovitskiy, and T. Brox. Octree Generating Networks: Efficient Convolutional Archi- tectures for High-Resolution 3D Outputs. In International Conference on Computer Vision, 2017.
K. Tertikas, D. Paschalidou, B. Pan J. J.and Park, M. A. Uy, 1. Emiris, Y. Avrithis L., and Guibas. Generating Part-Aware Editable 3D Shapes Without 3D Supervision. In Conference on Computer Vision and Pattern Recognition, 2023.
S. Tulsiani, H. Su, L. J. Guibas, A. A. Efros, and J. Malik. Learning Shape Abstractions by Assembling Volumetric Primitives. In Conference on Computer Vision and Pattern Recognition, pp. 2635- 2643,,6,, 2017.
S. Vasu, N. Talabot, A. Lukoianov, P. Baque, J. Donier, and P. Fua. Hybridsdf: Combining Free Form Shapes and Geometric Primitives for Effective Shape Manipulation. In International Conference on 3D Vision, 2022.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkorcit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin. Attention is All You Need. In Advances in Neural Information Processing Systems, 2017.
N. Wang, Y. Zhang, Li, Y. Fu, W. Liu, and Y. Jiang. Pixel2mesh: Generating 3D Mesh Models from Single RGB Images. In European Conference on Computer Vision, 2018
P. Wang, L. Liu, Y. Liu, C. Theobalt, T. Korura, and W. Wang. Neus: Learning Neural Implicit Surfaces by Volume Rendering for Multi-Viey Reconstruction. In Advances in Neural Information Processing Systems, 2021.
P.S. Wang, Y. Liu, and X. Tong. Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations. In ACM STGGRAPH, PH, 2022.
D. Wieser, H.-J Schmidt, S. Müller, C. Strangfeld, C. Nayeri, and C. Paschereit. Experimental Comparison of the Aerodynamic Behavior of Fastback and Notchback DrivAer Models. SAE Int. J. Passeng. Cars Mech. Syst., 7(2):682-66) 691, November 2014.
J. Wu, C. Zhang, T. Xue, Freeman, and Tenenbaum. Learming a Probabilistic Latent Space of Object Shapes via 3D Sennerative-Avversanee Modeling. In Advances in Neural Information Processing Systems, pD. 82 90, 2016.
R. WU, Y. Zhuang, K. Xu, H. Zhang, and B. Chen. PQ-NET: A Generative Part Seq2seq Network for 3D Shapes. In Conference on Computer Vision and Pottern Recognition, 2020.
Z. Wu, S. Song, A. Khosla, F. Yu, L. Zhang, X. Tang, and J. Xiao. 3D Shapenets: A Deep Representation for Volumetric Shapes. In Conference Computer Vision and Pattern Recognition, pp.
2015.
Q Xu, W. Wang, D. Ceylan, R. Mech, and U. Neumann. DISN: Deep Implicit Surface Network for High- Quality Single-Vien View 3D Reconstruction. In Advances in Neural Information Processing Systems, 2019.
X. Yan, L. Lin, N. J. Mitra, D. Lischinski, D. Cohen-Or, and H. Huang. ShapeFormer: Transformer- Based Shape Complction via Sparse Representation. In Conference Computer Vision and Pattern Recognition, 2022.
K. Yang and X. Chen. Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds. In ACM Transactions on Graphics, 2021.
Y. Yang, C. Feng, Y. Shen, and D. Tian. Foldingnet: Point Cloud Auto-Encoder via Deep Grid Deformation. In Conference Computer Vision and Pattern Recognition, June 2018.
K. Yao, L. Zhang, X. Yan, Y. Zeng, Q Zhang, L. Xu, W. Yang, J. Gu, and J. Yu. CAST: Component-Alignu 3D Scene Reconstruction from an RGB Image. arXiv Preprint, 2025.
X. Zeng, A. Vahdat, F. Williams, Z. Gojcic, O. Litany, S. Fidler, and K. Kreis. LION: Latent Point Diffusion Models for 3D Shape Generation. In Advances in Neural Information Processing Systems, 2022.
18

---

Published in Transactions on Machine Learning Research (10/2025)
B. Zhang, M. Nießner, and P. Wonka. 3DILG: Irregular Latent Grids for 3D Generative Modeling. In Aduances in Newral Information Processing Systems, 2022.
B. Zhang, J. Tang, M. Nießner, and P. Wonka. Veeha: A 3D Shape Representation for Neural Fields and Generative Diffusion Models. In ACM SIGGRAPH, 2023.
C. Zou, E. Yumer, J. Yang, D. Ceylan, and D. Hoiem. 3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks. In International Conference on Computer Vision, 2017.
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A
Table of Contents
B
Implementation Details
B.
Network Architecture
B
Training Procedure
B33
Encoder and Diffusion Models
B.4
Datasets
B.5
Baselines
B.6
Metrics
C
Design Analysis
Part Optimization
D
Part Interpolation
F
Results on +rivAerNet++
G
Additional Experimental Results
Shape Reconstruction
G.
Shape Generation
Shape Manipulation
Single- View Reconstruction
B Implementation Details
In this section, describe the architecture of PartSDF (Appendix B.1 its training procedure (Ap- pendix B and the point cloud encoder and diffusion models we used (Appeudix B.3). Then, we detail our datascts and their processing (Appendix B.44), the basclines against which we compare and any hyper- parameter choices (Appendix B.5), and finally the metrics used in this work and how they were computed (Appendix B.6).
