GALA: Geometry-Aware Local Adaptive Grids for Detailed 3D Generation
Authors: Dingdong Yang
Yizhi Wang
Konrad Schindler
Ali Mahdavi Amiri
Hao Zhang
Venue: ICLR 2025 Poster (2025)
Keywords: Generative Model
3D
Computer Graphics
Primary area: generative models
TL;DR: A new representation for 3D geometry generation

Abstract: We propose GALA, a novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern, diffusion-based schemes. The key idea of GALA is to exploit both the global sparsity of surfaces within a 3D volume and their local surface properties. *Sparsity* is promoted by covering only the 3D object boundaries, not empty space, with an ensemble of tree root voxels. Each voxel contains an octree to further limit storage and compute to regions that contain surfaces. *Adaptivity* is achieved by fitting one local and geometry-aware coordinate frame in each non-empty leaf node. Adjusting the orientation of the local grid, as well as the anisotropic scales of its axes, to the local surface shape greatly increases the amount of  detail that can be stored in a given amount of memory, which in turn allows for quantization without loss of quality. With our optimized C++/CUDA implementation, GALA can be fitted to an object in less than 10 seconds. Moreover, the representation can efficiently be flattened and manipulated with transformer networks. We provide a cascaded generation pipeline capable of generating 3D shapes with great geometric detail. For more information, please visit our [project page](https://santisy.github.io/GALA/).

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GALA: GEOMETRY-AWANE LOCAL ADAPTIVE GRIDS FOR DETAILED 3D GENERATION
Dingdong Yang'
Yizhi Wang'
Konrad Schindler?
Ali Mahdavi-Amini
Hao Zhang'
Simon Fraser University.
2ETH Zurich.
A
(a) Input Mesh
B
277k bit Reconstruction
(c) Subdivision
(d) Zooming Local Adaptive
Figure I: Given a watertight mesh (a), our representation, GALA, for geometry-aware local adaptive grids, distributes set of root node voxels (coral) to cover the mesh surfaces. An octree subdivision applied each root, with a subset shown in (c). In each non-empty octree leaf node (green), local grid (red dots) is oriented and anisotropically scaled to adapt to and tightly bound the local surface geometries. Only 277K parameters with 8-bit quantization yields an accurate representation (e).
ABSTRACT
We propose GALA, novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern, diffusion- based schemes. The key idea of GALA is to exploit both the global sparsity of surfaces within 3D volume and their local surface properties. Sparsity is promoted by covering only the 3D object boundaries, tree root voxels. Each voxel contains an octree to further limit storage and compute regions that contain surfaces. Adaptivity is achieved by fitting one local and geometry- aware coordinate frame in each non-empty leaf node. Adjusting the orientation of the local grid, as well as the anisotropic scales of its axes, to the local surface shape greatly increases the amount of detail that can be stored in a given amount of memory, which turn allows for quantization without loss of quality. With our optimized C++/CUDA implementation, GALA can be fitted to object in less than seconds. Moreover, the representation can efficiently be flattened and manipulated with transformer networks. We provide cascaded generation pipeline capable of generating 3D shapes with great geometric detail. For more information, please visit our project page
empty space, with ensemble of
INTRODUCTION
The generation of high-quality 3D assets remains costly task in terms of processing time and resources involving human efforts or machine compute. A continuing research pursuit is to develop efficient 3D representations to streamline the traditionally expensive 3D creation workflow

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Figure 2: GALA enables diverse and detailed conditional 3D shape generation, including Airplanes, Lamps, Tables and Chairs. Best viewed on screen with high magnification.
Gupta et al. 2023) ; Jun Nichol (023): et al. (202);; Nichol et al. (2022): : Shue et al. (2023),
with the ultimate goal of speeding up the generative process without compromising the diversity and quality the generated assets as reflected by their structural and geometric details.
To date, a variety of 3D representations including voxel (Li et al. 2023) and tetrahedral grids chek et al. 2024). meshes (Liu et al., 2023b), point clouds (Luo & Hu 2021: Zhou et al. 202 ).
(Kliis
neural fields (Jun & Nichol 2023), and triplanes (Chan et al. 2022 Shue et al. 2023 Gupta et al. 2023), have been employed for 3D generation, often leveraging powerful diffusion- generators. However, argued recently by (Yariv et al. 2023), none of these representations fulfiil all of the three critical criteria for high-quality and scalable 3D generation: parameter efficiency for detail representation, preprocess efficiency for handling large datasets and mesh conversion, well as simplicity of a tensorial form to suit modern-day neural processing. In response to this, they proposed Mosaic-SDF which encodes a signed distance function using "mosaic" of aligned volumetric grids distributed over the shape surface, with different centers and different (still isotropic) scales.
In this paper, we accentuate that the key 3D representation efficiency when using such an ensemble- of-tiles approach is adaptivity of the local coordinate grids to the geometry of the presented shapes. To this end, we propose represent a 3D shape using set of geometry-aware and local adaptive grids. Our novel representation, coined GALA, pushes the limit of adaptivity on three fronts:
To exploit the global sparsity of typical object surfaces within a 3D volume, we place forest octrees, rather than uniform subdivisions, the object boundaries, where local grid is associated with each non-empty octree leaf node to store SDF values.
Our local grids are not globally aligned. Instead, each grid may be differently oriented based local PCA analysis of surface normals within the corresponding octree subdivision.
Last but not least, anisotropically scale each grid better capture geometric details.
Our GALA representation can be implemented to yield sets of vectors that can be easily processed by transformer-based neural networks (Vaswaní al. 2017). while the octree forest provides hierarchical 3D representation with limited depths. In Table 1 we compare GALA with several state-of-the-ae tfetthrrrrtt representative methods over several useful criteria.
The contributions of our work are threefold:
Our geometry-awarc locally adaptive, and anisotropic grids enable more efficient (Table I) and accurate sampling of shape structures, capturing geometric details, such as thin strings
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and plates, which may be missed by both regular grid-based methods (Hui al. et al. 2023) and Mosaic-SDF whose grid tiles are neither shape- nor detail-awe -aware.
2022 Li
2. We have developed an efficient implementation pure CUDA and libtorch for the entire GALA extraction process. This process costs about 10 seconds for each watertight input mesh on Nvidia A A00 GPU, which among the fastest ones of popular fitting methods, enabling fast data processing for large datasets.
3. The hierarchical structure of the octree forest in GALA facilitates the development of a practical cascaded 3D generation scheme with improved efficiency and quality.
Purameter Count
Fitting Time
Representation Precision
Generation Network
Methods
Description of representation
S2VS Zhang al.
2023
Autoencoded vector set Deformable tetrahedral grid
$ 262k
Mcidum/Low
Transformer
MeshDrrustoni Liu aL.
1.05M
20m-30m
High/Medium
UNet
Neural Wavelet Hul Hur et 2016
Two levels of wavelet cocficients
536k
1s
Medium
3D UNet
Mosaic-SDF Yanv et al.
