TGA: True-to-Geometry Avatar Dynamic Reconstruction
Authors: Bo Guo
Sijia Wen
Ziwei Wang
Yifan Zhao
Venue: NeurIPS 2025 spotlight ()
Keywords: Avatar
3D Reconstruction
3DGS
Primary area: applications

Abstract: Recent advances in 3D Gaussian Splatting (3DGS) have improved the visual fidelity of dynamic avatar reconstruction. However, existing methods often overlook the inherent chromatic similarity of human skin tones, leading to poor capture of intricate facial geometry under subtle appearance changes. This is caused by the affine approximation of Gaussian projection, which fails to be perspective-aware to depth-induced shear effects. To this end, we propose True-to-Geometry Avatar Dynamic Reconstruction (TGA), a perspective-aware 4D Gaussian avatar framework that sensitively captures fine-grained facial variations for accurate 3D geometry reconstruction. Specifically, to enable color-sensitive and geometry-consistent Gaussian representations under dynamic conditions, we introduce Perspective-Aware Gaussian Transformation that jointly models temporal deformations and spatial projection by integrating Jacobian-guided adaptive deformation into the homogeneous formulation. Furthermore, we develop Incremental BVH Tree Pivoting  to enable fast frame-by-frame mesh extraction for 4D Gaussian representations. A dynamic Gaussian Bounding Volume Hierarchy (BVH) tree is used to model the topological relationships among points, where active ones are filtered out by BVH pivoting and subsequently re-triangulated for surface reconstruction. Extensive experiments demonstrate that TGA achieves superior geometric accuracy.

TGA: True-to-Geometry Avatar Dynamic Reconstruction
Bo Guo
Sijia Wen-* Ziwei Wangb Yifan Zhao²
Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, School of Artificial Intelligence, Beihang University
State Key Laboratory of Virtual Reality Technology and Systems, SCSE&QRI, Beihang University (keaibb, sijiawen, wangziwei26, zhaoyf edu. cn
Abstract
Recent advances in 3D Gaussian Splatting (3DGS) have improved the visual fi- delity of dynamic avatar reconstruction. However, existing methods often overlook the inherent chromatic similarity of human skin tones, leading to poor capture of intricate facial geometry under subtle appearance changes. This is caused by the affine approximation of Gaussian projection, which fails to be perspective-aware depth-induced shear effects. To this end, we propose True-to- -eeettet-eeeeryy Avatar Dy- namic Reconstruction (TGA), perspective-aware 4D Gaussian avatar framework that sensitively captures fine-grained facial variations for accurate 3D geometry reconstruction. Specifically, to enable color-sensitive and geometry-consisten Gaussian representations under dynamic conditions, we introduce the Perspective- Aware Gaussian Transformation that jointly models temporal deformations and spatial projection by integrating Jacobian-gul guided adaptive deformation into the ho- mogeneous formulation. Furthermore, we develop Incremental BVH Tree Pivoting to enable fast frame-by-frame mesh extraction for 4D Gaussian representations. A dynamic Gaussian Bounding Volume Hierarchy (BVH) is used to model the topological relationships among points, where active ones are filtered out by BVH pivoting and subsequently re- re-triangulated for surface reconstruction. Extensive experiments demonstrate that TGA achieves superior geometric accuracy. Project page: htttps:/ tit.tb..o/oT...
Introduction
The demand for personalized, high-fidelity reconstruction of human faces and heads under complex facial movements is fundamental to wide range of applications, including digital twins, film pro- duction, graphics simulation, and entertainment. In particular, acquiring dynamic and geometrically accurate 3D head reconstructions from multi-view recordings is common requirement for generating digital and virtual replicas of real individuals.
Despite recent advances in high-fidelity 3D Gaussian Splatting (3DGS) [ -aasdd avatar reconstruc- tion, existing methods 2 often overlook the inherent chromatic similarity of human skin tones. Specifically, under varying viewpoints and frame transitions, subtle and gradual facial expression changes remain challenging for vanilla 3DGS. The root cause lies in the limited perspective-awarenee (we will discuss in Sec. 3.2) of affine approximation used in Gaussian projection, which compromises accurate color blending. As a result, the simplistic projection model struggles to maintain chromatic consistency and further geometric fidelity for dynamic face modeling.
*Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Mesh and Normal
Textured Mech
Frame-to-frame
b) Different Identity & 60" Views
c) Application
Figure Example results of our TGA. Our method generates (a) high-fidelity frame-by-frame textured meshes from multi-view videos, (b) captures avatar-specific details across wide viewing angles, and (c) delivers realistic cross-reenactment performance.
In response, we propose True-to-Gemmett Avatar Dynamic Reconstruction (TGA), a perspective- aware 4D Gaussian avatar framework that sensitively captures fine- grained facial appearance varia- tions to enable geometrically accurate 3D mesh reconstruction from 4D Gaussian representations.
We first introduce Perspective-Aware Gaussian Transformation that jointly models temporal defor- mations and spatial projection effects, enhancing perspective-awareeens to subtle changes avatar facial appearance. Traditional 3DMM 6 -based Gaussian methods 2
3 7 warp primitives based on the area of their parent triangle across time steps. Such uniform scaling leads to either extending shrinking Gaussian coverage, resulting in over- under-blending of colors in facial regions. To address this, we apply Jacobian-guree guidddd deformation to adaptively warp each Gaussian according the directional variation of its parent triangle, ensuring precise color coverage across dynamic frames. Furthermore, to be perspective-aves the intricate geometry under subtle changes in avatar skin tone and facial expressions, we adopt homogeneous formulation in place of the insufficient affine approximation in vanilla 3DGS, enabling perspective-cconiisten projections. The Jacobian-guides deformation is jointly incorporated into the homogeneous formulation. As a result, color blending becomes more chromaticity-sensitie reinforeing geometry-color alignment and providing a reliable foundation for downstream mesh extraction.
to the projection process for better capture of
Based on the obtained Gaussian avatar field, we introduce an opacity field [ for surface extraction. The geometrically accurate avatar surface is extracted by directly identifying a level set of an opacity- guided signed distance field on tetrahedra, which are triangulated from Gaussians and their bounding points. To enable fast dynamic mesh extraction, we design straightforward yet effective Incremental BVH Tree Pivoting approach adaptively update the tetrahedral grids. Specifically, we dynamically organize the bounding volume hierarchy (BVH) of Gaussians in a binary tree, which models the topological relationships among primitives. As the BVH tree updates by branch rotation according to Gaussian dynamics, the BVH is pivoted to simulate the topological movements Gaussians. Active 3D points- refeered to hopping Gaussians- contribute facial expression changes, are filtered out by BVH Pivoting. These filtered regions are then incrementally triangulated, thereby accelerating the surface extraction process.
Overall, our contributions are the following:
We propose perspective-awure 4D Gaussian avatar framework that captures intricate geometry under subtle facial variations, by integrating soobbanngguided adaptive deformation with homogeneous projection enable Perspective-Awart Gaussian Transformation.
We design Incremental BVH Tree Pivoting approach, which filters out and re-triangulates hopping Gaussians. This enables fast and adaptive surface extraction by focusing computa- tion active regions undergoing facial expression changes.
We empirically demonstrate the advanced performance of the proposed method, demon- strating significant improvements reconstruction accuracy, dynamic capability, training efficiency, and inference time.

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Perspectie-Aware Transformation
Fast Reconstruction
frame
Gaussian
BVH
Hemagrment
Construct
Jp+t E= JRSS Rt
Foctulation
Projestaam See
& Updatg
Mush Normal
Canonical Goussians
Deformed Guussiams
3DGS Rendkrod
Hopping Points
Brunch Pisnting 33
FLAME Tracking
<) Optimization
Marching Tetrahedra
Detoreed Nernal
Loss eic
Sec. 123
Deformed Normal
Tetrahedronn
Mesh Rendered
Figure 2: Method Overview: Given multi-view RGB sequences, we first track facial dynamics with FLAME (a). During the Perspective-aware Transformation (b), we apply Jacobian-guice deformation and homogeneous projection for accurate geometric modeling. After optimization (c), we build and dynamically update Gaussian BVH (d), where BVH pivoting adaptively filters hopping points, enabling geo-accurate surface extraction via Marching Tetrahedra (rightmost column).
2 Related Work
3D Morphable Face Models. Parametric template models based on PCA have become fundamental computer graphics and vision for representing human body geometry, including the face 9
[0]
and head [S] 11, with extensions to the neck [12 and the full body [13]. To overcome the rigid
linearity of PCA, more recent approaches [14 L5
21 replace traditional PCA-
basis underlying classical mesh-based 3DMMs. Furthermore, neural neural-based methods [22 23 24
enhance expression realism with continuous, implicit morphable representations of geometry.
Dynamic Avatar Representations. Avatars have inherent dynamics, especially when performing actions such as smiling or speaking. which accompanied by significant topological changes. This makes the representation of dynamic scenes more complex and challenging. Neural Radiance Fields
(NeRFs) 25 26 27 -base methods [25] 28 29 30
32 33 can capture temporal changes and model such d dynamics but not computationally feasible. 3DGS [[basedd dynamic methods [34] (35
31
36
40 have emerged as a more efficient alternative, but remain insensitive chromatic variations due to their affine approximation. Building upon the 3DGS paradigm, we enhance it with Perspective-Awar Aware Gaussian Transformation module for improved dynamic modeling.
37
38
45 have explored NeRF-based volume rendering model avatar heads with detailed appearance. Recent approaches [46] 47
Human Head Reconstruction. Previous works
48 3
50 incorporate implicit deformation fields to capture frame-wise Gaussian motion.
Meanwhile, another line of work (5T 52 2
53 4 explicitly rig Gaussians to 3DMM-baasdd meshes
for controllable facial animation. Topo4D [54] further reconstructs dynamic meshes and high-fideline fidelity textures via topology-boue learned forward deformations, ScaffoldAvatar [57] employs patch-
Gaussians, NPGA (55) leverages neural parametric head models (56) for patch-based based expressions with hicrarchical Gaussian splatting for high-fidelity avatars. While most 3DGS-basee methods target photorealistic rendering and animation, Topo4D (54) SurFhead [4], and our work focus on geometry-accurate accurrae facial mesh reconstruction. Specifically, our method builds upon the explicit 3DMM-31 3DGGS binding and deformation framework for better controllability.
3 Method
With the goal of achieving geometrically accurate 4D avatar reconstruction in our mind, we first focus on capturing subtle variations in facial appearance while ensuring deformation consistency across frames (Sec. (.2).. By leveraging trained Gaussians with high sensitivity to facial features, our approach further enables fast and precise avatar mesh extraction (Sec. (.3). We start with the overview of GaussianAvatars 2 and also define the main symbols(Sec., 3.1
3.1 Preliminary
Representation. GaaasianAvatars 2 associates each triangle of the FLAME mesh (. tracked by VHAP (58), with 3D Gaussian and moves coherently with its corresponding parent-triangle
3