B.1 Network Architecture
The final architecture of PartSDF, as presented in this work, is as follow:
The dimensionality of the part latent space is Z = 256, such that Zp E 256 Vp, and the hidden size of the single-part layers dap 512, with the exception of the model trained on the Chair dataset where is 256. This because there are more parts, thus we expect each part to be simpler and helps to alleviate the memory increase. We use weight normalization (Salimans & Kingma, 2016) on these layers, as in (Park] et al. 2019). PartSDF has 8 hap layers, counting the input and output ones, with cross-part layer hep between each pair, described in Section 3.2 All layers, except the output one, are followed by ReLU non- lon-lincaisiies. Note that each hep has only P + trainable parameters, e.g., 25 + 5 = 30 parameters in the case of cars.
B.2 Training Procedure
The decoder model of PartSDF is trained for 2000 epochs using batch size of 16 and 8192 sampled points per shape. We use the Adam optimizer (Kingma & Ba 2015) with default parameters in PyTch (Paszke) et al. 2017). setting a learning rate of x 10-4 for the model and 1 x 10-3 for the latent vectors. The learning rates are reduced by a factor 0.35 at 80% and 90% of the total training epochs. The latent regularization weight is set to À = 10-4, and the non-intersection loss uses a softmax temperature parameter set to 0.02.
To supervise the SDF, we follow the sampling strategy used in DeepSDF (Park et al.) 2019 0: 95% of the sampled points
the surface, and 5% are uniformly distributed in space. The SDF values computed
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using the IGL library (Jacobson et al. 2018 assuming watertight meshes. During training, the SDF values are clamped between 0.1 and 0.1 to locus the capacity of the network around the surface.
Trainings are conducted on a single NVIDIA V100 GPU with 32GB of memory, taking 1 days to train depending on the dataset size.
B.3 Encoder and Diffusion Models
we use a point encoder to map point clouds of the full shapes to PartSDF parameter space, i.c. part latents and poses. For this, we leverage the model of 3DShape2VecSet (Zhang et al. 2023) using their official implementationff We use a smaller version of the model with self-attention layers (against 24 in the original work), and without the final cross-attention layer with query positions (see Fig. 3 in their work) we want to output part latents and poses instead of implicit values. We use learnable queries instead of point queries (see Fig, 4(a) in (Zhang et al. 2023 to encode the point cloud, which creates order the latent set, allowing us to recover the parameters of specific parts. Note that we concatenate latent and pose for every part, such that the encoder outputs them both in a single vector.
Point Cloud Encoder. In Section
Diffusion Model. In order to generate composite shapes with PartSDF, we use a diffusion model to generate the part latents and poses (Soction 4.2), more specifically SALAD (Koo al., 2023) with their official implementation For the second diffuusin on the latents, we however make use of transformer decoder instead of encoder that each part latent can attend to all part poses, and the part latents are normalized before training. This last point was found crucial for the diffusion as our latent vectors tend to have significantly lower norms than random vectors sampled from multivariate Gaussian distribution. Indeed, as in Park et al. 2019), latent vectors are initialize such that Expll = 1, while Gaussian noise in d-dimensions has Ex X Vd.
B.4 Datasets
For all datasets, we preprocess the meshes by centering them using their bounding box and rescaling them into the eube [-0.9, 0.9)3, ensuring the longest edge of the bounding box measures 1.8. This leaves margin around the shape to prevent the surface from leaving the meshing region, defined as the [|1 cube.
To create the SDF supervision, we perform two types of sampling (Park et al. 2019). ). First, we sample points on the surface of the mesh and perturb them with Gaussian noise, using variances of 0.005 and 0.0005 to generate points near the surface. Second, we uniformly sample points within the [=1, cube. The SDF values for all sampled points are computed using libigl (Jacobson et al. 2018). The samples and their SDF are mixed in a 95/5% ratio (near-surface to uniform samples) and stored for training. During training, a subset of these precomputed points is used, randomized at each epoch.
Additionally, each part, given a subset of the original mesh, is fitted with cuboid or cylinder. The orientation, translation, and scale of the primitive is then used as that part's pose.
As explained in Section 4 obtaining high-quality composite shape data is challenging, with online data usually containing non-walertight. meshes, or without part decomposition or an inconsistent one. Therefore, we use three curated datasets in this work.
Cars.
In order to perform Computational Fluid Dynamics (CFD) simulations the cars, see Appendix D below, need them to be correctly closed and physically plausible, i.c. wheels and body correctly separated. We therefore hand-process a subset of ShapeNet (Chang et al.} 2015 's cars: The wheels and body are manually selected and separated, and then remeshed to become waterlight (Wang et al. 2022
Mixers. This dataset was proposed by (Vsuu ot al. 2022 and consists in liquid mixors made contral lube, an interior helix, and two attach points. It. has the advantage of having an available, and consistent,
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part decomposition, which is suitable to learn a composite shape representation. The main challenge lies in the thinness of the tubes and helices, and the latter's complexity.
Chairs. We use a clean subset of ShapeNet's chairs with semantic segmentation provided by PartNet (Mo ett al, 2019), with seat, backrest, armrest, and leg classes. To enable SDF computation, we first. make the chairs watertight (Stutz & A.Geigor 2018). Then, the PartNet segmentation, originally provided as a point cloud, is transferred to the mesh using voting scheme: each face is assigned the most frequent class among its closest points. To refine this segmentation, we further divide the armrests and legs into individual parts by detecting connected components. Chairs that fail this finer segmentation are removed to ensure a consistency within our dataset. Additionally, we discard shapes at intermediate steps if they exhibit issues such as misaligument with the segmentation point cloud or a high Chanfer-Distance relative to the original shape.