2723
Grids on boundary boundury
355k
2m
High
Transformer
GALA
Trees with adaptive
277k
10s
High
Transformer
Table 1: Properties of different representations for 3D generation. The representation precision is
defined as the reconstruction errors with respect to input meshes. See subsectioo 4.3 more.
RELATED WORK
2.1 3D REPRESENTATION FOR GENERATION
We will first review the related work on 3D representation for generation, focusing on various methods characterized by shared features.
Grid-based Regular iad-based representations (Hui et al. 2022 2024 Li et al. 2023) utilize fixed-resolution grid for encoding various 3D quantities such as occupancy, signed distance function (SDF), color and etc. Such methods, however, may not capture extremely fine structures at the very initial stage of discretization. Additionally, regular grid-based representations allocate a substantial portion of their capacity the empty spaces, leading to potential cubic rate of parameter increase. In contrast, the adaptive local grids GALA are able to capture thin structures and the octree forest allows for scaling the representation power with only linear increase of parameters. Deep Marching Tetrahedra (Shen et al.) 2021) (DMTet) uses deformable tetrahedral grids to improve the representation efficiency compared with regular grids. However, the fitting time (Liu al. 2023a of DM'Tet is about 10 times ours, the parameter count of DMTet is 3 times ours (See Table for specific numbers.) while represent geometry more accurately than it.
Triplane To mitigate the cubic complexity inherent in regular grid-based methods, triplane ap- proaches (Chan al. 2022 Shue al., 20233 Gupta et al., (203) employ three planes, each aligned with an axis in 3D space. Information at each 3D location is queried by first tri-linear interpolation from the three planes, followed by processing through various neural network architectures. Although triplane-base based representations enhance parameter efficiency compared to regular grid-based methods, the tri-linear interpolation may result in oversmoothed outcomes and also missing geometric details.
Point Cloud Point cloud- bosu- representations (Luo & Hu 2021 Zhou et al. 2021 Zeng et al.) 2022) describe 3D shapes by placing points on geometry boundaries. To accurately describe the shape, excessive number of points will be needed, which is not practical for the following generation task. Limited number of points will loss details of the shape. Moreover, post-processing methods (Kazhdan) et al. 2006 [Png et al. 2021) are required to convert point clouds to meshes, which may introduce additional inductive bias.
Neural Implicit Neural implicit representations Park et al. 2019 Chen & Zhang 2019) model 3D
shapes by learning mappings between coordinates and desired 3D quantities. When combined with the autoencoding framework, latent codes (Zhang al. 2003 Chou al. 2023) are derived. A drawback of these methods is that the autoencoding may result in oversmoothed geometric features. Furthermore, mesh extraction from neural implicit representations requires querying numerous points
hhtps://yntorrc..n////ppeee

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in space, yielding expensive neural network evaluations. In contrast, GALA enables direct and efficient extraction of geometries without the involvement of any neural network.
Lastly, would address the work of Mosaic-SDF (Yariv et al.) 2023) individually. Different from our method, Mosaic-SDi. only has a single level of voxels and each voxel has isotropic scale for each axis. In this sense, it has limited adaptation in representing the geometry. Moreover, it has to model the whole distribution as whole at once while previous researches (Saharia et al.) 2022 Pernias et al. 2023) have shown hierarchical or cascaded generation may benefit the generation.
2.2 GRAPH AND TREE GENERATION
General graph generation relies on the Graph Neural Network and message passing mechanism. Oth- ers like HGGT (Jang et al. 2023) use graph compression methods such - and sequentially generate tree nodes in an autoregressive way. In our case, generating arbitrary topology graph is unnecessary because we focus on generating octrees. OGN (Tatarchenko et al. (017) uses recursive way of generating octree voxels and Octree Transformer (Ibing et al. (2033) uses autoregressive way of generating tree nodes by transformers. In contrast with their methods, we use the widely adopted and effective generation paradigm, the diffusion model. BrepGen (Xu et al. 2024) generates fixed topology bace-edge-veriic vertice trees hierarchically by diffusion. Since the topology is fixed, the corresponding relation can be easily injected when training the diffusion model. We plan to adopt similar cascaded generation scheme to BrepGen based on our GALA representation.
METHOD
We will introduce our methods in two parts: subsection 3.1 the construction of GALA from the input watertight meshes and (ubsecttonn 3.2 the cascaded generation of GALA.
p
q, Sg. m, V)
Mosaic-SDF
GALA
Figure 3: In our representation, GALA, tree root nodes, as voxels, are initialized over mesh surfaces (gray line), each with location p E R& and scale E R. Descendant node voxels are deduced recursively in the octree way, with overlapping, and expanded ratio E R into depth d. Only at a non-empty leaf node subdivision (light green) would a local adaptive grid of resolution m E N be extracted with location Pg RR, orientation quaternion q R4 scales Sg RR3 and values
V E R== No: at m, are hyperparameters. In contrast, Mosaic-SDF Yariv et al. 2023) (left) employs mosaic patches, each fully occupied single-level, axis-aligned, and isotropic grid.
3.1 CONSTRUCTION OF GALA
We illustrate the overall GALA structure in 2D in Figure 3 and will dissect the construction pro- cess into: subsubsection 3.1.1 Octree forest initialization, subsubsection 3.1.2 Local adaptive grid
extraction, subsubsection 3.1.3 Refinement and subsubsection 3.1.4 Fitting- aware Quantization.
3.1.1 OCTREE FOREST INITIALIZATION
Given the number of trees N., we find the centroids of tree root node voxels by Farthest Point Sampling (FPS) (Eldr et al. (197) of densely sampled points X' the mesh of the input object. Then, to determine the scale of each root voxel i, we assign each sampled point x E X' to its nearest centroid and define the scale scalar the infinity-norm radius of each cluster:
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5; max |X -Piloo xEC.
C,
E
i
arg min ke RE.0....Noo-11
||x P
(I)
In this way, we ensure that the forest will fully cover the shape boundaries. After setting the tree root voxels, we recursively deduce the further levels of octree nodes in an overlapping way where we slightly expand the divided spaces at each level by ratio a. This expansion operation enables more voxels contribute to the geometry modeling at early tree levels. See Bo4 the ablation study of a.
3.1.2 LOCAL ADAPTIVE GRID EXTRACTION
(a)
(c)
10
(b)
(d)
Figure 4: Illustration of local adaptive grid extraction in 2D. Within each subdivision (blue square), (a) an OBBTree (Gottschalk et al., 1996) determines the orientation of the local bounding box according to the convex hull of the subdivided local geometry. determine the orientation of the local adaptive grid using PCA on bounded normal vectors (77). (c) Moreover, we rescale the grid anisotropically to better capture the local geometry, as informed by the histogram (d) of sampled points (small dark gray dots) on triangle meshes projected along each axis of the grid. The +/- are grid samples with negative/positive signs.
(b) Different from OBBTree, we
Properly placing the local adaptive grid within each subdivision is essential our method. The OBBTree (Gottschalk et al.] 1996) determines the orientation of the local bounding box using eigenvectors of the covariance matrix derived from points sampled on the convex hull faces of the subdivided geometry (Figure Ja)). However, we take different approach. Instead of only defining bounding box, we use grid designed to capture as much geometric information as possible. Because the orientation derived from convex hull sample points may not align with the actual geometric structure, we align the grid orientation with PCA the local normal vectors 7/ instead (Figure 4 ()).