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across time steps. Specifically, each Gaussian is parameterized by center position μr, a positive- definite, diagonal matrix scaling matrix S, and a rotation matrix R on the neutral FLAME mesh [3]: G(x) = e -x (x-1) nu Σ *(x-x) where Σ = R Besides, the Gaussian primitive has appearance properties, a prior opacity a and color c. To deform the canonical 3D Gaussian the posed space, the vanilla 3DMM-Gausians method transforms its position and covariance attributes according to its parent:
rR n' = kip + S' = =S,
where the isotropic scalar is derived from the triangle's ' relative extent, f and r are the barycenter and relative rotation matrix of the parent-triangle, respectively.
Rendering. Given the 3D representation (1,, 2, a, c), the trainable parameters are optimized through the following differentiable rendering function
n-1
C(p) Σ C. (H, E,y)
II - am D(p. E,,
(2)
where C(p) is the rendering color at pixel of rendered image C, and D(u M, 7) is a divergence of view ray y from 9 computed from the projected 2D Gaussians by EWA volume splatting [59].
3.2 Perspective-Aware Gaussian Transformation
Our goal is to capture intricate geometric details under subtle variations in avatar skin tone and facial expression. Previous 3DGS-based methods 12 3 7 rely solely on affine approximations when projecting Gaussians onto 2D image planes. However, as illustrated by the blue circle in Fig. 3
this naive projection leads unreliable alpha blending, resulting in chromatic inconsistencies and spatial distortions. To address this issue, it is essential to revisit the projection mechanism from the perspective of Perspective Awareness.
As illustrated by the affine-approximater projected blue Gaussian in Fig. 3 even though its center is correctly splatted using perspective projection (as shown in 1), the outermost isocontour remains significantly misaligned. This misalignment arises because the affine projection naively projects the Gaussian orthogonally onto the image plane, neglecting the depth information in the Gaussian covariance. Such a simplification fails to be perspective-aware enough to subtle chromatic variations. To achieve true perspective awareness, is imperative 'look into' the Gaussian itself and fully exploit its depth dimension-only then can we faithfully simulate perspective projection.
Specifically, first introduce Jacobian- deformation mechanism to adaptively warp Gaussians across frames. This deformation is integrated into a homogeneous formulation that preserves depth information, enabling perspective-aware projection. As result, the model can sensitively capture intricate geometric details driven by subtle chromatic variations in facial expressions.
Jacobian Gradient for Adaptive Deformation. While the rigging method in Eq. 1 computationally efficient, struggles to preserve the chromatic consistency across frames. Specifically, its rigid and linear isotropic scaling uniformly extends or shrinks Gaussians according to their parent-triangle' s property (Fig. 3 (a)), leading to under-blending discontinuity across frames. To address this, inspired by [60], we introduce advanced warping method for Gaussians:
JE
E
J = ÊE
where E is composed of edge direction vectors of the binding triangle, and É is deformed by Eq. Then, Gaussians are warped as follows:
Σ JRSS JJJ
='=
By doing so, Gaussians gain adaptive and anisotropic deformability (Fig. (b)) and maintain chromatic consistency across frames, making them ready to capture subtle variations.
Homogeneous Formulation for Gaussian Projection. To be perspective-awar for Gaussian depth dimension and further capture subtle changes in avatar skin tone and facial expressions, we extend prior methods 661 62 originally designed for 2D Gaussians by introducing a homogeneous formulation that replaces the affine approximation for 3D Gaussians. This accurately models the outermost isocontour under perspective projection and further enables high blending sensitivity to

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Porspective Projection
2) Affine Approximation
5) Homegencous Foumlation
Shriebogg comerage
redecties io parem-tiingle
Unilorm Warping
b) Adupative Warping
Frame
Frame n++1
Figure 3: Perspective-Aware Gaussian Transformation. Compared with 2) Affine Approximation (fails to capture shear effects and causes inaccurate color blending), our homogeneous formulation compensates for it, while maintaining a sensitive response to subtle color variations like 1) Perspective Projection. For temporal deformation, uniform warping may shrink coverage, but our adaptive warping maintains an accurate spatial footprint.
fine-grained facial appearance changes (green circle in Fig. (2)). The homogeneous transformation for 3D Gaussian to be normalized in a local tangent plane is:
H
Sy 0
S.Fr 0
Sw:F 0
RS
1
To jointly account for non non-uniform deformations driven by facial expressions across frames, we further refine the Gaussian's 's in the local metric through Jacobian lacobian-based transformation. This enables adaptive Gaussian deformation while preserving global perspective accuracy. Specifically, we parameterize a viewing ray 7 passing through pixel at (x, y) as the intersection of two perpendicular
planes: the x-plane h2 = (-1, O, x)) and the y-plane hg = (0, - 1,00, -1 The ray is then transformed into the deformed Gaussian's 'ss local space by:
h = h ((MHJ)-1) h2/" (MHJ) h2/
where M is the transformation matrix from world to screen space. It should be noticed that as combining transformation MHJ, the viewpoint, 3D anisotropic structure of Gaussian and facial expressions, are encoded into perspective projection. After projection, we normalize the homogeneous coordinates to recover 3D positions of viewing ray deformed tangent plane:
h
h
h
h
h =
where hü denotes for the i-th component. This step performs perspective-dividee by normalizing the homogeneous coordinates (dividing by h²), which reconstructs the true 3D intersection point between the viewing ray and the deformed tangent plane of the Gaussian in perspective space. Unlike the affine approximation that assumes an orthogonal footprint, this perspectiveddivide "looks into" the Gaussian covariance. Finally, we evaluate the divergence of camera ray from Gaussian in straightforward way. Specifically, with
= (h h. h x hh",h?.h") 1- (h h - (h.,hhhhh))
define the divergence D derived from the perpendicular distance o² between the Gaussian center and its closest point on the viewing ray in local tangent plane, ||v|| stand for magnitude of a vector v:
D(n, M, {
0² |mm|
Volume rendering, Then, we obtain screen points by H' MHJ, the center o of projected splat and the outermost bounds e is computed as:
e; - - (C, HD) f
(1,1,1,-1) ((1, 1,,1,,1-110 (H₃ HD))
o, (f, H. H')
(10)
where H; is the i-th row of H', (z, y) stands for dot product. The volumetric alpha blending is conducted compute the rendered color in a perspective-aware way:
C(p) Σ
D(p De, y) II D(H,
(1I)
5

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Optimization. We introduce deformed normal regularization to maintain the learned structure of often-occluded regions such as teeth and eyeballs:
Per In Dw
(12)
where D. denotes the Gaussian normal in the w-th frame, computed as the inverse camera ray direction -ny in the deformed tangent plane and then transformed back world space: nw Rot (-y), Rot is the rotation component of matrix MHJ. The deformed normal is n " J no. where J. is from Eq. in the w-th frame and ng the canonical normal.
Finally, we optimize our model with the following loss:
L= + AaCa + AnCa + XxCecaling + Apopiiition AnrCur
(13)
where L. is combination of photometric loss Ligh and a D-SSIM term following 3DGS D. To ensure accurate geometry reconstruction, we incorporate geometric loss terms from [8 including depth-distortion La and normal consistency La. Toward a better alignment between Gaussians and parent triangles, ters following these works and Aar as 0.01.
regularization terms Lecaling and Eposition from [2]. We set the hyperparame-
3.3 Incremental BVH Tree Pivoting for Fast Avatar Reconstruction
To enable rapid and coometry--ccurrale extraction of avatar meshes from the opacity fields introduced in Sec.3.2 we adopt an incremental triangulation strategy for dynamic points induced by facial expressions, referred to as "hopping points'. The core of our approach lies in organizing Gaussians into a dynamic BVH tree, which accurately simulates vertex topological movements through Gaussian BVH pivoting, thereby facilitating efficient and adaptive mesh reconstruction.
3.3.1 Incremental Triangulation
For the initial frame, we employ 3D Delaunay triangulation to generate tetrahedral grids for each Gaussian and its bounding points. We then perform opacity evaluation, defined as the minimum opacity across all visible and relevant training views (depending on different areas in the FLAME model, e.g., the side view for hair) that observe the point. Finally, binary search is conducted over the opacity-SDF field all tetrahedral grids to locate the zero level set.
For subsequent frames, we employ incremental triangulation guided by hopping points filtering via dynamic Gaussian BVH tree pivoting, illustrated in Fig. significantly reducing computation time compared to full re-triangulation. Since Gaussian movements fluctuate between frames, applying fixed threshold screen Gaussian centers and covariances can result in: 1) incomplete culling, causing significant degradation in mesh extraction quality; or 2) excessive computation, which reduces the frame rate. Leveraging on our dynamic Gaussian BVH, which accurately simulates the topological movements of vertices, hopping points are swiftly filtered through branch rotation.
3.3.2 Hopping Gaussians Filtering via Dynamic BVH Pivoting
We begin by constructing a static binary radix BVH tree 63 from given set of 3D Gaussians, where each leaf node represents the tight bounding box of Gaussian cluster, and each internal node denotes the bounding box encompassing its two child nodes. To dynamically simulate the topological movements of Gaussians over time, we perform pivoting of the Gaussian BVH tree at each frame.
BVH Pivoting. To better illustrate this topological simulation, we demonstrate our BVH structure shown in Fig. where yellow "a", red "b", blue "c", and green "d" bounding boxes correspond facial features, alongside its tree repre- sentation of the avatar. As facial expres- sions occur (e.g., eye opening), these bounding volumes are locally refitted according to the movement of enclosed Gaussians. As the extent of box "d" significantly expands to tightly enclose
Refit
Update
b
Filter
ApyH Boor.
Retriangulate
Trieskefnn
Hupping Set
Branch Rocate
Figure 4: BVH Pivoting for Hopping Points Filtering.