Each dataset is split into train, validation and test sets tuned using the train and validation sets, and final models, reported in the main lext, are trained on validaton and evaluated on the test set. Part poses are obtained by fitting each part with cuboid or cylinder.
Model hyperparameters are
B.5 Baselines
DAE-Net. DAE-NET (Chen et al. 2023 is recent method that learns unsupervised part decompo- sition to perform co-segmentation. It creates multiple part templates that are deformed to reconstruct a shape given its voxelization as input, allowing the original shape to be segmented based on the predicted decomposition. As mentioned in our main text, unsupervised methods like DAE-NET are typically designed to discover new shape decompositions, which is unsuitable for engineering design where parts have specific predefined meanings and uses. Additionally, as shown in our experiments, the reliance on voxelized inputs significantly limits its representation ability. We use the official implementation] and conduct grid scarch to tune the sparsity loss weight y (see Eqs. (5) and (6) in their work). The optimal values found were y = 0.001 for cars and mixers, and = 0.002 for chairs, consistent with their reported results.
Similarly, BAE-NET (Chen et al. 2019) encodes a voxelized input to generate part implicit fields, which can be used for co-segmentation. The key difference, and the reason for comparison to our approach, is that BAE-NET also introduces a weak supervision scheme where ground truth segmentations are provided for a small subset of the training shapes (typically ranging from to 8 shapes). In this setting, the model propagates the learned decomposition across the entire dataset. Similar to DAE-NET, BAE- NET suffers from the limitations of voxelized inputs, which restrict its reconstruction accuracy. However, as shown in Figure 5 the weak supervision allows it to recover the desired decomposition in most cases, although certain parts, such as car wheels, are sometimes segmented together rather than individually. We use the official implementation"] to train the models. For the weak supervision, we experiment with 1, 2, 3, and shots, finding that 8-shot supervision consistently yields the best results. Therefore, we use these models.
BAE-Net.
PQ-Net. As a fully supervised baseline, we compare against PQ-NET (Wu et al. 2020 PQ-NET employs two-stage training process: first, an implicit auto-encoder is trained to reconstruct all individual parts, followed by a GRU-based RNN (Cho et al. 2014) that learns to auto-encode sequences of parts, represented by their latent vectors and bounding box parameters. For shape generation, latentGANs (Achlioptas et al, 2018) are used to sample in the RNN's latent space. Like the previous basclines, PQ-NET relics on voxelized data and often reconstructs 'inflated' shapes. While this helps against thinner parts, such as mixer helices and chair legs, the overall reconstruction accuracy remains low. Additionally, backpropagating through RNNs is notoriously difficult (Pascanu et al. 2013), and the non-continuous nature of its sequence generation makes it less suitable as shape prior for optimization tasks. We train PQ-NET using the author's 's official implementation
c https://githin http:/hhwww..occmc//288/888// Net
NET
https///gthhubb.cmm//hriii..tt
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Table 4: Model sizes. Size of the different models term of trainable parameters. *: Most parameters are in the MLPs of the Self-Attention layers between the latent vectors. : We only consider the paramcters of the blending nelwork and ignore the object generalor, which is only relevant for generation.
# of parameters
3DShape2VecSer
106.1M
Ours- 1P
2.5M
DAE-NET
3.1M
BAF-NET
5.3M
PQ-NET
12.8M
PASTA
9.0M
Ours
2.5M
PASTA. Li et al. 2024 proposes another supervised method mostly aimed at generating shape in a part-aware manner. is made of two parts. First, an autoregressive transformer (Vaswani et al. 2017] is trained to output a sequence of part, each represented through their bounding box (or equivalently, their pose). Secondly, transformer decoder performs cross attention between these part bounding boxes and the query points to output an occupancy value for each, using small final MLP, PASTA's decoder only rely on the part layout, as described by their respective bounding boxes, and as such entangles the part geometry to them. It is unable to output varying geometry without affecting the part poses. Additionally, PASTA outputs a single occupancy per shape and do not produce individual part. We use the official implementation train PASTA on our data.
3DShape2VecSet.. In order to evaluate the reconstruction and generation quality of our shapes against a more powerful baseline, we also compare to a state-of-the-ae part-agnostic method, namely 3DShape2VecSet (Zhang et al.) 2023). The core of the architecture former (Vaswani et al.) (017)) model that encodes a point cloud into an wnordered set of latent vectors, which are then decoded at queried positions to oblain occupancy values. For generation, KT-divergence loss is added during training to make the auto-encoder variational and help second-stage diffusion model. This diffusion model is trained to generate sets of latent vectors, thus sampling 3DShapc2VesSet's latent space. As noted in the work, the models are very heavy, requiring multiple GPUs for training. Using the author's official implementatior we train auto-encoders withou the KT-divergence loss for reconstruction experiments and with the KL-divergence for the generation experiments (as reference, we use the same PartSDF decoder for both experiments). We use the provided apper-parameter..
a large auto-encoder trans-
B.5.1 Model size comparison
We compare the models' size term of their number of trainable parameters. As can be seen in Table PartSDF is the smallest model, with 3DShape2VecSed being ~ 40x larger. In practice, 3DShape2VecSin also requires multi-GPU training, noted in its paper, while PartSDF can be trained
single GPU,
To understand the good performance of PartSDF in spite of its smaller size, we note that 3DShape2VeeSet is an aulo-encoding method designed for point cloud reconstruction and diffusion--ased generation, not for per- shape optimization. In contrast, PartSDF an muto-decodiin framework that well-suited for optimization and manipulation tasks. For completeness, we also experiment with optimizing 3DShape2VeeSt latents at inference time on the Car dataset, with two settings: "+AD', where latents are randomly initialized and optimized, as in PartSDF, and "+AE+AD", where latents are first obtained from the point-cloud encoder and then further optimized. We report the results in Table 5
In the +AD setting, 3DShape2VecSet struggles to optimize its latent vectors and the reconstructions exhibit bumpy surfaces and floaters, hence the lower IC and poor CD. This is consistent with observations made in
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Table 5: Auto-decoding with 3DShape2VecSet. Reconstruction results when using auto-decoding with 3DShape2VecSet with randomly initialized latents (+AD) or encoded from point-cloud (+AE+AD).