Additionally, rescale the grid so that at least one set of grid samples locates the most geo- metrically dense spot and adjacent grid samples with different signs capture more zero isosurfaces (Figure c)). To achieve this, utilize the histogram H of sampled points projected along each grid axis u, and move nearest and smaller grid samples to the histogram peak (Figure d), Algorithm
Algorithm Rescaling the Grid with Histogram
1: Input: orientation u, and scale s at axis i;
c t- center of max(H)
center Py and bounded meshes M
Get grid index Ig + arg max/ (2l < <c
2: Split half axis of length si into nıs bins
7: if I, 0 then
3: Sample points x E M
4: Count
(x- P.)-u: into histogram H [x P.]l
9: end if
g 21,
We will show the effectiveness of our local adaptive grid extraction by ablation studies in secciiiio 4.5 After determining the locations, orientations and scales of anisotropic local grids, truncated ground truth SDF (Hui al. 2022) values (truncated to 0.1.0..111 are used initialize the grid values

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V. All the above initialization and extraction processes before refinement cost few seconds (as 2.56 = 1.30s in ShapeNet Airplane). More detailed information on the time measurement, see A.4
3.1.3
REFINEMENT
After extracting the local adaptive grids, we further refine the grid values V by backpropagation to represent the input geometry accurately. For each queried location x, the queried value ex!
Ux Σ, (x, i) Σwi (xx iX(xxx)
1
(2)
w(x. i) = ReLULLLLLL - 11(x - 11 10,00,.. ss 'loo),
(3)
where I(x, i) (Equation 2)
is the tri-linear interpolation of grid values V within the anisotropic local grid that encapsulates the query x and w(x, i) (Equation 3) is the weighting function which defined by the -norm neighborhood centered at the grid center p and oriented O, 3 and scaled
s, as the adaptive grid. All grid values will be optimized by MSE loss M = [[ Ucr (x)ll2) using backpropagation, where (xr(x) is the truncated ground truth SDF value at location directly computed from input meshes. We assign V/x 0.1 if x does not lie in any local grid. We will flip signs of interior parts in slices Rext of the SDF extraction grid I fx to -0.1 via a DFS method when extracting meshes from GALA. Mesh extraction algorithm is detailed in A.1
3.1.4 FITTING-AWARE QUANTIZATION
To increase the storage (see more at B.3) and memory efficiency of GALA as well as lower the difficulty of aligning float values in space inspired by the discrezation step in MeshGPT (Siddiqui et al.;
2024), we quantize the local adaptive grid related quantities q. Pa: Sg. V during the fitting process by
Strought-Thoouhh Estimator (STE) (Bengio al. 2013 Han al.) 2015). We quantize the orientation in the unit of 60 of Euler angles and Sy. Pg. V in 8 bit of the range [0, 0.1., [-0.5 0.5]. 0.1, 0.1).
3.2 CASCADED GENERATION OF GALA
Motivated by previous cascaded generation works (Saharia et al. 2022; Ho et al. 2022 Xu et al. 2024 Hui al. 2022 Chen et al. 2021) which successfully generate complicated 2D 3D data in a coarse-to-fine manner, we generate sets of information Xo, Xy, Xv, of GALA step by step where flattened vectors of root node X. fx, E IR (p, s)}, local adaptive grid configuration Xp = [xp E [q. sg. py]} and grid values Xv = fxv E IR"") } are composed (Refer to A.2 for more details the data preparation). Specially, since the configurations of local adaptive grids Xp already encode rich local geometric information as articulated in subsubsection 3. 3.1.2 we are able to directly regress Xy from Xv, which greatly alleviates the generation training burden.
X
X
Xy
Transforment
Transforment
cansforma
||((b) Xv ll
+
U
(X)
local
FF
Root
Stuel
(X+)
(1) Root Voxel Diffusion
Grid Config Diffusion
(3) Grid Value Regression
Figure 5: GALA generates shapes in cascaded manner by (1) Root voxel diffusion; (2) Local
adaptive grid configuration diffusion; (3) Local adaptive grid value prediction by regression.
2017 Peebles Xie 2023). (1) The class label y conditioned distribution of root voxels P(X,, y) firstly modeled by diffusion model (Song et al. 2020 Ho et al.) 2020). (2) Configurations
All sets of vectors are processed by transformer- networks (Vaswani et al.
anisotropic local grids X generated following that via modeling P(Xp X by diffusion model. (3) Lastly, grid values V are predicated from grid configurations V via X, = F(X,. .y) and trained by L2 regression loss.
More specifically speaking, we see in Figure 5 (2), siblings of padded leaves are grouped and

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folded once and previously generated root voxel information Zo.; X, is added directly the nodes of its corresponding descendants together with local positional encodings (PE) of trees to differentiate siblings among them. In all, following the popular diffusion training paradigm (Ho et al.) 2020 Song et al. 2020), we update the diffusion network weights 0 via the v-prediction (Salimans & Ho 2022
Vollv - vo (X L, y, x2)
V w= == - 0g6
where x - V + + v1 dre, X
(O, 1) is the diffusion forward process. är is defined by a; = I ar 04 = 1- 3, where Br is the variance schedule. or = /11 - ãr and cosine noise scheduling (Nichol Dhariwal (02T) is used. The network weights & for the first step are updated in similar manner as described above. For more details, please refer to A.5
4 EXPERIMENTS AND RESULTS
4.1 IMPLEMENTATION DETAILS
For the hyperparameter of GALA, set tree root number N, 256, child node expanding ratio = 0.2, grid resolution m = 5 and depth d = 1. The number of histogram bins H is 2m. For the refinement process, 8192 points are queried near surfaces on each run for 400 iterations. Details of the pure C++/CUDA implementation and anonymous code release link will be found at A.3
For the cascaded generation, each network for every generation step is consisted of 24 transformer layers with model channel 1024. Adam (Loshchilov & Hutter (017)) with Ir 8e-5 81 0.9, B3 0.999 is adopted. We test the reconstruction and generation ability our methods on the whole ShapeNet (Chang et al., (2015) dataset. We follow the dataset split of previous works (Zhang)
et al. 2022 2023
Yariv et al. 2023) and train conditional generation on the whole ShapeNet classes.
4.2
METRICS
We evaluate reconstruction results using Chamfer Distance (CD) between two sampled 3D objects and also report the Light Field Distance (LFD) (Chen et al. 2003), a widely adopted (Chen et al. 2020 Gao et al.) 2022. Zuo et al. 2023) visual similarity metric that is well-known from computer graphics. To evaluate the generation results, we adopt the metric of Maximum Mean Discrepancy
(MMD), Coverage (COV), and I-nearest neighbor accuracy (I-NNA) based Chamfer Distance
(CD) and Earth Mover Distance (EMD) (Luo & Hu 2021
Zeng et al. 2022).
