Title: TGA: True-to-Geometry Avatar Dynamic Reconstruction
Venue: NeurIPS 2025
Accepted: yes
Keywords: Avatar

3D Reconstruction

3DGS
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

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 the PerspectiveAware 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. Project page: https://superkeaibb.github.io/TGA/ .

1 Introduction

The demand for personalized, high-fidelity reconstruction of human faces and heads under complex facial movements is fundamental to a wide range of applications, including digital twins, film production, graphics simulation, and entertainment. In particular, acquiring dynamic and geometrically accurate 3D head reconstructions from multi-view recordings is a common requirement for generating digital and virtual replicas of real individuals.

Despite recent advances in high-fidelity 3D Gaussian Splatting (3DGS) [1]-based avatar reconstruction, existing methods [2, 3, 4] 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-awareness (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.

a) Frame-to-frame

b) Different Identity &

±

60

°

Views

c) Application

Mesh and Normal

In response, we propose True-to-Geometry Avatar Dynamic Reconstruction (TGA), a perspectiveaware 4D Gaussian avatar framework that sensitively captures fine-grained facial appearance variations to enable geometrically accurate 3D mesh reconstruction from 4D Gaussian representations.

We first introduce a Perspective-Aware Gaussian Transformation that jointly models temporal deformations and spatial projection effects, enhancing perspective-awareness to subtle changes in avatar facial appearance. Traditional 3DMM [5, 6]-based Gaussian methods [2, 3, 4, 7] warp primitives based on the area of their parent triangle across time steps. Such uniform scaling leads to either extending or shrinking Gaussian coverage, resulting in over- or under-blending of colors in facial regions. To address this, we apply Jacobian-guided deformation to adaptively warp each Gaussian according to the directional variation of its parent triangle, ensuring precise color coverage across dynamic frames. Furthermore, to be perspective-aware to the projection process for better capture of the intricate geometry under subtle changes in avatar skin tone and facial expressions, we adopt a homogeneous formulation in place of the insufficient affine approximation in vanilla 3DGS, enabling perspective-consistent projections. The Jacobian-guided deformation is jointly incorporated into the homogeneous formulation. As a result, color blending becomes more chromaticity-sensitive, reinforcing geometry-color alignment and providing a reliable foundation for downstream mesh extraction.

Based on the obtained Gaussian avatar field, we introduce an opacity field [8] for surface extraction. The geometrically accurate avatar surface is extracted by directly identifying a level set of an opacityguided signed distance field on tetrahedra, which are triangulated from Gaussians and their bounding points. To enable fast dynamic mesh extraction, we design a straightforward yet effective Incremental BVH Tree Pivoting approach to 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 of Gaussians. Active 3D points-referred to as hopping Gaussians-that contribute to 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 a perspective-aware 4D Gaussian avatar framework that captures intricate geometry under subtle facial variations, by integrating Jacobian-guided adaptive deformation with homogeneous projection to enable Perspective-Aware Gaussian Transformation.

We design an Incremental BVH Tree Pivoting approach, which filters out and re-triangulates hopping Gaussians. This enables fast and adaptive surface extraction by focusing computation on active regions undergoing facial expression changes.

We empirically demonstrate the advanced performance of the proposed method, demonstrating significant improvements in reconstruction accuracy, dynamic capability, training efficiency, and inference time.

d)  Fast Avatar Reconstruction

Construct

& Update

BVH

Hopping

Points

Marching

Tetrahedra

Mesh & Normal

Branch Pivoting

Sec. 3.3

Canonical Gaussians

Deformed Gaussians

b) Perspective-Aware Transformation

Homogeneous

Formulation for

Sec. 3.2

3DGS Rendered

a) FLAME Tracking

Deformed Normal

Loss & etc.