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Input RGB
HRN
NHA
NPHM
Topo4D
SurFHead
Ours
Figure 5: Comparison of reconstruction quality from NeRSemble
33
dataset against our baselines.
both "a" and "b", the BVH tree achieves branch rotation (swapping between "b" and "c") to ganize the hierarchy and do topological simulation. It is important to emphasize that rather than balancing the tree, these rotations employed to simulate Gaussian movement across volumes, minimizing the overall bounding extent soot-sommtimes by introducing imbalance into the tree structure. Specifically, we implement these binary-tree rotations inspired by (64)
Branch Rotations. On each frame, the BVH tree updated by post-order traversal, see Sec. B. for details. For rotations, part (d) of Fig, 2 which illustrates candidate node swaps considered in pivoting. Lift Rebalancer (red rotation) occurs between a parent node's 's child and grandchild, adjusting subtree hierarchy levels to optimize local structure. Reorder Rebalancer (blue rotation) works among siblings to bypass local optima and achieve better global optimization. Each rotation operation is assigned cost to filter hopping Gaussians. The green rotation produces mirrored-equivales trees from Reorder Rotation and is omitted to avoid redundant computations.
Handling Hopping Points. When the rotation cost of the middle level nodes exceeds threshold, the Gaussians within exhibit strong mobility and are filtered as hopping points, will be incrementally 3D triangulated.
Experiments
4.1 Experiments Settings
Implementation Details. To initialize TGA, we adopt VHAP (58) to preprocess the multi-view RGB video dataset for head tracking. We compare our approach against state-of-the-arr avatar reconstruction methods via both qualitative and quantitative experiments. Specifically, we evaluate TGA on Chamfer distance, normal error, and recall (65] using the Multiface dataset [66], which provides 3D ground truth. We further evaluate the performance in terms of mesh extraction time, mesh rendering quality, and Gaussian-based novel view synthesis and self-reenactment quality. Thanks to our perspective-corred ray tracing for precise evaluation of Gaussian contributions, TGA converges within 300k iterations. All experiments are performed on NVIDIA RTX 4090 GPUs, using the same hyperparameters as Avaaars [2]

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Method
Li-CD4
MAE
Recall@2.5mm²
HRN 667
2.64
22.3
0.698
3DDFA 68
4.35
22.9
0.649
HRN
Topo-D
NPHM
NHA 42
6.02
28.9
0,462
NPHM [24]
3.35
20.5
0.764
SF 4
2.50
24.8
0.751
Input
Topo4D
[34
2.33
19.3
0.772
Ours
2.16
17.7
0.802
SurFHeaa
Ours
GT
Comparison of reconstructed meshes and normals on the Multiface [66]. Although frontal- view differences appear minor, 3D error metrics show that TGA remains the closest to the GT.
Figure 6:
Memory Overheads. The memory overheads of training and mesh extraction is no more than 24 gigabytes since we load images on-the-fly. When scaling to longer frame sequences and with stable number of Gaussians, the training memory usage remains mostly constant, and the storage for BVH tree pivoting related to the number of Gaussians since it is conducted frame by frame.
Datasets. We evaluate our method on the NeRSemble 33 Multiface [66] and NHA Dataset 42
The NeRSemble captures detailed facial dynamics, and the data calibrated with sub-millimeter accurate camera poses and high-quality foreground segmentation. The Multiface dataset captures subjects covering dense multiview camera captures, rich facial expressions, and ground truth mesh to evaluate the 3D reconstruction efficiency. The NHA real dataset contains sequences that are suitable for the evaluation full dynamic head approaches. We use to evaluate the novel-view synthesis and self-reenactment rendering performance of our method.
4.2 Baselines
HRN 67 is a hierarchical representation network that achieves detailed face reconstruction. generates displacement map from each view and fuse them to obtain the final mesh. 3DDFA- V3 uses geometric guidance for facial part segmentation for face reconstruction. We reconstruct mesh for each view and then fuse them to obtain
view-consistent final mesh. NHA [42 learned from a monocular RGB portrait video that features a range of different expressions and views. NPHM 24 generates a signed distance field of human head given an identity code and an expression code, and can then be translated into mesh via marching cubes [69]. SurFhead [ employs 2DGS 770 and Avatasan 2 to reconstruct photorealistic avatars and high-fidelity surface normals and meshes from videos. Topo4D [54] introduces novel texture regularization.
4.3 Avatar Reconstruction Results
Mesh Geometry. We compare TGA against our baselines the NeRSemble dataset 333 by reconstructing each avatar from 16-view RGB sequences and present qualitative results in Fig. [ Comparative experimental results demonstrate that TGA faithfully capture facial shape and expression details, greatly aiding avatar identity recognition and accurate emotion interpretation. Although HRN [67] reconstructs detailed wrinkle patterns, it still misses personalized eye and nose features. 3DDFA-V3 (68) exhibits jaw-shape inaccuracies. NHA [42] employs high-capacity neural networks for photorealistic rendering, but its geometry remains underconstrained. NPHM 24 excels at expression representation yet fails to preserve identity. Topo4D [54] and SurFHead 4 achieve strong identity reconstruction; however, Topo4D lacks fine facial detail, and SurFHead is constrained by depth maps rendered from 3DGS.
Additionally, conduct qualitative and quantitative evaluation of the reconstructed meshes the Multiface Dataset (66) in Fig. 6 We focus on three metrics: Lı-Chanfer distance, normal MAE (Mean Angular Error), and Recall (65] which measures the percentage of ground-truth points within a 2.5 mm threshold of any reconstructed point. TGA consistently produces meshes that closely match the ground truth from both frontal and side viewpoints.
Mesh Rendering. Moreover, we evaluate the mesh-based rendering results on the four subjects (shown in Fig. 5) from the frontal view in Tab. Since TGA currently does not incorporate intrinsic
8

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PSNR (dB)
30
Subject 140
Subject 165
Subject 218
25
40
Frame
80
100
Figure 8: PSNR curves of novel view synthesis results subjects from the NeRSemble
33
decomposition or reflectance modeling, we employ flat shading based solely on vertex colors for rendering. We additionally evaluate the temporal quality and consistency of our results on temporal using VMAF [71), metric designed to capture both perceptual quality and temporal coherence. The qualitative mesh rendering results are represented in the appendix
Gaussians Rendering. Although our method primarily targets geometry-accurate 3D recon- struction, TGA also exhibits strong performance in self-reenactment and novel-view synthesis. We present the comparison with SurFhead 4 and GHA [51] in Fig. 7 and Tab. [ respec- tively. The self-reenactment results indicate that, by leveraging the Perspective-Awart Gaus- sian Transformation, the proposed method can achieve more faithful rendering of dynamic re- gions (eyes and mouth) with fewer iterations than other 3DGS-based avatar methods. Addi- tionally, we present sequential novel view syn- thesis rendering frames and their corresponding PSNR curves. The Fig. @emmonttraess the stability and temporal consistency of TGA.
GT
SurFhead
GHAA
Ours
Figure 7: Self-reenactment on the NHA NeRSemble [33] dataset.
42 and
Inference Time. Furthermore, we benchmark mesh-extraction times against baseline methods in Tab. For Gaussian-based methods, meshes are extracted via Truncated Signed Distance Function fusion on uDGG-reeddered depth maps following 2DGS [70] To ensure fairness, we selected sequences of 100 frames from the Multiface Dataset (66), using 16 key views for tracking and resizing images
to the resolution employed by NeRSemble [33]. HRN 667, 3DDFA (68) and NPHM [24] takes approximately 2-5 minutes per frame to inference.
Table 1: Average mesh extraction time, mesh-based rendering and NVS rendering performance.
Mesh-based Rendering
Gaussian-based Rendering
Method
InferenceL
PSNRT
SSIM1
I.PPS.)
VMAF 2D
PSNR
SSTM
I.PPS.
VMAF
GA
0,542
0.496
30.29
0.934
0.066
51,2
200
Topo4D
S4
23.69
0.637
0.285
53,9
30.88
0,931
0.064
61.4
While Train
SF 4
21.09
0.558
0.479
39.1
29.94
0.933
0.062
43.6
~>20s
Ours
23.77
0.645
0.311
47.2
31.32
0.936
0.058
65.8
~-8
4.4 Ablation Study
Perspective-aware Gaussian Transfor- mation (PGT). We demonstrate the ge-
Table 2: Ablations on each modules in the PGT.
ometric (CD, MAE and Recall for ex-
L,-CD
1
Recallif 2.5mm
PSNR1
LPIPS]
tracted meshes) and chromatic (PSNR, SSIM, LPIPS for Caussian-basele render- ing) impact of the perspective-aware Gaus- sian transformation in Tab. 2 and Fig. 9 First, the homogeneous formulation yields noticeable improvement in mesh quality. Second, the Jacobian gradient is essential for guiding deformation of canonical Gaussians dynamic regions, such as the eyes (red box in Fig. 9 Without the trans- formed normal loss, Jacobian guided deformation fails to propagate effectively into the geometry, as evidenced by the results in Tab.
llomogenenus Fur
0,058

---

Input RGB wio Homogeneous
w/o Jacobian
Ours Full
wio Homogeneous
w/o Jacobian
Ours Full
Figure 9: The close-ups, taken from + 60 view, highlight the effect of our PGT module.
Hopping Points Filtering. Furthermore, we evaluate sopping-point filtering via our BVH pivoting mechanism in Fig. [0] rather than rely- ing on fixed A threshold on Gaussian centers across frames. When filtering with fixed A Gaussian center between frames, the blue points illustrate (a) incomplete culling and (b) excess screening. In contrast, our BVH pivoting accu- rately filters out the hopping Gaussians (c). It should be noted that when the avatar slightly opens the eyes mouth, the forehead topology remains largely unchanged, obviating the need for re- re-triangulation in that region.
a)
Hopping
Figure 10: Effect hopping Gaussians filtering.
Accelerated Mesh Extraction. We also evalu- ate mesh extraction speed across different train- ing iterations by reporting the number of mesh vertices at key checkpoints and the time required for mesh extraction per frame. As training progresses, although the scene contains more points, the Gaussian BVH tree has learned better topology of the avatar face. As shown in Tab. 4 while the total triangulation time (3rd column) increases with O(n log n) complexity, our method effectively reduces the computational burden (4th column).
Table 3: Effect of Incremental Strategy for Fast Avatar Reconstruction.
Iteration
Vertex Num
1st Frame
x-th Frame
50k
258k
12s
1.9s
100k
372k
26s
3.4s
200k
489k
49s
5.7s
300k
563k
61s
8.4s
4.5 Discussion
Limitations. Our method struggles in regions like hair and eyes, where translucency, non-rigid motion, and strong specular reflections violate modeling assumptions, leading opacity inconsistency and hollow-eye artifacts. It also fails under severe expression deformations, causing mesh tearing or topology distortion, since the BVH-hopping Gaussians assume smooth motion. Performing fresh triangulation can effectively remove accumulated errors.
Societal impact. Our method advances high-fidelin facial reconstruction, but also poses potential risks of misuse, such as identity theft, unauthorized avatar replication, or deepfake generation. These concerns call for thoughtful reflection on ethical implications and the adoption of practical safeguards to minimize possible harm. But with proper and responsible use, we believe our method can bring significant benefits applications in virtual/augmented reality.
Conclusion
In this work, we proposed TGA, a perspective-awee aware 4D Gaussian avatar framework that captures fine-grain fine-grained facial geometry under dynamic conditions. By integrating Jacobian coobiannguuded deformation into a homogeneous projection, our method preserves color consistency and geometric accuracy. Coupled with an efficient BVH Tree Pivoting strategy for incremental mesh extraction, TGA achieves state-of-the-ar performance in dynamic avatar reconstruction. Future work will explore its extension to relighting, full-body modeling and real-time applications.
10

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6 Acknowledgment
This study is partially supported by the National Natural Science Foundation of China under Grants Nos. 62302024, 52441202 and 62202010, the Beijing Nova Program No.20250444786, the Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, and the Fundamental Research Funds for the Central Universities.
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17