4.3 RECONSTRUCTION RESULTS
We compare our reconstruction results with 3DShape2eecSet (S2VS) (Zhang al.. 2023). Neural Wavelet (NW) (Hui et al.) 2022) and MeshDiffusion (DMTet, 64 x 4) (Liu et al. 2023a). We measure the reconstruction metries on 50 objects of ShapeNet classes (airplane, car, char, basket, guitar), 10 objects per class. From Table 2 we can see that our reconstruction is more accurate than other baselines. means local adaptive grids. Without A, uniform grid samplings will placed within tree voxels in the axis-aligned way. Visual comparisons
results w/o A are shown in B.I where the local adaptive grid setting captures more accurate details on geometry surfaces. Qualitative comparison of reconstruction is shown in Figure 6 As most geometric details with one of the fewest parameter numbers.
see from Figure we preserve the
Metric
S2VS
NW
MeshDiffusion Ours, w/o A
Ours
LFD | CD (x10-3)
2429.92
1869.80
1301.14
1146.74
1109.36
4.32
4.17
2.61
1.52
1.18
#Parameters
< 262k
536k
1.05M
263k
277k
Table 2: Reconstruction quality across 5 ShapeNet classes (airplane, basket, car, chair, guitar; 10 random objects per class).
Because we do not have the official code release from Mosaic-SDE Yaariv et al. 2023). we requested the reconstruction results from the authors of Mosaic-SDF and compare the reconstruction of ours
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from Figure 7 the car is challenging example with them qualitatively in Figure 7 As exterior and interior structures such as very thin and shown in Mosaic-SDi and with complicated close surfaces. GALA capture exterior and interior geometry structures at the same time. In contrast, the result of Mosaic-SDF fails to capture internal structures. As for the guitar example, GALA has the better connection of guitar strings and the thickness of strings is closer the ground truth than it of Mosaic-SDF.
Input (GT)
Ours (GALA)
MeshDiffusion (DMTet)
S2VS
S2VS
NW
Figure 6: Qualitative comparison of reconstruction results between ours and other important baselines. S2V$1 (Zhang et al. 2023) is evaluated from the public checkpoint provided the official repository and S2VS* is our own implementation. All evaluated at resolution 256 Zoom in to more details.
Mosalc-SDF
(GALA)
GT
Mosaic-SDF
Ours (GALA)
Figure 7: Qualitative comparison of the reconstruction result with Mosaic-SDF (Yariv et al. 2023).
Mosaic-SDF results are provided by the author directly. We reveal the complicated internal structures of the input GT and the reconstructed results by slicing them based on Slice3D (Wang et al. 2023
4.4 GENERATION RESULTS
airplane
chair
COV(1.5) %)
MMD(J)
I-NNA(L.8)
COV(1.%)
MMD(L)
I-NNA(U.%)
CD
EMD
CD
EMD
EMD
CD
EMD
EMD
CD
EMD
3DIGL
41.09
32.67
4.69
4.73
82.67
84.41
37.87
39.94
20.37
10.54
74.11
69.38
NW
51.98
45.05
3.36
4.19
68.32
73.76
43.79
47.04
16.53
9.47
59.47
64.20
S2VS
51.98
40.59
3.80
4.45
69.06
76.73
51.78
52.37
16.97
9.44
58.43
60.80
MoF
52.48
51.49
3.54
3.78
62.62
69.55
48.22
55.03
15.47
9.13
51.04
55.62
52.91
51.49
2.48
57.43
52.21
53.10
13.28
8.17
53.10
54.57
Table 3: Generation quality for ShapeNet classes of airplane and chair. By convention, MMD-CD has been multiplied by 10 and MMD-EMD by 102 for readability.
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show cascaded generation GALA produces shapes better than other baselines quantitatively. We also provide qualitative results on|Figure to show that our generation gives much geometry details in generation results. Please the supplementary file for more generation results.
From Table 3
$2V5
NW
Oun
S2VS
Ours
Figure The qualitative comparison generation results. Additional results of ShapeNet vessel and train are shown between S2VS and ours to demonstrate the detailed generation of ours.
4.5 ABLATION STUDIES
Local Grid Extraction. We conduct the abla- tion study the components in local adaptive grid extraction, including determining orienta- tion by bounded normals 77) and rescaling with histogram (70). Table showw the effectiveness of our local adaptive grid extraction design and limited degradation by the quantization proce- dure. We further give some qualitative examples in Figure to show that corresponding compo- nents help better capture the detailed geometries.
Metrics
vanilla
+ 7
+ 7े H.
CD (x10-3)
1.55
1.33
1.18 (1.08t)
HD (x10-3)
1.46
1.19
1.06 (0.98t)
Table 4: Ablating the anisotropic local grid extrac- tion components (77 H) on the same set of data of reconstruction test. f; without quantization.
GT
with
with
wro A.
Figure Qualitative examples of GALA fitting results on Left: rescaling the local grid with histogram not; Right: determining the grid orientation with normals or not. Zoom in to see more.
More Tree Setting. We examine the effect of varying tree counts N. (with depth d 2) on three examples, as shown in Figure 10, As we can see in Figure 10 using N, 32 with fewer than 200k parameters already yields low-error reconstructions across the three distinct example objects. Furthermore, even at N, = 16 and fewer than 100k parameters, our method effectively captures significant geometric details, such the missiles on the airplane's 's rear and the lamp's strings, demonstrating the method's great adaptability.

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2.5
arplann sesket
C
#eerm
-500
-400
Par Paramm (K)
300
200
1.0
-10
16
48
64
60
Tree Root Number No
No
Figure 10: Influence of tree count No (with depth d = 2) on three examples.
4.6
NOVELTY OF GENERATED RESULTS
Generated
Search
In Figure II] we show two shapes generated by our method and three closest training shapes retrieved via nearest neighbour search (NN) using LFD (Chen et al. 2003). We can see that generations have detailed and dis- tinct geometric structures from those in the training set, demonstrating our method's generative novelty.
Figure Two generated shapes visually (left to right) training shupes retrieved using LFD.
4.7 APPLICATION: AUTOCOMPLETION
Due to the hierarchical structure of GALA and the cascaded generation pipeline, we are able to roughly outline the objects to be generated using coarse and partial root voxels. Based on the work RePaint (Lugmayr et al. 2022), we autocomplete the given root voxels by substituting intermediate results at timesteps with the given ones during denoising process. See Figure 12 for the results.
Figure 12: Given the partial root voxels (orange), we autocomplete rest (blue) and generate geometries.
4.8 TEXTURING THE GENERATED MESH
Genarated Masn
Reference image
Mesh
First carving the mesh and then adding textures is a standard work- flow in 3D asset creation within the industry. allows flexibility of creating various textures while reusing the fine meshes already crafted. Many previous works (Zhang et al. 2024 Perla et al. 2024: Cao al. 2023 Chen et al..20233 Richardson et al.] (023) in deep learning also adopt similar strategies. Therefore, to show our generated meshes be easily textured, in FFiuure 13] we use Easi-Tex (Perla et al. 2024) to texture examples of our generated meshes by reference images.
Figure 13: Texturing generated meshes.