Sec. 3.2

Deformed Normal

c) Optimization

frame

J=EE-1

μ'=Jμ+t

∑=JRSSTRTJT

2 Related Work

3D Morphable Face Models. Parametric template models based on PCA have become fundamental in computer graphics and vision for representing human body geometry, including the face [6, 9, 10] and head [5, 11], with extensions to the neck [12] and the full body [13]. To overcome the rigid linearity of PCA, more recent approaches [14, 15, 16, 17, 18, 19, 20, 21] replace traditional PCAbasis underlying classical mesh-based 3DMMs. Furthermore, 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 are accompanied by significant topological changes. This makes the representation of dynamic scenes more complex and challenging. Neural Radiance Fields (NeRFs) [25, 26, 27]-based methods [25, 28, 29, 30, 31, 32, 33] can capture temporal changes and model such dynamics but not computationally feasible. 3DGS [1]-based dynamic methods [34, 35, 36, 37, 38, 39, 40] have emerged as a more efficient alternative, but remain insensitive to chromatic variations due to their affine approximation. Building upon the 3DGS paradigm, we enhance it with a Perspective-Aware Gaussian Transformation module for improved dynamic modeling.

Human Head Reconstruction. Previous works [41, 42, 43, 44, 45] have explored NeRF-based volume rendering to model avatar heads with detailed appearance. Recent approaches [46, 47, 48, 3, 49, 40, 50] incorporate implicit deformation fields to capture frame-wise Gaussian motion. Meanwhile, another line of work [51, 52, 2, 53, 4] explicitly rig Gaussians to 3DMM-based meshes for controllable facial animation. Topo4D [54] further reconstructs dynamic meshes and high-fidelity textures via topology-bound Gaussians, NPGA [55] leverages neural parametric head models [56] for learned forward deformations, ScaffoldAvatar [57] employs patch-based expressions with hierarchical Gaussian splatting for high-fidelity avatars. While most 3DGS-based methods target photorealistic rendering and animation, Topo4D [54], SurFhead [4], and our work focus on geometry-accurate facial mesh reconstruction. Specifically, our method builds upon the explicit 3DMM-3DGS 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. 3.2). By leveraging trained Gaussians with high sensitivity to facial features, our approach further enables fast and precise avatar mesh extraction (Sec. 3.3). We start with the overview of GaussianAvatars [2] and also define the main symbols(Sec. 3.1).

3.1 Preliminary

Representation. GaussianAvatars [2] associates each triangle of the FLAME mesh [5], tracked by VHAP [58], with a 3D Gaussian and moves coherently with its corresponding parent-triangle

across time steps. Specifically, each Gaussian is parameterized by a center position µ , a positivedefinite, diagonal matrix scaling matrix S , and a rotation matrix R on the neutral FLAME mesh [5]: G ( x ) = e -1 2 ( x -µ ) ⊤ Σ -1 ( x -µ ) where Σ = RS 2 R ⊤ . Besides, the Gaussian primitive has appearance properties, a prior opacity α and color c . To deform the canonical 3D Gaussian to the posed space, the vanilla 3DMM-Gaussians method transforms its position and covariance attributes according to its parent:

where the isotropic scalar k is derived from the triangle's relative extent, t and r are the barycenter and relative rotation matrix of the parent-triangle, respectively.

Rendering. Given the 3D representation θ = { µ , Σ , α, c } , the trainable parameters are optimized through the following differentiable rendering function

where ˜ C ( p ) is the rendering color at pixel p of rendered image ˜ C , and ˜ D ( µ , Σ , γ ) is a divergence of view ray γ from θ 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 [2, 3, 4, 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 to 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-approximated projected blue Gaussian in Fig. 3, even though its center is correctly splatted using a 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 , it is imperative to 'look into' the Gaussian itself and fully exploit its depth dimension-only then can we faithfully simulate perspective projection.

Specifically, we first introduce a Jacobian-based deformation mechanism to adaptively warp Gaussians across frames. This deformation is integrated into a homogeneous formulation that preserves depth information, enabling a perspective-aware projection. As a 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 is computationally efficient, it 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 an advanced warping method for Gaussians:

where E is composed of edge direction vectors of the binding triangle, and ˆ E is deformed by Eq. 1. Then, Gaussians are warped as follows:

By doing so, Gaussians gain adaptive and anisotropic deformability (Fig. 3 (b)) and maintain chromatic consistency across frames, making them ready to capture subtle variations.