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A Theoretical Analysis
A.1 Homogeneous Projection and Perspective-Aware Transformation.
Let C(p) E I be the rendered color at pixel = (æ, y) obtained by compositing of K Gaussians,
((p) Σ
(p)) II(1 - Ay(p)) A₁ ax D3 expl 106
jek
where of denotes the normalized projected deviation of Gaussian in image space. Denote the full perspective Jacobian Ipespp 2x3 by
1/2
fx z2
Jerssp
(
1
2
and the affine approximation by Jar = di f 0) that drops the shear terms. Let V,C and V,C be the image-space gradients computed with Inersp and Janr respectively. Then, for any camera pose where at least one off-diagonal entry of Jpensp is non-zero (i.e. any non-frontal view):
1 ||
St JA /
where JA Jeessp Jafr contains only the shear components, and Sg a symmetric positive matrix that depends on Dx. and the transmittance of the front Gaussians. Consequently VV > V i.c. the comogeeneous-projcctin
renderer is strictly more view-sensitive than its affine counterpart.
Proof. For brevity, write Th-1 = =Ilj<x(1 (1-A,) and note that < Tx-1 S 1. By direct differentiation we have
ApAj Aj
v,C Σ Ck Th- V
A jck
A&
V,A, = -0g DEok Vp
All dependence on the projection model is confined to V With either Jacobian choice it can be expressed linear map acting the shear term JA:
V b S₁ Jeersps
V
Sy J.n.
Vici = Epeii Ja.
Substituting in V C and expanding
1 yields
| / Ellart- + (V,C, EaThh-aaDDisss.
The cross-term in the inner product vanishes because JA contains only off-diagonal elements while V,C depends exclusively on Jur (diagonal). Hence the second equality in (4) follows, and the Frobenius-norm term is strictly positive whenever JA + 0.
Implication. Because facial albedo varies weakly, rendering fidelity primarily depends on how strongly the visibility term responds slight shifts in viewpoint shape. As shown in Sec. the homogeneous-projee projection formulation amplifies this response, leading to higher sensitivity to view changes and thus improved reproduction of fine-scale, view-dependent facial appearance.
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B
Algorithm
B.1 Pivot and Filter Hopping Points.
Here, we represent the proposed algorithm for Pivot and Filter Hopping Points Sec. 3.3.2
Algorithm 1: Pivot and Filter Hopping Points
Input: T (BVH Tree), (Gaussians), (Hop Threshold)
Output: Updated hopping points H
function PIvOT(n, G, H)
2
RefitAABB((()));
if n. is leaf then
L
Splitaandidate(n);
else if has leaf children then Merge(n);;
7
else if ne.epph 2 then
foreach p E Lift & Reorder Rebalancers do ComputeSAH(m,, p);
10
if BestRotation())) + NONE then
I1
ApplyBestRRotaiion(n)) RefitAABB(((m)), ComputeCost(r, p); if Cosi(n) > t then H HUgGm))
12
13
function LRD(n, G, T)
15
if n. + NULL then
16
LRD(n.lett, G. 7), LRD(n.rghht, 9, H),);
17
Pivor(a, G, T);
foreach frame do H + 0. LRD(T, 9, H, r), IncrementalDelannay(O0
19
C Additional Results
We provide more novel view synthesis, self-reenactment, mesh rendering sequences here.
C.1 Gaussian Rendering Results.
We represent the novel view synthesis and self-reenactment results on the NeRSemble dataset where one frame is sampled every 5-8 frames for visualization.
33
210
175
460
Figure Novel view synthesis rendering results on subjects of the NeRSemble dataset
33
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304
306
Figure 12: Self-reenactment rendering results on subjects of the NeRSemble dataset 33
C.2 Mesh Rendering Results.
Since TGA currently does not incorporate intrinsic decomposition or reflectance modeling, we employ flat shading based on vertex colors for rendering.
104
140
165
175
210
460
Figure 13: Mesh rendering results by Meshlab subjects of the NeRSemble dataset
33
218
460
Figure 14: Mesh sequence rendering results by Blender on subjects of the NeRSemble dataset [33].
D More Discussion
D.1 Impact of the focal length.
Shorter focal lengths (i.e., wider fields view) introduce stronger perspective distortion, making the affine approximation less accurate. Our homogeneous formulation can address this by incorporating full-depth information, enabling more accurate color blending and better geometry reconstruction under Wide-FoV conditions.
20