CONCLUSION AND FUTURE WORK
We present GALA, geometry-aware local adaptive grids for detailed 3D generation. We demonstrate that GALA can represent detailed geometries efficiently with fewer parameters. Additionally, we propose a cascaded generation approach for GALA that produces detailed geometry. We also deliver an efficient C++/CUDA implementation of GALA that completes fitting in seconds, significantly enhancing the practical usage of our method. For future work, compact graph representations (Bourit) Ias et al. 2021 Jo et al. 2022; Jang et al. 2023) may facilitate tree compression within the forest and further the generation step. Also of interests is to remove the watertight constraint on the input meshes and extend GALA and the ensuring generation to unsigned distance fields (UDFs).
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A IMPLEMENTATION DETAILS
A.1 FLIP SIGNS OF THE INTERIOR PARTS AND EXTRACT MESH
We will flip the signs of connected components of 0.1 surrounded by negative values in SDF slice IR (slicing along z-axis) extracted from GALA, where l is the extracted SDF grid (Rextxt) resolution. is Depth-first Search (DFS) algorithm as described in Algorithm 2 This post-proeessing procedure will eliminate redundant geometry blobs in interior parts of ob- jects as illustrated in Figure 14 After getting all the slices, form the grid and use Marching Cube (Lorensen) & Cline 1998) to extract mesh from Algorithm 2 Flip Signs of the Interior Parts
Fllp Signs
0.3
Figure 14: Flip signs of 0.1 islands (connected components) surrounded by negatives.
concatenate them together to
1: Input: A fitted GALA, and
2: Extract SDF slice TR from GALA
According Eq (2,3) of the main text.
3: Initialize visited matrix V of size x E to false
4: Define directions D {(0, 1), -0,- (-1,0))
5: for = to t 8 do
6: for = to
7:
if [[ - 0.1| < EPS & -V then > Check possible islands of 0.1 SDF values.
8:
stuck (()
9:
10:
Vli.j] + true isSurrounded +- true
11:
12:
positions + 0
13:
while not stack.empty() do
14:
(x, y) + stack. positions.add y)
16:
for all (dæ, dy) E do
(na, ny) + (z + dz, y + dy)
18:
if nar < 0 nr 2 f ny < V ny 2 l then
>>
Boundary condition.
isSurrounded
false
20:
continue
end if
22:
if [||na, ny] 0.1| < EPS & -V[na, ny] then stack.pushh (ouu(((uuu (nnz, ny))
Push 0.1 to the island.
23:
24:
Vínz, ny) true
25:
end if
26:
if S Slncr my) 2 & |S|ner, ny) 0.1 EPSS then Check other positives. isSurrounded <- false end for end while if is SuSrrounded then
27:
28:
end if
29:
31:
for all (xx.) y) E positions do
33:
S(z, - S[x, v]
Flip the sign of the 0.1 island.
34:
end for end if
35:
36:
end
37:
end for
38:
end for
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A.2 DATA PREPROCESSING
For each root non-empty leaf tree node, information will be saved illustrated in Figure 13 The voxel position p and scale s (Figure 13 Right) would only be recorded and generated at the root level. The p, of subsequent levels of tree nodes will be deduced deterministically from the root voxels. The parent index and sibling index (Figure L5]Left) is only recorded for recover the tree structure and will not be explicitly generated. Quaternion is used represent the orientation of the local grid. Moreover, local grid locations and scales are stored and generated. All the quantities within the tree node vector will be normalized [0.1] I] by min, max statistics calculated within each data domain (p, 8, ettetc) of specific datasets.
Voxel Position
Grid Scales Sg
Parent Index
772
4
3
3
3
Siblling Index
Grid Values V
Quaternion
Grid Position Pa
Vaxel Length
Octree node information
Figure 15: Octree Node Information. Left: the Parent Index ......, No x 8'-1 1] and Sibling Indxx [O,.... 7], I is the tree level and Ng is the tree root number. When = 0, placeholder values put the two indices; Middle: local adaptive grid related information, the scales Sy and position Pg of the grid are stored; Right: the values of root voxels p.
The GALA of each object will be flattened and stored as the format illustrated in Figure 16
Root Num No
Non-empty Leaf Num
Roots
Leaves
Header part
Body Part
Figure 16: The data format of GALA be flattened and stored.
A.3 DETAILS OF THE PURE C++/CUDA IMPLEMENTATION
Start
Marmalioe
Sampling
Construct BY
Sampleed Points
Tree Vouels
Orientaiio by Normals
Rescale Gild
Local Grids
DNI
Figure 17: The algorithm flowchart of our GALA extraction.
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We show the algorithm flowchart Figure 17 of the initialization stage of GALA, which is built upon CUDA, Libtorch, a third-party R-Tree based SDF query library and few head only utility libraries such C++ argpars We will dig into the details of the implementation step by step follows.
Normalize Vertices We shift the vertices by the center location (( (Pmm +-min
yru +
Veiss Sreas + Pamn
and
2
2
then scale them by the diagonal distance (v/ /Tmax Fmin 2 + (ymax V/min) )2
(Zmax
2min
Construct Bounding Volume Hierarchy (BVH) In order to quickly search relevant mesh information in the space, we construct Bounding Volume Hierarchy (BVH) on GPU parallelly via radix tree according to (Karras 2012). We encountered some bug when doing the GPU parallel bottom-up AABB (Axis-Aligned Bounding Box) construction of the radix tree where very few random items of AABB (~ 0.01 %) at z-dimension were randomly corrupted for each run. To circumvent this, we copy the whole tree back to CPU, conduct a DFS post-order traverse construct the AABB and copy the results back to GPU.
Densely Sampling Points On Meshes We sample 10 N₂ points on meshes where N, is the numher of triangles of the imput mesh. We randomly sample points on triangles using barycentric coordinates. The number of points sampled each triangle is proportional to its surface area.
Initial Point of Farthest Point Sampling As described in the main text, in order to augment our representation, the extraction algorithm also accepts the index of the initial FPS point. This enables possible data augmentation of GALA representation by choosing different initial FPS points for the same input mesh
Determining Orientation by Normals As detailed in the main text, we estimate the orientation of the local grid using the eigenvectors of the covariance matrix of the bounded normal vectors. We get the eigenvectors in each local grid in parallel on each GPU thread using Jacobi eigenvalue algorithm (Golub & Van Loan 2013), where the maximum iteration set as 50 and the tolerance for maximum off-diagonal value le
A.4 TIME MEASUREMENT OF GALA FITTING
Refinement Time (serandss)
Refinement Time (seconds)
6
25
40
20
Counts
30
Extraction Refinement Time
Counts
15
Extraction
Refinement Times
20
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
5
Extrection Time (secords)
Extraction Time (seconds)
(a) ShapeNet Airplane: 2.56 1.30, 5.60
1.86
(b) ShapeNett Chair: 3.17 1.66, 5.79 + 1.67
Figure 18: The fitting time statistics of GALA on ShapeNet Airplane and Chair class.