CD (4)
IoU (%, f)
IC (t)
ploU (%, 1)
3DS2VS
2.73
92.03
0.887
3DS2VS+AD
57.97
92.49
0.848
3DS2VS+AE+AD
1.15
98.78
0.942
Ours-1P
1.37
97.41
0.924
Ours
1.28
97.95
0.930
94.25
3DS2VS
+ noise
+ noise
Ours
+ noise
+ noise
Reconstruction with noisy latents. When gradually adding gaussian noise to the latent vectors in 3Dehape2VecSet and PartSDF, we observe degradation of the shape with the former. With the latter, the output remains a slightly different, but valid, car. The noise is taken to be 5% (+noise) and 7.5% (++noise) of the latents average norm.
Figure 11:
the DeepSDF paper's supplementary material (Sec. E, Fig. 19). This highlights that its latent space is not well suited for direct optimization, one of the main reasons we did not adopt VecSet-style latent space for PartSDF. With +AE+AD, performance improves and slightly surpasses that of PartSDF in reconstruction accuracy.
However, 3DShape2VecSet is not good for the applications we are targeting: does not provide explicit part representations and its latent space is not designed for controllability demonstrate this, we add small amounts of Gaussian noise to the latent vectors of 3DShape2VecSet and PartSDF before reconstruction. In Figure II the standard deviation of the noise is taken to be 5% and 7.5% of the latents average norm. Adding such small amounts of noise to 3DShape2VesSet's latent vectors quickly degrades the shape, while PartSDF's output remains valid car. In other words, PartSDF's latent space better behaved and, thus, better suited for shape optimization.
per-part optimization. To
B.6 Metrics
Reconstruction. As mention in the main text, to assess roconstruction accuracy of the 3D shapes, use three metrics: For surface accuracy, use the Chanfer-Distance (CD), which measures the symmelric distance between sets of points, X' { and y MM sampled from the surface of the ground truth and reconstructed surfaces respectively. Their CD is then written
CD(X
yE) Σ minl|x
Sanull-yylie - 211 +
1 M yEy
Σ minlly - x
(12)
N
xEX
XEX
this work, we use A = 30'000, unless specified otherwise.
To evaluate the volume accuracy, we use Intersoction over Union (IoU). It is defined the ratio of volume between the intersection of the shapes over their union. In practice, we compute it using occupancy values
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We additionally report per-part average IoU (pIoU) as a way to mcasure part reconstruction accuracy, noting that CD and IC might have issues the ground-truth parts are not watertight. In order to compute the occupancy of an open part, we rely on a strategy similar our SDF supervision, see Figure 4 First, the occupancy of the full shape is computed look for the closest part to it. This part will get occupancy of 1 that point and all the others will get. 0. Therefore, part occupancy can be seen as the intersection of the full shape's occupancy with the part's s "closest region' as visualized in Figure [igure[(b.) b). Note that for baselines without part correspondences, dee DAE-NET and PQ-NET, we must first match the reconstructed parts to the ground truth (GT) ones: For Published in Transactions on Machine Learning Research (10/2025)
grid: We find the smallest bounding box that contains the two shapes, then sample points on 128 grid. For each point we get the binary occupancy of each shape os, (x) and os, where (x(x) is 1 if
x is inside the shape and 0 otherwise. The loU is then computed as
Ex (x) 0s, (x)
S2) = Σx max (1, os,
(13)
(s, (x) + os, (x))
Finally, we use Image Consistency (IC) [Gillladd et al. 2022) to evaluate the appearance and surface normals, using renderings of the shapes. Let K. be a set of 8 cameras located at the vertices of a cuboid that encompasses the shape, looking at its centroid. For each camera & E X, we render the binary silhouettes S E (0.1) 256x256 and normal map N₂ E IR 12266x266x3 of shape St, and similarly Sr and Nr for shape S2. 1]
The IC between these shapes is defined as
Ic) = K
1O 8x) COS(N,, N&),
(14)
KEK
where IoUnn is the Intersection over Union between binary images and COS is the average cosine similarity between two normal maps. We refer interested readers to (Guillard et al. 2022 for more details.
the grid. Then, for each point where the occupancy is 1, we
each shape and each reconstructed part, we match it with the GT part with which has the highest loU.
To evaluate the plausibility and diversily of the generated shapes, as compared to a held out test set, we report the Minimum Matching Distance (MMD) and Coverage Score (COV) (Achlioptas et al. 2018) respectively, using the Chamfer-Distanee the (pseudo-)distance metric.
Generation.
MMD is the average distance between each shape from the test set. T and the generated set G. It is written as
MMD(G,T)
Σ min CD(X.)), Vea
(15)
[T'|
XeT
where we make the abuse of notation that CD(X,)) means the Chamfer Distance between samples on the surfaces of X and y.