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D.2 Generalization in sparse-view scenarios.
TGA primarily designed for multi-view dynamic reconstruction, but can ensure reasonable results under sparse-view. Specifically, the FLAME model offers strong geometric priors that effectively guide reconstruction in low-coverage settings. The proposed Perspective-aware Transformation leverages subtle photometric changes to optimize Gaussian attributes from limited viewpoints. Additionally, the Jacobian-guie guided deformation improves inter-frame consistency by enhancing the temporal coverage of Gaussian primitives.
D.3 Performance on longer videos and longer-term consistency.
Our method can produce relatively stable outputs on longer sequences. When scaling to longer frame sequences and keeping the number of Gaussians stable, the overall training time and rendering metrics are expected be close Tab. (since have to train for 300k iterations), and the runtime of BVH tree pivoting is closely related to the number of Gaussians rather than sequence length.
Specifically, the proposed BVH pivoting mechanism designed support long-range consistency. It incrementally tracks topological variations Gaussian pointcloud and reuses triangulations when no significant local deformation is detected. Additionally, periodic re-triangulation provides a way to reset the accumulated geometric errors and recover accuracy.
E
More Comparisons
77 about We further compare TGA with existing approaches 3DGUT 772 73 and deformation. The improvement over EWA splatting, modified with FLAME- based quantitative results show that our method achieves superior performance in the scope of dynamic avatar reconstruction.
Table 4: Comparisons with existing approaches on improvement over EWA splatting.
Method
PSNR
SSIM
LPIPS!
3DGUT 772 73
29.96
0.938
0.084
3DGS-marcher 74
30.54
0.941
0.079
Ours
31.37
0.952
0.058
Future Work
Our current work primarily focuses dynamic reconstruction under controlled indoor lighting and does not explicitly support lighting variations. Lighting changes can indeed affect 3DGS based methods due their reliance on photometric consistency. In future work, plan incorporate intrinsic decomposition and physically-based rendering into the reconstruction pipeline to better disentangle geometry, reflectance, and illumination. Such integration would enable the model to handle complex and dynamic lighting conditions, thereby extending TGA to more casual and wild scenarios with improved photometrie robustness and relightability.
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Reviews:
[{"review_id": "FYUCBMqPlB", "reviewer": "Reviewer_e15x", "summary": "This submission aims to improve geometric accuracy for mesh-rigged Gaussian avatars trained on multiview videos. It tackles the problem that existing works ignore perspective effects when deforming mesh-rigged Gaussians. \n\nThe technical contributions are twofold. First, this work introduces perspective-aware projections in 2DGS head avatars. Second, it proposes to use BVH trees to hierarchically organize Gaussian Primitives and quickly extract meshes after training the avatar.\n\nThe paper performs quantitative evaluations of geometry on the Multiface dataset and qualitative comparisons on NeRSemble and NHA, comparing with six related works, reporting geometry metrics.", "questions": "- What deformations still cannot be modeled with the new formulation and why? \n- How does the focal length affect the performance improvements for the proposed homogeneous formulations for the Gaussian projection? Would the effects for smartphones (small focal length) be even greater?\n- Why did the authors choose not to report PSNR, SSIM, LPIPS, and not to show more visual results?", "limitations": "There is no discussion of limitations. I would encourage the authors to openly communicate the failure cases and show examples.\n\nThere is no discussion of the societal impact. This could be included in the supp. mat.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n\n- This work tackles an important weakness when deforming mesh-rigged Gaussians. Previous approaches only consider affine transformations, but perspective transformations are the more correct way of modeling these deformations. \n- Obtaining more accurate geometries and adding facial details to expressions is desirable. Given the popularity of Gaussian-splatting-based avatars, this work could have a substantial impact on the research community.\n- The mesh extraction is very fast thanks to identifying hopping points using the BVH tree.\n- The paper performs quantitative comparisons with six related works and outperforms them in geometry metrics.\n- The ablation table clearly shows the improvements when introducing perspective-aware transformations (Tbl. 2).\n- Fig. 2 and 3 are helpful to understand the pipeline and impact of the affine vs. perspective transformations.\n\n\nWeaknesses\n- The submission shows surprisingly few qualitative results. There is only one qualitative comparison on meshes in Fig. 5 and a tiny comparison on RGB renderings in Fig. 6. Why didn't the authors add more visuals in the supp. mat? It would be very important to include more examples, specifically video results, in the supp. mat. I observe that the formulation seems to struggle with hair. In the bottom row in Fig. 5, the reconstructed mesh (\"Ours\") fails to reconstruct the hair and models it as skin surface instead. Showing more qualitative results would help a reader better understand the benefits and limitations of the proposed method.\n- The quantitative comparisons do not include reconstruction metrics like PSNR, SSIM, and LPIPS. I would recommend including them, since this is also done in related works [4]. \n- It would be important to discuss strengths and limitations in more detail. What cannot be modeled with the new formulation and why? It would also be interesting to ablate the impact of the focal length and quantify the benefits of the new formulation. How does the focal length affect the performance improvements for the proposed homogeneous formulations for the Gaussian projection? Would the effects for smartphones (small focal length) be even greater? This could be evaluated on synthetic data or rendered scans from Multiface.\n\nMinor Weaknesses / Suggestions to Authors\n- Clarity in Eq. 3: The variable J should be introduced. I had to look into [21] to understand its meaning. Similarly, E should be described in more detail and ideally spelled out explicitly.\n- Fig. 5 has the zoom-ins cut off for \"Ours\".\n- The capitalization is not always consistent, e.g., \"perspective-aware\" (l. 33) vs. \"Perspective-aware\" (l. 35).\n- l. 119 should cite the works that rely on affine approximations.\n\n\n\nConclusion\n\nThe paper tackles and important problem and shows promising quantitative results. However, the submission should provide many more qualitative examples and discuss limitations to help a reader understand the impact of the proposed formulation and its potential downsides.", "was_revised": true, "final_justification": "This work tackles an important weakness when deforming mesh-rigged Gaussians. The technical contributions (perspective-aware projections and BVH tree for fast mesh extraction) are solid and demonstrate good results.", "rebuttal": "Thank you for your valuable feedback and for recognizing our technical contributions toward improving geometric fidelity and extraction speed. We have carefully considered your suggestions and will revise the final version of the paper and supplementary materials accordingly.\n\n___\n\n**Q1: Additional qualitative results.**\n\nWe apologize for the limited number of qualitative examples shown in the main paper and for not including videos in the supplementary material. Due to NeurIPS rebuttal guidelines, we are unable to upload additional images or video results at this stage. However, we have already prepared extensive visual results on the **recently released NeRSemble V2 dataset** and will include them in the revised version along with the supplementary material.\n\nTo quantitatively demonstrate the effectiveness of our proposed method in terms of reconstruction quality, we have included additional comparative experiments. Specifically, we conduct several evaluations against state-of-the-art methods, GaussianAvatars (GA) and SurFhead (SF), on tasks including novel-view synthesis, self-reenactment, and temporal consistency. We report overall average metrics and further showcase per-subject qualitative fidelity using randomly selected Subjects #442, #487, and #537.\n\n- Novel-view synthesis.\n\n  We conduct novel-view synthesis experiments and achieve the best results among all compared methods.\n\n  | Methods  | GA    | SF    | Ours      | GA    | SF    | Ours      | GA    | SF    | Ours      | GA     | SF     | Ours      |\n  | -------- | ----- | ----- | --------- | ----- | ----- | --------- | ----- | ----- | --------- | ------ | ------ | --------- |\n  | Subjects | #442  | #442  | #442      | #487  | #487  | #487      | #537  | #537  | #537      | Avg.V2 | Avg.V2 | Avg.V2    |\n  | PSNR↑    | 29.85 | 29.42 | **31.42** | 29.04 | 27.65 | **30.76** | 31.52 | 29.03 | **31.97** | 30.43  | 29.97  | **31.37** |\n  | SSIM↑    | 0.948 | 0.942 | **0.962** | 0.933 | 0.923 | **0.942** | 0.938 | 0.923 | **0.953** | 0.934  | 0.931  | **0.952** |\n  | LPIPS↓   | 0.121 | 0.125 | **0.054** | 0.072 | 0.073 | **0.063** | 0.057 | 0.131 | **0.056** | 0.067  | 0.087  | **0.060** |\n\n- Self-reenactment.\n\n  We conduct self-reenactment experiments, and our method consistently outperforms prior methods in terms of PSNR, SSIM, and LPIPS.\n\n  | Methods  | GA    | SF    | Ours      | GA    | SF    | Ours      | GA    | SF    | Ours      | GA     | SF     | Ours      |\n  | -------- | ----- | ----- | --------- | ----- | ----- | --------- | ----- | ----- | --------- | ------ | ------ | --------- |\n  | Subjects | #442  | #442  | #442      | #487  | #487  | #487      | #537  | #537  | #537      | Avg.V2 | Avg.V2 | Avg.V2    |\n  | PSNR↑    | 25.47 | 25.27 | **25.61** | 26.65 | 26.97 | **27.06** | 25.12 | 25.75 | **26.48** | 25.98  | 25.97  | **26.42** |\n  | SSIM↑    | 0.904 | 0.898 | **0.916** | 0.912 | 0.919 | **0.922** | 0.851 | 0.887 | **0.902** | 0.901  | 0.903  | **0.912** |\n  | LPIPS↓   | 0.147 | 0.149 | **0.098** | 0.081 | 0.077 | **0.074** | 0.101 | 0.139 | **0.077** | 0.081  | 0.098  | **0.073** |\n\n- Temporal consistency.\n\n  To further assess the visual quality of our proposed method, we additionally evaluate our results on **temporal consistency using VMAF[1]**,  a metric designed to capture both perceptual quality and temporal coherence. Our method achieves the highest VMAF scores across all sequences.\n\n  |          | #442-GA | #442-SF | #442-Ours | #487-GA | #487-SF | #487-Ours | #537-GA | #537-SF | #537-Ours | Avg.-GA | Avg.-SF | Avg.-Ours |\n  | -------- | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- |\n  | VMAF[1]↑ | 51.3    | 45.9    | **67.4**  | 49.5    | 44.3    | **66.2**  | 51.0    | 41.6    | **67.9**  | 50.8    | 42.7    | **67.2**  |\n\nAdditionally, regarding your concern about the \"hair and skin error\" in the bottom row of our result in Fig. 5, we believe this may be a misunderstanding caused by the limited viewpoint shown in the \"Input RGB,\" which only displays a frontal view. The subject in question is Subject #253 from the NeRSemble dataset. From other viewpoints, we can tell that our method correctly reconstructs the hair and does not misinterpret it as skin. Moreover, the average calculation is based on multiple frames of the reconstructed results, which can also verify the accuracy of the reconstruction.\n\nWe hope that the additional quantitative experiments and clarifications we have provided help to resolve your concern. As you rightly pointed out, this misunderstanding likely stems from the lack of sufficient qualitative comparisons. To address this, we will include more comprehensive visual results and supplementary material to further support our claims.\n\n___\n\n**Q2: No evaluation on photometric metrics (PSNR / SSIM / LPIPS).**\n\n**3DGS-rendering**: We report the photometric metrics PSNR and SSIM in Tab. 1 of the original manuscript. We additionally compute LPIPS and obtain **0.057** on the NeRSemble dataset (V1), which achieves the best compared to SOTA methods.\n\n**Mesh-based rendering**: We evaluate on four subjects (from Fig. 5) from the frontal view. Currently, TGA does not consider intrinsic decomposition or reflectance modeling. Therefore, we adopt **flat shading based solely on vertex color for rendering**.)\n\n| Subjects | #104  | #264  | #302  | #140  |\n| -------- | ----- | ----- | ----- | ----- |\n| PSNR↑    | 23.69 | 24.12 | 24.40 | 24.89 |\n| SSIM↑    | 0.653 | 0.592 | 0.617 | 0.722 |\n| LPIPS↓   | 0.304 | 0.351 | 0.349 | 0.238 |\n\n\n___\n\n**Q3: What cannot be modeled with the new formulation?**\n\nWe appreciate your suggestion to discuss the limitations of our formulation. The proposed perspective-aware Gaussian transformation faces challenges in specific regions, such as hair and eyes. \nSpecifically, **hair** regions are difficult to model accurately due to their translucency and non-rigid nature, which violates the assumptions of FLAME-based mesh tracking. As a result, Gaussian primitives in these areas may exhibit unstable coverage or opacity inconsistency under view changes.