In this section, we present detailed time measurements of our GALA fitting process. The measure- ments were conducted under the configuration of 6 virtualized logical cores (hyper-thread) of AMD EPYC 7413 @2.65GHz and Nvidia A100. We show the fitting time statisties plots in Figure 18 of 250 objects from ShapeNet Airplane and ShapeNet Chair respectively. The extraction (blue) time includes all initialization and local adaptive grid extraction process, namely all the procedures other than the refinement. Based on the comprehensive statistics shown in FFigure 18) we show that our implementation indeed achieves very fast fitting in less than 10 seconds overall, as stated in the main text. Additionally, the peak GPU memory usage during GALA fitting is recorded at less than 800MB.
Phtts://iitub..o//syyuuu hhtps//githhh..cm//rraaaaaaaggga
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Since the SDF query algorithm supports multi-threading CPU logical cores will further decrease the fitting time. In a 30 logical cores (virtualized) AMD EPYC 7J13 and Nvidia A100 machine, the total fitting time will be less than 6 seconds. We also provide reference record on a lower-end local desktop machine, configured with Nvidia RTX 3060 and Intel 19-12900K, showing approximately 3 seconds for extraction and 27 seconds for refinement.
A.5 MORE DETAILS ON CASCADED GENERATION
Ag-
Transforarr
Transfommss
Cross Affernter
embesbingg
P(,
Vyg (Xi
Attention
ambedding,
Ciess Atteetie
Pack
Miceire
X
RMXX10
F(X..)
P(KalX..
Figure 19: The network details of the cascaded generation pipeline, composed by steps: (1) root voxel diffusion P(X.ly) by diffusion; (2) Local adaptive grid configuration generation P(Xp (Xo: bo.)) by diffusion; (3) Local adaptive grid value prediction Xy F(Xp, y) trained by regression.
As shown in Figure 19 our generation networks are based on transformer networks (Vaswani et al. 2017). The root voxel conditions and local positional encodings of the tree are injected in in-context manner through addition. while the timestep condition is injected using the adaLN-Zero block from DiT (Peebles & Xie 2023), and the object class condition is injected via cross-aie noss-attention. Additionally,
noise augmentation is applied, as in previous works (Ho et al.) 2022 Xu et al.] 2024 Saharia et al. (002)), mitigate the impact of the training/inference discrepancy in cascaded generation. Furthermore, zero-terminal (Lin et al. 2024) is adopted to ensure the last timestep of diffusion starts from zero signal-to-noise ratio (SNR). Classifier-fres guidance (Ho & Salimans
2022) is used,
with an additional null label trained during diffusion training, and w = is applied during classifier-fre guidance in diffusion inference.
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B OTHER ABLATION STUDIES
B.1 MORE ILLUSTRATION ON w/o A
As can from Figure 20 since the anisotropic local grid setting (A4 enables close and adaptive sampling on object surfaces, the full setting of GALA captures much more accurate and artifact-free surfaces than w/o A.
Figure 20: Qualitative comparison between GALA (ours, Middle) and GALA without anisotropic local grids (w/o A, Right). The Left the ground truth (GT).
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B.2 MESH EXTRACTION EFFICIENCY
As in the Mosaic-SDF Yariv et al. 2023) paper, we report the mesh extraction time at resolution 256s
and 512$ NVIDIA A in Table 5 We show that with implementation, the mesh extraction process of ours is very efficient. To further dissect the running time of our mesh extraction process, we show the flip-sign algorithm on CPU()) consists half of the time. Further improvement can be done by adopting GPU graph traversal algorithm like (Merrill et al. 2012). The configuration is the
same as stated in subsectioo A.4
Method
Resolution
Timc(s)
Method
Resolution
Timo(s)
3DIGL Zhang al. 2022
256
18.44
3DIGL 7hang al. 2002
512
159.56
S2VS
/hang el 2025
256a
5.62
S2VS 7hang et 2023
512
24.49*
Mosatc-SDF Yarıv al.
2023
256
2.74
Mosaic-SDF Yarrv al. 2023
512
21.84
2.39
18.73
256
512
(1.26 1.23!)
(8.79 4 9.94)
Table 5: Extraction efficiency comparison with Mosaic-SDF and other baselines on NVIDIA A100.
means the running time of the DFS-based flip-sign algorithm detailed in Subsection A.1 CPU. means when measuring the inference time of S2VS, we conduct queries of 256* or 512 slice every time and loop for the whole grid in order to avoid OOM issue on GPU.
B.3 STORAGE EFFICIENCY
In Figure 21 we compare the file sizes of different representations in order to illusrate the high storage efficiency of our GALA. The representations to be compared in this figure, from the left to the right,
(GALA), S2VS (Zhang et al. 2023), M-SDF Yarrv et al. 2023), Neural Wavelet (Hui et al. 2022). raw object mesh files, Mesh Diffusion (DMTTtt) LLi et al. (023a). Make-A-ahhhee A-Sappe (Packed wavelet coefficients) (Hui et al.) (024). Raw object mesh sizes are measured on converted tighr- meshes on ShapeNet Airplane. Each file of ours occupies only 0.28MB disk space, which is practical benefit when processing large scale datasets.
File Size (MB)
2.56a1.37 MB
0,28
Dark Quantiand
Dur
Mattr
Noural Wasete!
Mode offeet Siiee
Melli Eittation
Shapp
Figure 21: Comparison of file sizes of each repre-
sentation.
B.4 ABLATION STUDY OF OVERLAPPING SUBDIVISION
We show the reconstruction performance by presenting Chamfer Distance (CD) different overlap ratios of subdivision in Figure 22 When = 0, the subdivi- sion performed usual octree subdivision, where a cube space is subdivided evenly into 8 cubes (here in Figuue 22)s 2D illustra- tion, it is a Quadtree). To avoid making the tree too sparse early levels while main- taining the tree structures, we expand the subdivision with ratio a, resulting over- lapping subdivisions. However, expanding too much would decrease the granularity of each subdivision, we find a sweet spot a = 0.2 by scanning it on the reconstruction test set.
1.8
1.6-
1.4-
8.00 0.00 ic
0.20
0.30
0.40
0.1
022
Figure 22: Ablation of child overlap a.
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C MORE COMPARISONS
We provide reconstruction and generation comparisons with additional baselines XCube (Ren et al. 2024) and OctFusion (Xiong al. 2024). XCube adopts coarse fine sparse voxel grid generation strategy which relies on the VDB (Museth 2013) data structure. OctFusion generates octree splits and latents encoded by VAE based the dual octree graph network (Wang al. 2022
C.I RECONSTRUCTION COMPARISON
To show the representation ability in the sense of reconstruction accuracy, we conduct the re- construction comparison with OctFusion (Xiong
Metries
XCube
OctFusion
Ours(small)
Ours
CD (x10 9)
3.25
2.83
1.18
cet al.) 2024) and XCube (Ren et al., 2024). For fair comparison, strictly follow the data preparation procedures of the two methods. For the provided universal toencoder (max-depth 8) to perform the recon- struction and for XCube, respectively. From Figure 23 and Table 6) we can see our strong representation ability over other two baselines. Note that, since the XCube autoencoder is trained on a per-class basis, we cannot provide concrete numbers for it on our reconstruction test set, as this set includes categories that the XCube autoencoders were not trained on. Figure 23 No Mesh Produced means we got an empty mesh file after running the provided script from the open-source release of XCube.