On the other hand, COV measures the fraction of shapes in the test set that are recovered with a greedy matching of generated shapes: each shape in G is matched with the closest shape in T. Rigorously, is computed as
COV(G,T) minxxr CD(X, Vy E GH
(16)
T
For both the baseline and our method, we generate 2000 shapes, and use 2048 surface samples to compute the CD, for efficiency concern.
C Design Analysis
Number of parts. We evaluate the influence of the number of parts on the Chair datasel by artificially fusing or splitting parts to vary the decomposition. We report the results in Table and visualize examples of parts decomposition in Figure 12 Inercasing the number of parts generally improves reconstruction metrics, as simpler per-part geometries are easier to represent. However, we observe slight Chamfer- Distance degradation due to few failures in removing armrests during reconstruction, which suggests that
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Table 6: Varying the number of parts. Reconstruction results on the Chair dataset with PartSDF when varying the number of parts in the decomposition.
# of parts
CD (J)
IoU (%, t)
IC (t)
ploU (%, 1)
1
3.74
93.78
0.913
2
1.61
95.91
0.931
93.08
3
2.00
96.55
0.936
93.24
4
1.27
97.13
0.943
93.69
5
1.51
97.23
0.943
93.63
7
1.32
97.21
0.944
93.12
8
1.30
97.17
0.942
93.67
9
1.39
97.37
0.945
93.22
12
1.76
97.48
0.945
93.01
parts
parts
parts
parts
parts
parts
parts
parts
12 parts
Figure 12: Part decompositions for the Chairs. We show an example of shape with its parts colored differently to visualize the part decompositions.
larger part counts may require more data and training to robustly capture cross-part interactions. Part loU remains relatively stable, with only minor variation (= 0.6%). Overall, while finer decompositions can improve expressivnness, they may reduce controllability by requiring more poses to be specified and sufficient training data to model all part relationships.
Architectural variants. We experiment with transformer-basee architecture Vaswani et al. 2017) to replace our cross-par decoder with ions-attention, see Table 7 While feasible, this increases parameter count (from ~2.5 to 4.8M), memory (traing samples reduced by factor 4 to avoid out-of-memonn errors) and training cost (from 2000 to 4000 epochs with lower lcarning-rate) for the same reconstruction accuracy. We also observed greater parts entanglement length even when its scale is kept constant, see Figure 13 where the car front and back move with the wheels instead of simply adapting their wells around them. We believe this can be solved, for example by adding some shape mixing during training, but note that our simpler cross-part decoder already enables it at lower memory and computation cost.
this architecture: displacing the car wheels also affect the car
The merger of two SDFs into a single one performed using the min op- erator, see, e.g., htttp://iqqilezzl//
SDF aggregation strategies.
which simply aggregates the parts. We tried replacing the min by a softmin variant and found that it performs similarly, if marginally worse, shown in Table for the Car dataset.
Scalability of PartSDF. The computational cost of PartSDF depends on both the number of parts P and the feature dimension D. The single-part layers hap scale as O(PD?), while the cross-part layers hop scale as D In our experiments, D E {256, 512) and < D, so runtime and memory scale approximately linearly with the number of parts. However, for very large P, the combined complexity becomes O(PD2 + P2D). similar to the cost of transformer layers (considering self-attention + MLPP).
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Table 7: Comparing architectures, Reconstruction results on the Car dataset using a Transformer- basedd decoder (Transf.) and softmin SDF-aggrogation strategy with decoder (softmin) against PartSDF.
CD (L)
IoU (%, t)
IC (t)
ploU (%, 1)
Transf.
1.25
98.00
0.931
93.44
softmin
1.31
97.90
0.930
94.78
Ours
1.27
98.02
0.931
94.89
Our proposed decoder
A transformer- based decoder
Manipulation with different architectures. We compare manipulation bet ween a Transformer- based variant against our cross- part decoder, by translating the wheels while keeping the body's scale fixed. For the Transformer-basee basod decoder, the length of the car is incorrectly affected.
Figure 13:
Although our layers remain more lightweight, modeling highly complex objects with many parts would require both large D and P to capture fine geometric details, which may limit scalability. Extending work to such cases is possible but will require strategies such as positional encoding, hierarchical part grouping, sparse cross-part interactions to improve efficiency.
Part Optimization
optimize shapes to demonstrate how PartSDF is used as part-aware shape prior. In this section, we provide further experimental details and results.
As described in Section 4.4
Experimental Setup. The goal of this experiment to optimize the shape of a car minimize its aerodynamic drag, expressed the drag coefficient (Ca), by modifying its main body under the constraints that wheels cannot be modified. Direct simulation of acrodynamic performance, such as Computational Fluid Dynamics (CFD) (OpenCFD). is computationally expensive and non-differentiable without adjoint solvers (Allaire 2015 To address this, we use a surrogate model to approximate drag-related metrics efficiently and differentiably (Baqué et al. 2018: Remelli et. al. 2020
We use a graph convolutional neural network (GCNN), specifically with GraphSage layers (Hamilton et al. 2017), predict the surface pressure distribution of a car. The predicted surface pressure integrated to compute the drag force (Equation (10)), ) which then normalized by the mass density of the fluid, its velocity squared, and the frontal surface area of the shape to obtain Ca. We simulate the cars in dataset, following the well-established sotup of the DrivAer model (Wieser et al. 2014), to compute the corresponding surface pressures and Cd values. The dataset thus created is used to trained the GCNN-based surrogate model.