Homogeneous Formulation for Gaussian Projection. To be perspective-aware for Gaussian depth dimension and further capture subtle changes in avatar skin tone and facial expressions, we extend prior methods [61, 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

1)PerspectiveProjection2)AffineApproximation

3)HomogeneousFomulation

Shrinking

Deformreferring

coverage

to parent-triangle

a) UniformWarping

b)AdapativeWarping

Sensitivetocolorvariation

Frame n

Frame n+1

fine-grained facial appearance changes (green circle in Fig. 3.(2)). The homogeneous transformation for 3D Gaussian to be normalized in a local tangent plane is:

To jointly account for non-uniform deformations driven by facial expressions across frames, we further refine the Gaussian's in the local metric through a Jacobian-based transformation. This enables adaptive Gaussian deformation while preserving global perspective accuracy. Specifically, we parameterize a viewing ray γ passing through a pixel at ( x, y ) as the intersection of two perpendicular planes: the x-plane h x = ( -1 , 0 , 0 , x ) ⊤ and the y-plane h y = (0 , -1 , 0 , y ) ⊤ . The ray is then transformed into the deformed Gaussian's local space by:

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 the viewing ray in the deformed tangent plane:

where h ′ i u denotes for the i-th component. This step performs a perspective-divide by normalizing the homogeneous coordinates (dividing by h 4 ), 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 perspective-divide 'looks into' the Gaussian covariance. Finally, we evaluate the divergence of a camera ray from Gaussian in a straightforward way. Specifically, with

we define the divergence D derived from the perpendicular distance ϕ ∗ between the Gaussian center and its closest point on the viewing ray in local tangent plane, ∥ v ∥ stand for magnitude of a vector v :

Volume rendering. Then, we obtain screen points by H ′ = MHJ , the center o of projected splat and the outermost bounds e is computed as:

where H ′ i is the i-th row of H ′ , ⟨ x, y ⟩ stands for dot product. The volumetric alpha blending is conducted to compute the rendered color in a perspective-aware way:

Optimization. We introduce a deformed normal regularization to maintain the learned structure of often-occluded regions such as teeth and eyeballs:

where n w denotes the Gaussian normal in the w -th frame, computed as the inverse camera ray direction -γ in the deformed tangent plane and then transformed back to world space: n w = Rot w · ( -γ ) , Rot w is the rotation component of matrix MHJ . The deformed normal is n d w = J -⊤ w n 0 , where J w is from Eq. 3 in the w -th frame and n 0 is the canonical normal.

Finally, we optimize our model with the following loss:

where L c is a combination of photometric loss L rgb and a D-SSIM term following 3DGS [1]. To ensure accurate geometry reconstruction, we incorporate geometric loss terms from [8], including depth-distortion L d and normal consistency L n . Toward a better alignment between Gaussians and parent triangles, we use regularization terms L scaling and L position from [2]. We set the hyperparameters following these works and λ nr as 0.01.

3.3 Incremental BVH Tree Pivoting for Fast Avatar Reconstruction

To enable rapid and geometry-accurate 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 of 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, as illustrated in Fig. 4, significantly reducing computation time compared to full re-triangulation. Since Gaussian movements fluctuate between frames, applying a fixed threshold to screen Gaussian centers and covariances can result in: 1) incomplete culling, causing a 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 a given set of 3D Gaussians, where each leaf node represents the tight bounding box of a 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. 4, where yellow "a", red "b", blue "c", and green "d" bounding boxes correspond to facial features, alongside its tree representation of the avatar. As facial expressions 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

Update

b

a

c

Filter

Retriangulate

Refit

Hopping  Set

Branch Rotate

d

Ours

NPHM

Topo4D

HRN

SurFHead

NHA

both "a" and "b", the BVH tree achieves branch rotation (swapping between "b" and "c") to reorganize the hierarchy and do topological simulation. It is important to emphasize that rather than balancing the tree, these rotations are employed to simulate Gaussian movement across volumes, minimizing the overall bounding extent cost-sometimes 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 is updated by a post-order traversal, see Sec. B.1 for details. For rotations, see part (d) of Fig. 2, which illustrates candidate node swaps considered in pivoting. Lift Rebalancer (red rotation) occurs between a parent node'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 a cost to filter hopping Gaussians. The green rotation produces mirrored-equivalent trees from Reorder Rotation and is omitted to avoid redundant computations.

Handling Hopping Points. When the rotation cost of the middle level nodes exceeds a threshold, the Gaussians within exhibit strong mobility and are filtered as hopping points, and will be incrementally 3D triangulated.