(x10²)
1.56
1.32
1.11
#Params
664k
68k
68k
277k
OctFusion,
Table Quantitative results of the reconstruction.
the separately trained autoencoders for ShapeNet airplane and chair
GALA (277k/8bit)
GALA (68k/8bit)
Input GT
OctFusion
XCube
Mesh Produced
Figure 23: The qualitative comparison of the reconstruction results with OctFusion and XCube.
Regarding the numbers of parameters for OctFusion and XCube reported Table we calculate them as follows: For OctFusion (Xiong et al. 2024), 68A 16 x 8 + 11634 x 3. The 16 8 is the initial predicted octree split and 11634 comes from Table 4 of OctFusion, where it reveals the average node number. For XCube (Ren et al. 2024), 664k 163 x 16 + 74761 8. Most hyperparameters are obtained from Table 4 of XCube's 's supplementary material. To account for the sparsity of the VDB structure used in XCube, use 74761 as the average node count, based on Table 4 of OctFusion.
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C.2 GENERATION COMPARISON
To compare the generation results, we show the qualitative comparison in Figure 24 geometric details generated in the samples.
We show more
Octfusion
XCube
Ours
Figure 24: Qualitative comparison of generation results with OctFusion and XCube.
We do not report quantitative results here because we use different train/test splits.
D RECONSTRUCTION ON LARGE SHAPES
To demonstrate broader extent of the representation ability of GALA, we show reconstruction results on large shapes with more than million triangles from Stanford 3D Scanning dataset (Turk & Levoy 1994. Curless & Levoy 1996; Krishnamurthy Levoy, 1996 Gardner et al. (2003). We showcase two representative object meshes from the dataset, Lucy (1.4M triangles, decimated from the original 28M) and Asian Dragon (1.6M triangles, decimated from the original 12M). As we can from Figure 28 GALA offers detailed representation on large shapes.
E
MORE RECONSTRUCTION COMPARISONS WITH MOSAIC-SDE
Based on our own GALA implementation, we also implemented our own version of Mosaic-SDF (MSDF), where we tried to strictly follow its original setting, such as m for each of the axis- aligned and isotropic grid sampling. Firstly, as we can see from the left part of Figure 25 with the same low parameter budget (82k) and even the additional quantization step, our GALA represents much more faithful geometric structures such smooth lampshade and accurate strings than MSDF, CD (x10-3) 1.3 vs. 1.7. Secondly, in the right part of Figure 25 our reimplemented MSDF shows smoother internal structures than the officially provided one but have more uneven exterior surfaces.
MSDF
MSDF
GT
GALA/82K/1.3
MSDF /82k/1.7
GALA
MSDF
Figure 25: Compare GALA with our self-implemented Mosaic-SDr (MSDF))
F TEXT-TO-3D ON OBJAVERSE
To validate the ability of out GALA representation on more complicated datasets, we conduct the text- to-3D generation experiment the Objaverse dataset (Deitke al. 2023) and show the preliminary
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subset of objects with matching texts (Luo et al. 2024) that contains about 130k object-text pairs due to limited time and resources. For implementation details, use T5 (Raffel et al. 2020)-basic model as the text tokenizer and encoder well keep the diffusion backhone unchanged with the one we adopt in the class-conditioned generation. As we from Figure 26 GALA representations be adapted more complicated datasets than ShapeNet.
results here. More specifically speaking,
A ring Ooo
teapot
A Skateboard
A hammer
A gun
A hat
Cup
Figure 26: The text-to-3D results subset of Objaverse object-text pairs.
G FAILURE CASES
At this section, we show examples of typical failure cases of the generation. As we can see from Figure 27| typical failure cases root in imperfect root voxel generation, which is the first step of our cascaded generation pipeline. Failed generation of properly connected root voxels would result in unconnected geometries. will be beneficial to study how to enhance the root voxel generation, for example using more advanced diffusion training schemes. On the other hand, it worth to note, although some of the root voxels are not properly connected, the final generated geometries are very well aligned, fine and reasonable, implying the power of GALA and our cascaded generation pipeline.
Figure 27: Examples of typi- cal failure cases. Root voxels visualized on the right.
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Input GT
GALA
Neural Wavelet
MeshDiffusion
Figure 28: The comparison reconstruction results on Stanford 3D Scanning dataset. apparent that GALA can reproduce details much better than the alternatives.
24


Reviews:
[{"review_id": "21wbqvNQ7s", "reviewer": "Reviewer_3cms", "summary": "The paper presents a storage-efficient new representation of 3D triangle surface meshes, GALA, which can be used for 3D generation trained by a transformer. To create the proposed representation, voxel tree root nodes are initialized over the surface of the mesh using FPS. In the local adaptive grid extraction step, the grid orientation is aligned with the geometric structure using PCA on the local normal vectors, and the grid is rescaled using a histogram. With this representation, the authors show that 3D reconstruction and generation can be performed using cascaded diffusion models. Experiments demonstrate the effectiveness of the proposed method in 3D reconstruction and generation, both quantitatively and qualitatively.", "questions": "I found that the authors have currently created an anonymous repository, and I am curious whether the authors intend to make the code public in the future.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "(1) The proposed representation has a low number of parameters, fast fitting time, high precision, and quick mesh extraction time, implemented using pure CUDA and LibTorch.\n\n(2) Initially, I think that the proposed representation is sensitive to the FPS results regarding the number of root tree nodes ($N_o$) and overlap ratios ($\\alpha$), so I doubt whether it can effectively cover the thin parts of meshes. However, the authors conduct numerous ablation studies on design choices to achieve optimal performance for general meshes.\n\n(3) The results show that the proposed method achieves SOTA performance on reconstruction and generation with a few number of parameters compared to existing baselines.\n\n(4)  The paper has high writing quality which makes it easy to understand.", "weaknesses": "(1) As shown in the Sec. C. Failure Cases, the proposed representation cannot cover the long thin mesh parts.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "3jRF1C4R7H", "reviewer": "Reviewer_fRPo", "summary": "The authors propose a new geometric representation based on storing optimized SDF values of a shape on an adaptive, overlapping grid of optimally scaled and rotated cells. This representation can be very efficiently generated for any shape and enables diffusion-based generation tasks.", "questions": "- How is each grid subdivided? As far as I can tell, the only explanation of this subdivision is “we recursively deduce the further levels of tree nodes in an overlapping way where we slightly expand the divided spaces at each level by ratio α.” Which is far from enough detail for a reader to replicate the results. Which cells are subdivided? According to which logic? Along which axis?\n- How is a mesh extracted from this adaptive grid? Are the authors setting up some regular grid and interpolating values at grid cells using Eq. (2), and then using Marching Cubes or some other reconstruction algorithm? Or are they somehow extracting a mesh directly from the stored SDF data at the adaptive cells? The latter seems very non-trivial and would be an important contribution on its own.\n- What does “the weighting function which is defined by the infinity ball centered at the grid center pig and rotation matrix Oi” mean? Isn’t \\omega(x,i) just Eq. (3)?\n- It was very hard for me to follow Sec. 3.2., I think partly because of the notation used: Are x_v (lowercase) and X_V (uppercase) the same thing? Am I right in understanding that in this cascading scheme, given an initial tree X_0, the grid configuration X_V and the SDF values at those points will not be affected by the conditioning? Since the class label is only involved in Step 1.