Following this, all model parameters, those of PartSDF and the surrogate's, are frozen for the shape opti- mization. It is performed by adjusting the latents Z and/or poses P of the parts, starting from the initial parametrization of existing car. In this experiment, the wheels are kept fixed and only the body is opti-
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G 0.378
C2 0.520
G2 0.338
C2 0.473
G 0.322
Ca = 0.397
Co 0.307
0.391
Figure 14: Additional shape optimization. The aerodynamic drag of the car is minimized with respect. to the latent vector of the car's body, with fixed wheels. We show the initial car pre-optimization (top) and the resutling car optimization (bottom), colored by surface pressure from low to high pressure (blue to red). We also visualize the parts in the insert. We report the drag coefficient Ca before and after the shape optimization, as computed by a physical simulator (OpenCFD).
mizod, which is only possible because of the composite shape representation of our model that also ensures coherence between the parts.
The optimization minimizes the integrated pressure drag predicted by the surrogate model, backpropagating through the meshing to adjust the part parameters (Equation [1 Regularization terms frog are applied to maintain consistency in the latent space and prevent excessive deviations:
A k-nearest neighbors (kNN) loss on the latent vectors to ensure they remain close to the training distribution, as introduced in (Remelli et al. 2020), and
an L2 regularization on the deviation of latent vectors and poses from their initial values, e.g.. |Z Zinit 2
To summarize, during single iteration of this optimization process:
Current part latents and poses (Z, P) are used to compute the car's SDF on grid, as required by the Marching Cubes algorithm.
2. Marching Cubes is applied on the SDF grid to obtain a mesh of the car surface S MC Z,P).
3. The mesh is passed through the GCNN surrogate to obtain the surface pressure p(S), from which the drag coefficient Cj is computed.
4. The gradient of Ca + Creg is computed with respect to (Z.P), which are then updated through stochastic gradient descent.
This setup allows us to efficiently optimize composite shapes for aerodynamic performance while leveraging the flexibility of PartSDF's framework.
Results. With this experimental setup, we optimize multiple cars from our dataset and simulate the resulting shapes in OpenFOAM (OpenCFD) to obtain their final drag cocfficient C2. Because simulations are expensive (> 10h depending on the meshing resolution of the 3D space), we must limit ourselves to a subset. of 35 cars. The average drag coefficients before and after optimizations are
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Figure 15: Part interpolation. On each row, we interpolate between the part latents and poses of one shape (left) to the other (right) and reconstruct the intermediate shapes. The overall shape structure is preserved while the parts change smoothly, remaining coherent with each others.
Before
After
0.378
0.325
with an average relative improvement of 12.7%. We visualize some optimization results in Figure 14 As can observed, only the body of the car has been modified while the wheels are unchanged. Nonetheloss, they stay consistent with each other and no penerrtent happens.
E
Part Interpolation
To demonstrate the smoothness and consistency of our latent and pose space, we perform an interpolation experiment. Given pair of shapes, we linearly interpolate between their part latent vectors and poses, with the exception of rotation quaternions for which we use spherical linear interpolation (slerp). At multiple interpolation steps, we reconstruct the intermediate shapes using our decoder and visualize such interpolation 'path' in Figure [5] illustrating smooth transitions between the pair of shapes. Notably, the part-based structure remains coherent throughout the interpolation. This highlights the effectivenoss of our learned latent and pose spaces in representing composite shapes.
F Results on DrivAerNet++
To evaluate PartSDF in realistic industrial setting, we trained our model DrivAerNet+ Elrefaie al. 2024), high-fidelity automotive dataset. designed for aerodynamic analysis and shape optimization. The
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GT
Ours
Figure 16: Reconstructions on DrivAerNet++ Reconstructions from the test set of the DrivAerNet- dataset. PartSDF successfully captures fine geometric details and preserves consistency between parts.
Figure 17: Manipulation on DrivAerNet+++ (Left) Wheels are translated, then the car body is elon- gated. (Right-top) We interpolate from an Estateback to a Notchback in a smooth manner. (Right-bottom) We sample random body and back latents with the same wheels and poses to generate varying designs with similar general scale.
dataset includes three base designs, each with thousands of geometric variations capturing diverse body, back, and wheel configurations.
We used these data to train PartSDF with separate parts for the car body, car back, and wheels, using the same architecture and loss functions as in our main experiments. Figure 16 shows reconstruction examples on held-out test shapes, demonstrating that PartSDF accurately captures fine geometric details and maintains part consistency these industrial-grade models.
Furthermore, illustrated in Figure 17 PartSDF enables smooth and coherent manipulation and interpola- tion between car designs. These results highlight the ability of PartSDF to generalize to high-fidelity shapes and support structured manipulation in practical aerodynamic design scenarios.
G Additional Experimental Results
In this section, we provide additional results and visualization on shape reconstruction (Appendix G.1 with object categories, generation (Appendix G.2 and manipulation (Appendix G.3
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Published in Transactions on Machine Learning Research (10/2025)
3eShape2VeeSet
Ours-IP
DRE-NET
BAE-NET
PQ-NET
PASTA
Ours
Ours-PC
GT
Figure 18: Additional shape reconstruction. Reconstructions of test shapes using the baselines and our model. We use a single part with Ours-1P and Ours-PC is the reconstruction using the point cloud encoder, as described in Section 4.1 For part-based method, we translate the helix outside of the mixers for visualization.
G.1 Shape Reconstruction
We provide additional examples of shape reconstruction on the test set in Figure 18 We also visualize the part poses as primitives and results using the point encoder. DAE-NET and BAE-NEs struggle to recover thin parts and complex shapes, while PQ-NET tend to inflates them without details. On the opposite, PartSDF recovers accurately the shapes and the parts. We note that with a point cloud encoder, the results may not be as accurate, e.g., the last chair where the armrest segmentation different, though it still sensible.