\nEye regions, particularly the **eyeballs**, are also problematic. Our method may fail to produce faithful approximations of the spherical geometry of the eyeball, often resulting in hollow-eye. This is primarily due to the high specularity of the multi-layered cornea, which introduces sharp photometric highlights. These are difficult to fit accurately using the current Spherical Harmonics (SH)-based appearance model. We will include the discussion of these limitations in the revised version of the paper.\n\n___\n\n**Q4: Impact of the focal length.**\n\nThank you for this insightful question. Shorter focal lengths (i.e., wider fields of view) introduce stronger perspective distortion, making the affine approximation less accurate. Our homogeneous formulation addresses this by incorporating full-depth information, enabling **more accurate color blending** and better geometry reconstruction under wide-FoV conditions. We will conduct experiments on rendered scans from the on FaceTalk [2] synthetic dataset's meshes and textures with small focal length and include them in the final version of the supplementary material.\n\n___\n\n**Q5: Discussion of failure cases.**\n\nWe will include this discussion and visual examples in the supplemental material.\n\nOne failure case occurs under extremely **rapid expressions movements**, such as sudden tongue protrusion or exaggerated frowning. In such cases, local mesh tearing or topological distortions may appear.  Our BVH-based hopping Gaussians strategy assumes relatively smooth and continuous deformations across frames, and is therefore less effective when the motion involves abrupt or large-scale topological changes.\n\nAdditionally, such rapid expression changes may temporarily degrade the quality of incremental triangulation due to inaccurate detection of active regions. This can be solved by re-triangulating points after the motion, which helps restore mesh consistency and correct any topology artifacts.\n\n___\n\n**Q6: Discussion of the societal impact.**\n\nWe will include this discussion in the supplemental material.\n\nOur method advances high-fidelity facial reconstruction, but it also poses potential risks of misuse, such as identity theft, unauthorized avatar replication, or deepfake generation. These concerns call for thoughtful reflection on ethical implications and the adoption of practical safeguards to minimize possible harm. But with proper and responsible use, we believe our method can offer significant benefits across various applications, including virtual reality, augmented reality, and the entertainment industry.\n\n\n___\n\n**Q7: Variable definitions and minor issues (figure cropping, capitalization, citations).**\n\nThank you for pointing this out. We will correct them in the final manuscript.\n\n---\n\n**Reference**\n\n[1] Toward a practical perceptual video quality metric. \n\n[2] FaceTalk: Audio-Driven Motion Diffusion for Neural Parametric Head Models."}, {"review_id": "lN53gVImt7", "reviewer": "Reviewer_GBVR", "summary": "The paper proposes TGA (True-to-Geometry Avatar), a perspective-aware 4D Gaussian avatar framework designed for high-fidelity dynamic head reconstruction. It introduces a perspective-aware Gaussian transformation by combining Jacobian-guided deformation and homogeneous projection for better geometry under subtle appearance changes. Additionally, it proposes an incremental BVH pivoting method for efficient mesh extraction. It is reported that the proposed method achieves state-of-the-art performance with improved geometric accuracy and faster inference.", "questions": "1. What are the specific requirements for the input video in this method? Are there any explicit constraints regarding the length of the video or the coverage range of camera angles?\n\n2. How sensitive is the proposed method to variations in lighting conditions of the input videos?", "limitations": "One limitation of the current method is its untested performance under sparse-view settings. All experiments are conducted using dense multi-view input (e.g., 16 views), but in practical scenarios such as consumer-level capture or monocular recordings, such dense view coverage may not be available. A discussion of this limitation, along with potential strategies for addressing it (e.g., view augmentation, priors), would strengthen the paper’s applicability.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strengths:**\n\n1. The paper introduces a novel perspective-aware Gaussian transformation, which significantly improves geometry-color alignment under subtle appearance changes compared to previous 3DGS-based methods.\n\n2. The proposed BVH-based incremental triangulation is efficient and well-motivated, enabling fast mesh extraction without sacrificing accuracy.\n\n3. The paper is well-organized and easy to follow. Experimental results on multiple benchmarks clearly show superior performance in both reconstruction quality and efficiency.\n\n**Weaknesses:**\n\n1. While the method performs well on multi-view datasets, its generalizability to other settings—such as sparse-view, in-the-wild monocular videos—is not fully explored or discussed.\n\n2. The evaluations in the paper are conducted on relatively short sequences (around 100 frames), and the performance on longer videos is not discussed. It remains unclear how the method handles longer-term consistency.\n\n3. The method focuses on geometry accuracy, but texture quality is not analyzed. Since appearance quality is critical for photorealistic avatars, it would strengthen the paper to include texture analysis.", "was_revised": true, "final_justification": "The rebuttal has addressed most of my concerns. I will maintain my original score for the paper.", "rebuttal": "We sincerely thank the reviewer for the constructive feedback and appreciation of our key contributions. We are glad that the effectiveness of our geometry-color alignment under subtle appearance changes and the fast mesh extraction via BVH pivoting were well recognized. We will incorporate the suggested changes in the final version of our paper and the supplementary material.\n\n___\n\n**Q1: Generalization in sparse-view scenarios.**\n\nWe appreciate the reviewer’s attention to this important aspect. TGA is primarily designed for multi-view dynamic reconstruction, but it can ensure **reasonable results under sparse-view**. \n\nSpecifically, the FLAME model offers strong geometric priors that effectively guide reconstruction in low-coverage settings. The proposed perspective-aware transformation leverages subtle photometric cues to optimize Gaussian attributes from limited viewpoints. Additionally, the Jacobian-guided deformation improves inter-frame consistency by enhancing the temporal coverage of Gaussian primitives.\n\nFurthermore, we conduct novel-view synthesis for views 16/6/3, and self-reenactment for view 1 (since there is no validation view for monocular video) on the **recently released NeRSemble V2 dataset**.\n\n| Views  | 16    | 6     | 3     | 1     |\n| ------ | ----- | ----- | ----- | ----- |\n| PSNR↑  | 31.37 | 29.86 | 27.49 | 24.95 |\n| SSIM↑  | 0.952 | 0.932 | 0.923 | 0.898 |\n| LPIPS↓ | 0.060 | 0.074 | 0.113 | 0.146 |\n\n___\n\n**Q2: Performance on longer videos and longer-term consistency.**\n\nOur method can produce **relatively stable** outputs on longer sequences. When scaling to longer frame sequences, and keeping the number of Gaussians stable, the overall training time and rendering metrics are expected to be close to Tab. 1 (since we have to train for 300k iterations), and the runtime of BVH tree pivoting is closely related to the number of Gaussians rather than sequence length. \n\nSpecifically, the proposed BVH pivoting mechanism is designed to support long-range consistency. It incrementally tracks topological variations in Gaussians and reuses triangulations when no significant local deformation is detected.\n\nWe further conduct experiments on concatenated sequences (100-500 frames) on the Multiface dataset, covering non-repetitive expressions. Additionally, periodic re-triangulation provides a way to reset the accumulated geometric errors and recover accuracy.\n\n| Frames | ~100 | ~200 | ~300 | ~400 | ~500 |\n| ------ | ---- | ---- | ---- | ---- | ---- |\n| CD↓    | 2.16 | 2.15 | 2.16 | 2.18 | 2.23 |\n| MAE↓   | 17.7 | 17.4 | 17.9 | 18.2 | 18.3 |\n\n___\n\n**Q3: Analysis on appearance and texture quality.**\n\nTo assess mesh-based rendering quality, we evaluate the frontal view of four subjects (#104, #264, #302, and #140) from Fig. 5, summarized below. \n\nCurrently, TGA does not consider intrinsic decomposition or reflectance modeling. Therefore, we adopt **flat shading based solely on vertex color** for rendering. We will explore high-quality texture generation and relighting techniques in future work.\n\n| Subjects | #104  | #264  | #302  | #140  |\n| -------- | ----- | ----- | ----- | ----- |\n| PSNR↑    | 23.69 | 24.12 | 24.40 | 24.89 |\n| SSIM↑    | 0.653 | 0.592 | 0.617 | 0.722 |\n| LPIPS↓   | 0.304 | 0.351 | 0.349 | 0.238 |\n\n___\n\n**Q4: Requirements for the input video.**\n\nThank you for spotting this. We will further include the requirements in the final version of the main paper.\nWe use **synchronized light-stage cameras** with ~30–60° angular intervals. While the pipeline works best with moderate viewpoint coverage (≥90° in total), it can tolerate partial occlusions due to the Perspective-Aware Gaussian Transformation. We apply VHAP to perform mesh tracking and extract pose and expression parameters on the datasets. Last, there is no hard constraint on input video length.\n\n___\n\n**Q5: Discussions on variations in lighting conditions.**\n\nThank you for pointing this out. Our current work primarily focuses on dynamic reconstruction under controlled indoor lighting and does **not explicitly support lighting variations**. We will further include this discussion in the revised supplementary material.\nLighting changes can indeed affect 3DGS-based methods due to their reliance on photometric consistency. However, our Jacobian-guided deformation and perspective-aware Gaussian transformation help alleviate blending artifacts caused by view-dependent reflectance, particularly on skin surfaces. These components enhance geometric stability and reduce artifacts under moderate illumination changes."}, {"review_id": "1MnnfQCqtb", "reviewer": "Reviewer_mgEK", "summary": "This paper introduces TGA, a perspective-aware 4D Gaussian avatar reconstruction framework. The primary motivation is to improve dynamic avatar reconstruction by targeting the limitations of current 3D Gaussian Splatting (3DGS) methods, which fail to model subtle facial geometric and chromatic details due to affine projection approximations. TGA integrates a Perspective-Aware Gaussian Transformation and an Incremental BVH Tree Pivoting mechanism for efficient dynamic mesh extraction. Experimental evaluations across benchmarks like NeRSemble, Multiface, and NHA demonstrate TGA’s improvements in geometric accuracy, convergence speed, and inference efficiency over several state-of-the-art baseline methods.", "questions": "1.\tHow does TGA handle more diverse data, such as in-the-wild video, low-light scenarios, or subjects with extreme/atypical head topology (e.g., hats, facial coverings)? Are there failure cases or modes of instability not covered in the current evaluation?\n2.\tCan the authors provide more details on the computational or memory overheads of the perspective-aware transformation and BVH tree pivoting, especially when scaling to longer frame sequences or higher scene complexity?", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1.\tThe introduction of a homogeneous formulation for Gaussian projection, combined with Jacobian-guided adaptive deformation, addresses limitations in affine approximations by enhancing color-blending and geometry-color alignment.\n2.\tThe Incremental BVH Tree Pivoting method efficiently identifies active \"hopping Gaussians\" and performs adaptive re-triangulation, resulting in faster mesh extraction and computational savings vital for real-time and scalable dynamic avatar modeling.\n3.\tThe manuscript provides thorough quantitative and qualitative results.\n\nWeaknesses:\n1.\tAuthors explicitly acknowledge in the checklist that they does not discuss the limitations of the approach or any potential negative societal impacts. This is a notable omission, especially given the implications of photo-realistic dynamic face reconstruction in terms of privacy and potential misuse.\n2.\tNo error bars, variance, or statistical significance assessments are provided for the quantitative experiments.\n3.\tTable 2 provides a formal ablation of TGA’s key components, but there is limited discussion on computational costs or memory overheads introduced by the more sophisticated deformation and projection scheme.", "was_revised": true, "final_justification": "I thank the authors for their detailed response, which has addressed my concerns about the paper's weaknesses and provided the requested discussion. I believe the work now meets the threshold for acceptance. Accordingly, I will keep my score, 4.", "rebuttal": "We would like to thank you for your valuable suggestions and for acknowledging our efforts in addressing the limitations of affine projection and enhancing mesh extraction efficiency. We will incorporate the suggested changes in the final version of the paper and the supplementary material.\n\n___\n\n**Q1: The limitations and further discussions of TGA.**\n\nThank you for spotting this. We will further include this discussion and visual examples in the supplemental material.\n\n- Discussion of limitations and failure cases.