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 2, "contribution": 3, "strengths": "I congratulate the authors for their submission. They build on existing work to propose a non-trivial, novel geometric representation that is particularly useful for detailed 3D generative tasks. While I am not an expert in 3D generative modeling, it seems clear that this work outperforms the state of the art in resolutive power, and outperforms its main competitor (Mosaic-SDF) on reconstruction tasks. There is little doubt in my mind that this work would be received positively in the neural geometric processing community.", "weaknesses": "The main weaknesses of this work are in the magnitude of the contribution and the clarity of the writing:\n\nContribution. It could be argued this work is limited to being an adaptive version of Mosaic-SDF, and that most choices made in the algorithm are the same choices any researcher would made if attempting to extend M-SDF to an adaptive realm (the authors of M-SDF themselves even mention “adding local coordinate frames” as a potential future work avenue). The authors of this work address this and also mention the cascading generation strategy as a difference with M-SDF; however, the magnitude of this contribution is not particularly explored: what would have happened if they used an identical flow-matching strategy to the one in M-SDF?\n\nClarity of writing. Several key aspects of the work are missing or unclear, to the point in which I don’t believe I understand important sections of the algorithm (see “Questions” below). Additionally, perhaps due to LaTeX template changes, groups of citations that should be grouped in parentheses are not, making reading difficult (e.g., 053, 080). The code link also seems to be missing.\n\nNonetheless, I do not think these weaknesses justify rejecting this work, which undoubtedly outperforms the state of the art and will definitely save authors’ time if they wish to improve the M-SDF performance in the future.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "J8bkQeS1Oi", "reviewer": "Reviewer_s24f", "summary": "The paper proposed GALA, a novel method for representing 3D shapes using local adaptive grids.  GALA's core concept is to leverage the global sparsity of surfaces within a 3D volume and their local surface properties. The representation enhances the local details by covering only the boundaries of the 3D object with a set of tree root voxels, rather than the empty space, with each voxel containing an octree to limit storage and computation to regions containing surfaces. By adjusting the orientation of the local grid and the anisotropic scales of its axes to the local surface shape, GALA can store a greater amount of detail within a given memory budget compared with Mosaic-SDF and other representations. The advantages of GALA are: (1) it effectively captures and reproduces intricate geometric and surface details, (2) it is computationally efficient, and (3) it is compatible with modern 3D generative modeling techniques, particularly those based on diffusion schemes.\n\nFurthermore, the authors provide a cascaded generation pipeline that is capable of generating 3D shapes with significant geometric detail, demonstrating the practical application and potential of GALA in the field of 3D generation.", "questions": "1. I noticed that the paper lacks a comparison with the reconstruction results of Mosaic-SDF, only comparing the generation results with it in Table 3. After reading the paper of Mosaic-SDF and I found that they also lack this experiment. However, my understanding is that \"Ours w/o A\" in Table 2 should be a structure similar to Mosaic-SDF. Are there any other differences?\n\n\n2. In Figure 7, when comparing the results with Mosaic-SDF, I didn't notice much difference. Can you provide more representative examples in the revised version? Or is this the maximum performance gap compared with Mosaic-SDF?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "Originality:\n\n1. This work's main contribution is to proposed a novel 3D shape representation which can preserve the local details by using local adaptive grids, while previous methods like Mosaic-SDF using regular grids.\n2. The proposed representation is simple and efficient, achieving a good compression ratio with very little storage space and quantization operations.\n3. Moreover, the authors also did comprehensive evaluation and application  like 3D shape diffusion to validate the effectiveness of the proposed representation.\n\n\nClarity:\n\n1. This pipeline in this submission is technically sound and is largely clearly written and well organized.\n2. For the comparison, the numerical results and the visual figures show a significant performance improvement over the baseline method in ShapeNet. But only a few subset with simple geometry (airplane and chair) is evaluated.\n3. For the ablation study, the authors show the importance of some designs like determining orientation by bounded normals and rescaling with histogram.", "weaknesses": "1. While this proposed expression can enhance the details of the reconstruction, I think it is very challenging for diffusion networks to generate the explicit parameters for the root node, grid values, and grid configuration step by step. If some parameter predictions are incorrect, it can greatly affect the quality of the geometry in the subsequent steps. According to the figures in the supplementary, some structures of the generated meshes are noisy. This also limits the practical application of this expression in generative models. It would be better to discuss in the conclusion, or analyze how the errors propagate in the steps and ultimately affect the geometry's quality.\n\n2. I think the authors have omitted some relevant citations regarding XCube and OctTree. XCube employs sparse convolution to achieve high-quality reconstruction and geometric compression, and it has also demonstrated its applicability to generative models. It would be beneficial to include additional quantitative and qualitative experiments and discussions focused on reconstruction quality, compression efficiency, and the applicability to 3D generative models.\n\n3. The authors only tested on some simple geometric details of ShapeNet; it would be better if they could show some more complex results, like objects in Objaverse or Thingiverse.\n\n[1] Ren, Xuanchi, et al., XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies, CVPR 2024\n\n[2] Bojun Xiong, et al., OctFusion: Octree-based Diffusion Models for 3D Shape Generation, Arxiv 2024\n\n[3] Objaverse: https://objaverse.allenai.org/\n\n[4] Thingi10K: https://ten-thousand-models.appspot.com/", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "K5BX1u8Ely", "reviewer": "Reviewer_bAQg", "summary": "This paper describes a 3D shape representation based on trees. The input shape is initially discretized into voxels, and the location of the voxel is decided through Furthest Point Sampling (FPS). Then, each voxel is further discretized into an octree which represents the surface details. Each octree uses a local adaptive grid, with adjusted orientation and scale, to encode the local surface.\nTo further compress the representation, the octree and voxel information ($X_0, X_\\bar{v}, X_v$) is quantized.\nFinally, $X_0, X_\\bar{v}, X_v$ can be generated by a diffusion model in a coarse to fine manner (first $X_0$ for the voxels, then $X_\\bar{v}$).", "questions": "Please see the weakness section.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "The proposed representation is memory efficient thanks to the quantization. It cleverly exploits a combination of SDF and Octrees. Furthermore, thanks to its structure, it is possible to flatten it out and use generative models to encode it.", "weaknesses": "There are aspects of this method that do not convince me. I hope the authors can clarify them.\n1. The main benchmark is Shape-Net, however, this dataset is known to be axis-oriented. It would be more convincing if the authors used additional datasets.\n2. How well does this method scale with large shapes (e.g., shapes from the Stanford dataset)?\n3. The authors claim to introduce a 3D representation, yet, they rely on a generative model to encode and decode shapes. The soundness of the representation is never evaluated. It seems that the representation is a convenient tool for model generation. If so, I would suggest the authors should reword the text.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)