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Published in Transactions on Machine Learning Research (10/2025)
Table 8: Additional categories. We report reconstruction metrics on test shapes for two new categories: Display and Knife.
CD (U)
IoU (%, f)
1C (t)
ploU (%, f)
Display
Knife
Display
Knife
Display
Knife
Display
Knife
3DShape2VesSon
4.95
1.72
92.57
80.33
0.949
0.870
Ours-1P
4.45
0.35
95.02
93.89
0.949
0.943
DAE-NET
98.75
489.58
58.67
46.63
0.772
0.567
45.76
42.39
BAE-NET
161.16
387.71
43.72
34.26
0.718
0.536
29.81
31.41
PQ-NET
95.73
41.60
42.81
30.45
0.775
0.560
41.44
36.09
PASTA
148.07
10.57
60.01
58.01
0.834
0.718
Ours
1.73
0.28
97.37
96.16
0.965
0.958
89.11
92.81
3DS2VS
Ours-IP 1P
DAE-Net
BAE-Net
PQ-Net
PASTA
Ours
GT
Figure 19: Additional categories. Reconstructions of test shapes using the baselines and our model on two new categories: Display and Knife.
Additionally, we expand our evaluation to additional categories from ShapeNet and PartNet: Display and Knife, featuring 640 and 324 shapes with and 3 parts respectively. Results are given in Table and Figure 19 They confirm that PartSDF delivers a strong performance beyond the original categories. particular, the CD value for our method using multiple parts markedly better on the Displays, mostly because baselines tend to fail drastically for few shapes, whereas our complete approach succeeds. Voxel- based approaches DAF-NET, BAF-NET, and PQ-NET particularly struggle thinner shapes, which result in very large CDs. We also observe that PASTA struggles all datasets because it only uses parts bounding box as information for reconstruction.
G.2 Shape Generation
In Figure 20 we visualize generation examples with PQ-NET and PartSDF. We also show the part latent gencration conditioned on poses for our model. The generated shapes with our method in combination of SALAD Koo al. 2023) are more detailed than PQ-NET + a latentGAN, with greater variety for cars and mixers (as reported in Table 2
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Published in Transactions on Machine Learning Research (10/2025)
3DShapeeVecSet
PQ-NET
PASTA
Ours
Ours!
Figure 20: Additional shape generation. Randomly generated shapes and their parts on all datasets. We also provide examples of pose conditioned generation (Ours?) where part latents are generated based on the poses' coarse description of the shape (top image for each pair). When possible, the helix is translated outside of the mixers for visualization.
G.3 Shape Manipulation
Finally, we perform more manipulation in Figure 21 with PartSDF on all dataset. By changing part latents, the affected parts have modified appearances but adapt to the original pose and to each others. For example,
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Published in Transactions on Machine Learning Research (10/2025)
Additional shape manipulation. We manipulate four shapes per dataset: (top) by changing the latent of specific parts (car body, mixer helix, and all chair parts) and (bottom) by editing part poses (car wheels, mixer width, chair width and height). In all cases, the parts adapts the modifications and each other, maintaining a coherent whole.
Figure 21:
Figure 22: Single-view reconstruction. Given a single RGB image (top), a lightweight ResNet-18 encoder predicts part latents and poses for our pretrained part decoder, which reconstructs the composite 3D shape (bottom). The model recovers coherent part layouts and overall geometry.
the car bodies have the same general scales but their wheel wells correctly the original wheels, the mixers helices fit the original lube, and the chairs keep the same overall structure while each parts are locally different. When editing their poses, the parts are moved and deformed, but also preserve their original features, e.g., the cars keep their original shapes but adapt to their new wheels, the mixers and their helices are rescaled but conserve their inside/outside relationship, and the size and height of chairs can be changed while maintaining the chairs' features. Note that this requires the part poses to be correct and coherent. Indeed, if they are manually set to be out of contact and disorganized in 3D space, the resulting shape will be meaningless.
Single-
Single-View View Reconstruction
While our main application focuses on shape optimization, we also experiment with single-view 3D re- construction to demonstrate the feasibility of integrating PartSDF into an image-based pipeline. For this proof-of-concopt, we trainod small image encoder predict the part latents and poses corresponding to our pretrained part decoder. The encoder is ResNet-18 model trained synthetic renderings from ShapeNet (Chang et al. 2015) using the dataset of 3D-R2N2 (Choy et al. 2016a).
In Figure 22 we show reconstruction examples on held-out test images. Despite the simplicity of this setup and limited training data, the results demonstrate that PartSDF can, in principle, recover coherent part- aware 3D structures from single RGB images. Extending this to real-image datasets is a promising direction for future work.