\n\n  One failure case occurs under **extremely rapid expressions movements**, such as sudden mouth opening or exaggerated frowning. In such cases, local mesh tearing or topological distortions may appear. Our BVH-based hopping Gaussians strategy assumes relatively smooth and continuous deformations across frames, and is therefore less effective when the motion involves abrupt or large-scale topological changes.\n\n  Additionally, such rapid expression changes may temporarily degrade the quality of incremental triangulation due to inaccurate detection of active regions. This can be solved by re-triangulating points after the motion, which helps restore mesh consistency and correct any topology artifacts.\n\n- Discussion of the societal impact.\n\n  Our method advances high-fidelity facial reconstruction, but it also poses potential risks of misuse, such as identity theft, unauthorized avatar replication, or deepfake generation. These concerns call for thoughtful reflection on ethical implications and the adoption of practical safeguards to minimize possible harm. But with proper and responsible use, we believe our method can offer significant benefits across various applications, including virtual reality, augmented reality, and the entertainment industry.\n\n___\n\n**Q2: Lack of Statistical Analysis.**\n\nThank you for pointing this out. We agree that reporting standard deviation or confidence intervals would provide a more rigorous picture of variance, and we will include them in the final version of our paper and supplementary material.\n\n___\n\n**Q3: Discussion on computational costs or memory overheads.**\n\nThank you for pointing this out. We summarize the **computational costs** of Perspective-Aware Gaussian Transformation (PGT) and BVH tree pivoting modules in Tab. 1 and 3 of the original manuscript, respectively. When scaling to longer frame sequences with a stable number of Gaussians, the overall training time remains comparable to that reported in Table 1, as we train for a fixed 300k iterations. The runtime of the BVH pivoting process primarily depends on the number of Gaussians rather than the sequence length. \n\nThe **memory overheads** of PGT and BVH tree pivoting is no more than 24 gigabytes since we load images on-the-fly. When scaling to longer frame sequences and with stable number of Gaussians, the training memory usage remains mostly constant, and the storage for BVH tree pivoting is related to the number of Gaussians since it is conducted frame by frame.\n\n___\n\n**Q4: How does TGA handle more diverse data?**\n\nThank you for this insightful question. We will include this in the final version of the supplementary material.\n\n- Sparse-view or monocular scenarios.\n\n  TGA is designed primarily for multi-view dynamic reconstruction, but it can ensure **reasonable results under sparse-view**. We will further include this in our future work.\n\n  Specifically, the FLAME model provides strong geometric priors to guide reconstruction; the perspective-aware transformation leverages subtle color cues to optimize Gaussian attributes under sparse-view inputs; and the Jacobian-guided deformation improves inter-frame consistency by enhancing the temporal coverage of Gaussians.\n\n  Furthermore, we conduct novel-view synthesis for views 16/6/3, and self-reenactment for view 1 (since there is no validation view for monocular video) on the **recently released NeRSemble V2 dataset**.\n\n  | Views  | 16    | 6     | 3     | 1     |\n  | ------ | ----- | ----- | ----- | ----- |\n  | PSNR↑  | 31.37 | 29.86 | 27.49 | 24.95 |\n  | SSIM↑  | 0.952 | 0.932 | 0.923 | 0.898 |\n  | LPIPS↓ | 0.060 | 0.074 | 0.113 | 0.146 |\n\n- Low-light scenarios.\n\n  In low-light environments, performance may degrade due to limited signal-to-noise ratio and unreliable photometric supervision, which affects both Gaussian optimization and projection consistency.\n\n- Atypical head topology.\n\n  For atypical head topology, mild occlusions such as hats or eyeglasses generally do not significantly affect reconstruction, as the underlying FLAME tracking remains stable. However, severe occlusions like face masks, which obscure large portions of the facial geometry, can lead to tracking failures, incomplete Gaussian coverage, and distorted surface warping."}, {"review_id": "faSnfM6ImE", "reviewer": "Reviewer_LnPM", "summary": "This paper utilizes 3D Gaussian Splatting (3DGS) to achieve dynamic avatar modeling. \n\nSpecifically, in the rendering stage of 3DGS, the original method projects a Gaussian particle from 3D space onto the camera image plane using EWA splatting for approximation, which introduces some inaccuracies. The authors address this issue by proposing Perspective-Aware Gaussian Transformation. In addition, they introduce an Incremental BVH Tree Pivoting approach to enable fine-grained avatar mesh reconstruction.", "questions": "Please refer to the \"Weakness\" section.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The discussion around how to accurately and efficiently project a Gaussian particle from 3D space onto the camera image plane is meaningful. It is possible that there are alternatives to EWA splatting that offer better trade-offs, and this paper contributes new insights in that direction.\n2. In terms of reconstruction quality, the proposed mesh reconstruction approach appears to produce promising results.\n\nWeaknesses:\n1. For the improvement over EWA splatting, there are other alternatives, such as 3DGUT [1]. However, the paper does not include a comparison or discussion with these existing approaches.\n2. It remains unclear whether the proposed Perspective-Aware Gaussian Transformation brings improvements in general scenarios. More analysis or ablation is needed to support its general effectiveness.\n3. I would also like to know whether the Perspective-Aware Gaussian Transformation helps in preserving or enhancing fine-level details such as hair and wrinkles. Currently, the paper lacks visual or quantitative results on these aspects.\n4. The authors claim that their Avatar Mesh Reconstruction method is fast, but there is a lack of comparison with other methods in terms of reconstruction speed.\n\n[1] Wu, Q., Esturo, J. M., Mirzaei, A., Moenne-Loccoz, N., & Gojcic, Z. (2025). 3dgut: Enabling distorted cameras and secondary rays in gaussian splatting. In Proceedings of the Computer Vision and Pattern Recognition Conference (pp. 26036-26046).", "was_revised": true, "final_justification": "I appreciate the efforts made by the authors. However, I still believe that the experimental section and the theoretical analysis require further improvement. The current version lacks sufficient comparative analysis with similar work, and the limited qualitative rendering experiments are not enough to fully support the authors’ claims. In terms of writing, I also see room for improvement—specifically, there is ambiguity about whether the emphasis is on 3DGS rendering results or on geometry extraction. (Some more detailed concerns were already pointed out by me during the rebuttal stage.) In particular, I find myself generally aligned with the concerns raised by Reviewer 2DhK and agree with the points they highlighted. Therefore, I choose to keep my score unchanged (3: Borderline Reject).", "rebuttal": "We would like to thank the reviewer for the valuable suggestions and for recognizing the significance of our contributions toward improving Gaussian projection accuracy and mesh reconstruction quality. Some of the raised concerns may stem from a misunderstanding of our pipeline structure, which we clarify below. We hope this clarification helps resolve the concerns.\n\n---\n\n**Q1: Comparisons with these existing approaches about improvement over EWA splatting.**\n\nThanks for pointing that out. We will further include these related papers in the revised version of our paper. Specifically, we compare TGA with 3DGUT[1] and 3DGS-marcher[2] modified with FLAME-Gaussian deformation. The quantitative results show that our method achieves superior performance in the scope of dynamic avatar reconstruction.\n\n|        | 3DGUT[1] | 3DGS-marcher[2] | Ours      |\n| ------ | -------- | --------------- | --------- |\n| PSNR↑  | 29.96    | 30.54           | **31.37** |\n| SSIM↑  | 0.938    | 0.941           | **0.952** |\n| LPIPS↓ | 0.084    | 0.079           | **0.057** |\n\n---\n\n**Q2: Lack of experiments about fine-level details and general effectiveness on the proposed Perspective-Aware Gaussian Transformation (PGT).**\n\nWe believe this may stem from a misunderstanding of our pipeline. As demonstrated in the original manuscript, we have conducted the reconstruction experiments of **challenging fine-level details in Fig. 5 and 7**, and ablated the **effectiveness of modules in PGT in Fig. 8**. Regarding rendering quality, improvements in novel-view synthesis are reported in Tab. 1.\n\nSpecifically, our method primarily focuses on high-fidelity ***geometry extraction*** for dynamic avatars while maintaining stable rendering quality, similar to prior Topo4D and SurFhead. The module Sec. 3.3, \"Incremental BVH Tree Pivoting\" only serves as a ***post-processing step*** to accelerate mesh extraction and does not affect the quality of reconstructed geometry. Therefore, the quantitative results shown in **Sec. 4 \"Experiments\" reflect the effectiveness of the PGT**.\n\nFurthermore, we conduct novel-view synthesis to evaluate the effectiveness of PGT and report the overall average metrics on the **recently released NeRSemble V2 dataset**. We randomly chose Subjects #442, #487, and #537 to show the individual qualitative fidelity. (\"Ours-\" denotes our method without module PGT.)\n\n| Methods  | GA    | SF    | Ours- | Ours      | GA    | SF    | Ours- | Ours      | GA    | SF    | Ours- | Ours      | GA     | SF     | Ours-  | Ours      |\n| -------- | ----- | ----- | ----- | --------- | ----- | ----- | ----- | --------- | ----- | ----- | ----- | --------- | ------ | ------ | ------ | --------- |\n| Subjects | #442  | #442  | #442  | #442      | #487  | #487  | #487  | #487      | #537  | #537  | #537  | #537      | Avg.V2 | Avg.V2 | Avg.V2 | Avg.V2    |\n| PSNR↑    | 29.85 | 29.42 | 29.38 | **31.42** | 29.04 | 27.65 | 29.04 | **30.76** | 31.52 | 29.03 | 30.89 | **31.97** | 30.43  | 29.97  | 30.39  | **31.37** |\n| SSIM↑    | 0.948 | 0.942 | 0.939 | **0.962** | 0.933 | 0.923 | 0.931 | **0.942** | 0.938 | 0.923 | 0.934 | **0.953** | 0.934  | 0.931  | 0.930  | **0.952** |\n| LPIPS↓   | 0.121 | 0.125 | 0.132 | **0.054** | 0.072 | 0.073 | 0.113 | **0.063** | 0.057 | 0.131 | 0.102 | **0.056** | 0.067  | 0.087  | 0.107  | **0.060** |\n\n---\n\n**Q3: Comparison with other methods in terms of reconstruction speed.**\n\nAs noted in the original manuscript, the reconstruction speed comparison is presented in the \"Inference\" column of Tab. 1 and discussed in lines 294–296.\n\n---\n\n**Q4: Paper formatting concerns.**\n\nThank you for spotting this. This issue may arise from a misreading of our figure annotations.\n\nSpecifically, in lines 123–124, we already refer to “Fig. 3” in line 123, and the phrase “as shown in 1” refers to the \"1\" part of Fig. 3 titled “Perspective Projection.” We would change this ambiguity in the final version of our paper.\nRegarding the references to “Fig. 3(a)” in line 137 and “Fig. 3(b)” in line 141, these correspond to the right-hand sections of Fig. 3, titled “Uniform Warping” and “Adaptive Warping,” respectively. \n\nWe believe this can address your concerns.\n\n---\n\n**References**\n\n[1] 3dgut: Enabling distorted cameras and secondary rays in gaussian splatting.\n\n[2] Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?"}, {"review_id": "DGo3TG78jX", "reviewer": "Reviewer_2DhK", "summary": "The paper introduces a new perspective-aware 3D Gaussian projection onto a 2D image plane that is depth-aware. The pipeline first uses the deformation gradient between canonical and deformed meshes and applies it to the Gaussian kernels. Next, the projection is reformulated into a homogeneous transform $4\\times4$.\n\n1) Pack Gaussians primitives into a 4×4 homogeneous transform $H$.\n2) Swap translation into column 3 $J$\n3) Apply camera $M$\n4) Compose full splatting matrix $B = MHJ$\n5) Encode the view ray as two intersecting planes and transform them into Gaussian space\n6) Perform the homogeneous perspective divide to get the intersection between a ray and the Gaussian's tangent plane.\n7) Compute the Gaussian fall-off. Compared to vanilla 3DGS, this is computed in 3D between the ray intersecting a plane and the Gaussian center. This maintains depth information and full perspective distortion compared to simple Mahalanobis distance in 2D in vanilla 3DGS.\n8) Recover the isocountour of the Gaussian in the image space and compute the axis-aligned bbox for 3DGS further processing and rasterization.", "questions": "1) Does $J$ in Eq. 6 swap the 3rd and 4th basis vectors?\n2) Why are there no supplemental videos attached?", "limitations": "1) We do not know how this pipeline works for dynamic sequences. It is important to provide videos of geometry and color.\n2) The geometry seems to be low-frequency after applying the homogeneous projection.\n3) The color seems to have many artifacts.\n4) Minimal evaluation, especially in the context of Perspective-Aware Gaussian Transformation.\n\nI am on the positive side of the paper; however, I need more results to make up my mind about the facial expressions.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Weaknesses**\n\n1) The paper did not provide qualitative results showing that the problem of chromatic inconsistencies and spatial distortions in vanilla 3DGS arises directly from its affine (first-order Taylor). Since this is the main motivation of the authors, I would expect some figures showing the claims and a more thorough ablation study on the differences, especially in the color space.