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Reviews:
[{"review_id": "9MaGkZUi9W", "reviewer": "Reviewer_aHYc", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths** \n\n- PartSDF consistently outperforms both supervised and unsupervised baselines in reconstruction and generation tasks. The method yields superior accuracy by training with samples directly from the original shape, allowing it to capture detailed part-specific geometry and structure.\n- The framework provides a versatile, fully differentiable, and multi-part representation. It enables precise control over individual components, which is crucial for engineering applications like design and optimization. The same decoder network can be used for various downstream tasks without modification.\n- The paper is well-written and well-organized. The loss terms are well defined for the whole network.\n\n\n**Weaknesses** \n\n- What about the time efficiency for generation or interpolation tasks?\n- What about the topology change during interpolation, since the SDF is topology-friendly? And if there are some parts that disappear during interpolation, will there be some abnormal shape generated?\n- For the supplementary (GIF), the presented cases are relatively simpler. Could you show some complex cases to demonstrate the SDF's ability?\n- Recently, there have been some large models for the part-level generation, such as the CAST (cast: component-aligned 3d scene reconstruction from an RGB image). I am curious about the comparison and performance.\n- From the presented results, the visual quality seems better to me. Why not demonstrate the ability by some practical application, such as the single-view reconstruction? I suggest adding this application and performing some comparison with the existing works.\n- The paper presents a good shape of the methodology and evaluations. I still suggest the author add more evaluations to present the complete evaluations for readers, since I still have unknown points about the methods. I think the other reader still has the same questions.\n- The limitations are very clear. The main limitation of PartsDF is that it requires predefined part labels for training. While this fits well with computer-aided design (CAD) workflows where parts are known, it limits the method's applicability to datasets without such decompositions. And for the open surface are also drawbacks. And during the discussion of the limitation, could you show some failure cases to incorporate the limitation?\n- For the dataset, could you show some noisy, incomplete, or non-watertight shape? I want to know the model can handle which kind of noisy, incomplete, or non-watertight shapes. Is it over-claim?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces a supervised implicit representation framework for modeling composite 3D shapes with distinct, controllable parts. The core contributions are:\n\n- A architecture that uses a shared implicit model to decode each part, represented by a latent vector and a pose. The full shape is formed by taking the minimum of the part SDFs, ensuring global coherence and seamless composition.\n- A new supervision technique that bypasses the need for clean, watertight part meshes. \n- Demonstrating the model's versatility as a shape prior for multiple tasks, including shape reconstruction, part-aware generation, and constrained optimization, all with the same core auto-decoder architecture.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "The following adjustments would strengthen the work in the reviewer's view, also including the weaknesses:\n\n1. The authors should investigate developing more advanced topological supervision for each part to further improve robustness and prevent topologically inconsistent predictions. I still have some concerns about the ability of topological representation, especially for the interpolation and optimization (The start shape is so close to the target shape).\n\n2. To handle parts that are pure surfaces (e.g., a car hood) that are not naturally handled by SDFs, the authors could explore using unsigned distance functions in future work.", "broader_impact_concerns": "The reliance on pre-labeled data is noted as a limitation, which could be a concern for fairness and bias if the curated datasets do not represent a broad range of shapes or designs.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "57sAFERHcb", "reviewer": "Reviewer_wdYS", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n  + Strong experimental section, with many uses from one architecture demonstrated, and ablation study on the loss function components.  \n  + Their method improves upon the baselines in almost all instances, including often improving upon reconstruction methods against baselines that do not also decompose into parts.  \n  + Compelling application (in one-part optimization) that well-motivates why this parts-based decomposition could be very useful.  \n\n\nWeaknesses:\n  - I would like to see how the baseline models compared in size to the proposed PartsSDF model.  Is the improvement simply because the proposed model is larger and trained larger?  If, for instance, 3Dshape2VecSet model is smaller, but scaled up to match Ours-1P, would it perform as well?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper provides a deep neural model for 3D shapes that can be used for reconstruction, manipulation, and optimization -- with the main novelty in how it handles the decomposition of the overall shape in to separate parts.  \n\nThe technical contribution is in the neural architecture, which has alternating layers between ones for the entire shape, and for representation by parts.  This allows for carefully structured loss functions.  \n\nThere is a nice and thorough experimental section on shape datasets (each with decomposition into about 5 parts), for cars, chairs, and mixers.  It demonstrates the networks ability in auto-encoding, generative modeling, and manipulation, and optimization.  The optimization in particular, where a car body is optimized without changing the wheels, shows the power and promise of the part-decomposed modeling.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "At least report the relative size of the baseline models interns of memory or number of parameters.  If possible and they are smaller, scale up some baseline model to see if they match the performance of the PartSDF model. \nAlternatively, you could show a version of PartSDF with fewer layers to shrink it in a way that would match baselines.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "wY5h0j2QFM", "reviewer": "Reviewer_J4Dm", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The authors proposes modeling composite shapes using independent part-level signed distance functions (SDFs), thereby allowing precise control over individual components while maintaining overall coherence.\n- The authors conduct detailed experiments and ablation studies, demonstrating superior performance in both reconstruction and generation tasks against supervised and unsupervised baselines.\n- The paper is well-written and is easy to understand.\n- The proposed single-decoder architecture is elegant and lightweight compared to more complex multi-step or post-processing methods.\n\nWeaknesses:\n- Experiments appear to focus on a narrow scope of the datasets. The generality of the method would benefit from tests on more diverse categories and real-world examples.\n- While comparisons include supervised and unsupervised baselines, it misses the discussions with some recently related work such as PartGen (CVPR 2025).\n- The paper would benefit from deeper analysis of design choices—e.g., how different numbers of parts, architectural variants, or SDF aggregation strategies affect reconstruction quality and control capability.\n- It's unclear how the method handles objects with a very high number of parts. Questions remain about model size, training cost, and performance degradation when handling more complex objects.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes PartSDF, a supervised implicit 3D shape representation that models objects as assemblies of independent, controllable parts while preserving global consistency. The method introduces a part-aware implicit architecture enabling precise per-component manipulation for engineering design workflows. The authors conduct detailed experiments, showing the state-of-the-art reconstruction and generation performance over supervised and unsupervised baselines.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See [weaknesses] above.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)