\n2) The RGB results, especially in Figure 6, are of low quality and contain many artifacts.\n3) **The paper did not provide sufficient figures or videos in the supplemental** which to me is a drawback since a method that presents dynamic avatars should, in principle, show a video. It is not possible to see dynamic appearance or deformation based on a single static frame.\n4) I appreciate the mathematical elegance of this formulation and a nice way to avoid certain approximations; however, I find it difficult to see that those changes bring real benefit in the obtained quality. There are not enough evaluations provided, especially qualitative ones.\n5) In my opinion, the homogenous projection should be evaluated not only with respect to vanilla 3DGS but also with ray marching. Especially in the context of the work: *Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?* by Celarek et al., which shows that vanilla 3DGS is not far behind ray marching despite many approximations, including pinhole perspective projection linearization.\n6) The related work section is not fully elaborated, and there are many missing articles. Also, some of their references are repeated, like: *Ultra high-fidelity head avatar via dynamic gaussians*\n\n**Strenghts**\n\n1) I really like the homogeneous projection formulation. The original 3DGS utilizes an affine Jacobian, linearizing the pinhole camera map through a first-order Taylor expansion. However, this yields an effectively orthogonal projection onto the image plane that ignores variation in 1/z. By postponing the perspective divide and embedding the Gaussian into homogeneous 4D space, the authors recover a much more accurate intersection between the 3D Gaussian and the camera-space tangent plane. This reformulation requires no extra computation and can be seamlessly integrated with existing rasterizers.\n2) Thanks to postponing the perspective division, the authors reformulated the Gaussian-style exponential falloff, and instead of computing 2D Mahalanobis distance, they use 3D perpendicular distance from the viewing ray to the Gaussian center.", "was_revised": true, "final_justification": "Overall, I like the proposed framework. I strongly agree with reviewer LnPM regarding the missing baselines, and I hope the authors can incorporate them, along with the rest of the results and materials (such as videos), in the final version. In good faith, I will keep my score as borderline accept.", "rebuttal": "We would like to thank you for your valuable suggestions and for recognizing the mathematical soundness and practical integration of our proposed homogeneous projection formulation. We will incorporate your suggestions into the final version of the paper and the supplementary material.\n\nAccording to the NeurIPS guidelines, we are not permitted to upload images during the rebuttal phase. However, we have already prepared extensive visual results, including dynamic sequences and expression-specific comparisons. We will include them in the final submission and supplementary material.\n\nFurthermore, to compensate during the rebuttal, we present our method’s visual effectiveness through **comprehensive quantitative metrics** and **existing qualitative results**:\n\n1. Quantitative side: We report the overall average metrics on the **recently released NeRSemble V2 dataset**, and randomly choose Subjects #442, #487, and #537 to show the individual qualitative fidelity.\n\n2. Qualitative side: We will provide **more detailed explanations** of the visual examples already included in the main paper. \n\n---\n\n**Q1: Chromatic inconsistency problem in vanilla 3DGS and evaluations on Perspective-Aware Gaussian Transformation (PGT).**\n\nWe understand that your concerns relate to the lack of sufficient evidence regarding *rendering effectiveness*, in order to prove whether the problem exists and how well PGT performs. First of all, we would like to emphasize that, in the task of 3DGS-based avatar reconstruction, state-of-the-art (SOTA) methods such as GaussianAvatars (GA) and SurFhead (SF, using the improved 2D Gaussian representation) are both built on the original rasterization idea.\n\n- Quantitative side: We believe that the PSNR, SSIM, and LPIPS (as ***chromatic*** metrics) demonstrate that SOTA methods based on vanilla 3DGSs suffer from chromatic inconsistency, and our PGT can effectively mitigate this issue. In the original manuscript, Tab 1. presents the average quantitative evaluation of **novel-view synthesis** comparing TGA with these methods. Furthermore, we conduct experiments on individual subjects, where \"Ours-\" denotes our method without module PGT:\n\n  | Methods  | GA    | SF    | Ours- | Ours      | GA    | SF    | Ours- | Ours      | GA    | SF    | Ours- | Ours      | GA     | SF     | Ours-  | Ours      |\n  | -------- | ----- | ----- | ----- | --------- | ----- | ----- | ----- | --------- | ----- | ----- | ----- | --------- | ------ | ------ | ------ | --------- |\n  | Subjects | #442  | #442  | #442  | #442      | #487  | #487  | #487  | #487      | #537  | #537  | #537  | #537      | Avg.V2 | Avg.V2 | Avg.V2 | Avg.V2    |\n  | PSNR↑    | 29.85 | 29.42 | 29.38 | **31.42** | 29.04 | 27.65 | 29.04 | **30.76** | 31.52 | 29.03 | 30.89 | **31.97** | 30.43  | 29.97  | 30.39  | **31.37** |\n  | SSIM↑    | 0.948 | 0.942 | 0.939 | **0.962** | 0.933 | 0.923 | 0.931 | **0.942** | 0.938 | 0.923 | 0.934 | **0.953** | 0.934  | 0.931  | 0.930  | **0.952** |\n  | LPIPS↓   | 0.121 | 0.125 | 0.132 | **0.054** | 0.072 | 0.073 | 0.113 | **0.063** | 0.057 | 0.131 | 0.102 | **0.056** | 0.067  | 0.087  | 0.107  | **0.060** |\n\n- Qualitative side: In the main paper, Fig. 6 presents the **self-reenactment evaluation** results. \n\n  In the top row (Person_0000 from the NHA dataset), the double eyelids are more chromatically preserved, while in the bottom row (Subject 140 from the NeRSemble dataset), the nasolabial folds and eye bags are more chromatically reconstructed compared to SOTA methods. We believe that such **skin details** can also address your concerns about facial expressions.\n\n---\n\n**Q2: Low-quality RGB results with artifacts in Figure 6.**\n\nWe would like to clarify that the results shown in Fig. 6 are from the self-reenactment (SR) setting, which involves driving an avatar using **unseen poses and expressions** from a held-out sequence of the same subject. This task is significantly more challenging than novel-view synthesis (NVS), where poses and expressions are known during training (as reported in Tab. 1).\n\nWe assure the reviewers that our method achieves better performance than existing state-of-the-art approaches in both settings. In particular, our novel-view synthesis results are free from noticeable artifacts. We will add more visual results in the final version of the main paper. \n\n- Quantitative side: We conduct **self-reenactment** experiments on each individual subject:\n\n  |        | #442-GA | #442-SF | #442-Ours | #487-GA | #487-SF | #487-Ours | #537-GA | #537-SF | #537-Ours | Avg.-GA | Avg.-SF | Avg.-Ours |\n  | ------ | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- |\n  | PSNR↑  | 25.47   | 25.27   | **25.61** | 26.65   | 26.97   | **27.06** | 25.12   | 25.75   | **26.48** | 25.98   | 25.97   | **26.42** |\n  | SSIM↑  | 0.904   | 0.898   | **0.916** | 0.912   | 0.919   | **0.922** | 0.851   | 0.887   | **0.902** | 0.901   | 0.903   | **0.912** |\n  | LPIPS↓ | 0.147   | 0.149   | **0.098** | 0.081   | 0.077   | **0.074** | 0.101   | 0.139   | **0.077** | 0.081   | 0.098   | **0.073** |\n\n- Qualitative side: In the main paper, the 3DGS-rendered image of Subject #218 (middle of Fig. 2) demonstrates that, under known poses and expressions, our method produces artifact-free results.\n\n---\n\n**Q3: Insufficient figures or video results for dynamic avatars.**\n\nWe fully agree that video demonstrations are essential to properly evaluate temporal consistency and expression tracking. We will further include more videos / sequential images in the final supplementary material. \n\nInitially, our intention was to demonstrate our method using average quantitative metrics such as PSNR, SSIM, Chamfer Distance, MAE, and Recall@2.5mm metrics (as shown in Fig. 7, Tab. 1 and 2), and to illustrate robustness through challenging expressions (Fig. 5 and 7), following GA and SurFHead. However, we now realize that these are not sufficient for fully conveying the temporal behavior of our method.\n\n- Quantitative side: We additionally evaluate our results on **temporal consistency using VMAF[1]**, a metric for perceptual quality and temporal consistency. We will include this and more visual results in the final supplementary material. \n\n  |          | #442-GA | #442-SF | #442-Ours | #487-GA | #487-SF | #487-Ours | #537-GA | #537-SF | #537-Ours | Avg.-GA | Avg.-SF | Avg.-Ours |\n  | -------- | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- | ------- | ------- | --------- |\n  | VMAF[1]↑ | 51.3    | 45.9    | **67.4**  | 49.5    | 44.3    | **66.2**  | 51.0    | 41.6    | **67.9**  | 50.8    | 42.7    | **67.2**  |\n\n- Qualitative side: In Fig. 1(a) “Frame-to-frame” of the main paper, the extracted meshes from an adjacent sequence (within a 20-frame window) of Subject #253 demonstrate the temporal robustness of our method. Specifically, the non-rigid facial motion (jaw movement) is consistently reconstructed without topological degradation.\n\n---\n\n**Q4: Comparisons with the ray marching method.**\n\nThank you for bringing this up. We will add these comparisons in the supplementary material. As discussed in [2], the power of efficient optimization and the large number of Gaussians allows 3DGS to outperform volumetric rendering despite its approximations. We agree with this observation, and our results further support this point. As shown in Line 244 of our paper, TGA converges within 300k iterations, earlier than 600k for GA and SurFhead.\n\nFurthermore, we evaluate avg. PSNR and SSIM between TGA with 3DGS-marcher[2] modified with FLAME-Gaussian deformation:\n\n| Iterations | GA          | SurFhead    | 3DGS-marcher[2] | Ours                |\n| ---------- | ----------- | ----------- | --------------- | ------------------- |\n| 100k       | 28.03/0.924 | 27.56/0.923 | 28.83/0.924     | **29.41**/**0.931** |\n| 200k       | 29.29/0.931 | 28.99/0.932 | 29.97/0.933     | **30.79**/**0.945** |\n| 300k       | 29.85/0.948 | 29.16/0.942 | 30.54/0.941     | **31.37**/**0.952** |\n\nIt can be seen that 3DGS-marcher[2] can converge earlier than GA and SurFhead, but it remains less suitable for dynamic avatar modeling.\n\n---\n\n**Q5: Related work section missing some papers and repeated references.**\n\nWe appreciate the reviewer pointing this out. We will correct the duplicated citation and extend the related work section such as [2-6].\n\n---\n\n**Q6: Does in Eq. 6 swap the 3rd and 4th basis vectors?**\n\nNo explicit swap of basis vectors is performed in Eq. 6.\n\n---\n\n**Q7: The geometry seems to be low-frequency after PGT.**\n\nThank you for raising this concern. This is caused by **image compression** or resolution issues in the current submission.  We will ensure that all images with consistent quality in the final version of the paper.\n\n\n---\n\n**Q8: More discussion about facial expressions.**\n\nOur method primarily focuses on **high-fidelity geometry extraction** for dynamic avatars while maintaining stable rendering quality. Fig. 5 and 7 illustrate the effectiveness of TGA under challenging facial expressions, and Tab. 1 shows improvements in novel-view synthesis rendering quality. Additionally, we will further additional visual results highlighting detailed facial expressions in the final version of the supplemental materials.\n\n---\n\n**References**\n\n[1] Toward a practical perceptual video quality metric. \n\n[2] Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?\n\n[3] NPGA: Neural Parametric Gaussian Avatars.\n\n[4] 3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting\n\n[5] Gaussianhead: High-fidelity head avatars with learnable gaussian derivation. \n\n[6] Headgas: Real-time animatable head avatars via 3d gaussian splatting."}]

Author rebuttal:

Meta-review: This paper introduces TGA, a framework for dynamic avatar mesh reconstruction that combines a perspective-aware Gaussian transformation with an efficient BVH-based incremental triangulation strategy. The approach directly addresses limitations of prior 3D Gaussian Splatting methods by improving projection accuracy, preserving fine geometric details, and enabling fast and consistent mesh extraction. Reviewers found the technical contributions sound and well-motivated, with quantitative results across multiple benchmarks showing clear improvements in geometric fidelity, temporal consistency, and inference efficiency.

The rebuttal and final remarks were thorough and convincing. The authors went beyond clarifying specific questions by expanding both qualitative and quantitative evaluations, including experiments on the NeRSemble V2 dataset and fairer comparisons with enhanced EWA-splatting baselines. They also discussed limitations in detail. These additions consistently demonstrated superior geometric accuracy, fine-detail preservation, and computational efficiency, which reinforce the significance and robustness of the proposed approach.

While one reviewer remained cautious, calling for broader comparisons and more qualitative visualization, the overall consensus is that this work is novel, timely, and impactful. I strongly recommend acceptance.
Decision: Accept (spotlight)