4 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-art 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-correct 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 GaussianAvatars [2].

GT

Ours

NPHM

HRN

SurFHead

Topo4D

Input

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 is 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 is 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 of full dynamic head approaches. We use it 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. It generates a displacement map from each view and fuse them to obtain the final mesh. 3DDFAV3 [68] uses geometric guidance for facial part segmentation for face reconstruction. We reconstruct a mesh for each view and then fuse them to obtain a multi-view-consistent final mesh. NHA [42] is learned from a monocular RGB portrait video that features a range of different expressions and views. NPHM [24] generates a signed distance field of a human head given an identity code and an expression code, and can then be translated into a mesh via marching cubes [69]. SurFhead [4] employs 2DGS [70] and GaussianAvatars[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 on the NeRSemble dataset [33] by reconstructing each avatar from 16-view RGB sequences and present qualitative results in Fig. 5. Comparative experimental results demonstrate that TGA can 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, we conduct a qualitative and quantitative evaluation of the reconstructed meshes on the Multiface Dataset [66] in Fig. 6. We focus on three metrics: L 1 -Chamfer 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. 1. Since TGA currently does not incorporate intrinsic

PSNR (dB)

30

Subject140

Subject165

Subject218

25

0

20

40

Frame

60

80

100

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], a metric designed to capture both perceptual quality and temporal coherence. The qualitative mesh rendering results are represented in the appendix C.2.

Gaussians Rendering. Although our method primarily targets geometry-accurate 3D reconstruction, 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. 1, respectively. The self-reenactment results indicate that, by leveraging the Perspective-Aware Gaussian Transformation, the proposed method can achieve more faithful rendering of dynamic regions (eyes and mouth) with fewer iterations than other 3DGS-based avatar methods. Additionally, we present sequential novel view synand temporal consistency of TGA.

SurFhead

GHA

GT

Ours

thesis rendering frames and their corresponding PSNR curves. The Fig. 8 demonstrates the stability

Inference Time. Furthermore, we benchmark mesh-extraction times against baseline methods in Tab. 1. For Gaussian-based methods, meshes are extracted via Truncated Signed Distance Function fusion on 3DGS-rendered 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 [67], 3DDFA [68], and NPHM [24] takes approximately 2-5 minutes per frame to inference.

4.4 Ablation Study

Perspective-aware Gaussian Transformation (PGT). We demonstrate the geometric (CD, MAE and Recall for extracted meshes) and chromatic (PSNR, SSIM, LPIPS for Gaussian-based rendering) impact of the perspective-aware Gaus-

sian transformation in Tab. 2 and Fig. 9. First, the homogeneous formulation yields a noticeable improvement in mesh quality. Second, the Jacobian gradient is essential for guiding deformation of canonical Gaussians in dynamic regions, such as the eyes (red box in Fig. 9). Without the transformed normal loss, Jacobian guided deformation fails to propagate effectively into the geometry, as evidenced by the results in Tab. 2.

Ours Full

w/o Jacobian

Ours Full

w/o Homogeneous

w/o Jacobian

w/o Homogeneous

Hopping Points Filtering. Furthermore, we evaluate hopping-point filtering via our BVH pivoting mechanism in Fig. 10, rather than relying on a fixed ∆ threshold on Gaussian centers across frames. When filtering with a fixed ∆ Gaussian center between frames, the blue points illustrate (a) incomplete culling and (b) excess screening. In contrast, our BVH pivoting accurately filters out the hopping Gaussians (c). It should be noted that when the avatar slightly opens the eyes or mouth, the forehead topology remains largely unchanged, obviating the need for re-triangulation in that region.

Accelerated Mesh Extraction. We also evaluate mesh extraction speed across different training 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 a 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,

1) frame

n

2) frame

n+1

a) Fixed

Δ

= 0.0039  b) Fixed

Δ

= 0.0034

c) Ours Hopping

our method effectively reduces the computational burden (4th column).

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 to 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 a fresh triangulation can effectively remove accumulated errors.

Societal impact. 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 bring significant benefits to applications in virtual/augmented reality.

5 Conclusion

In this work, we proposed TGA , a perspective-aware 4D Gaussian avatar framework that captures fine-grained facial geometry under dynamic conditions. By integrating Jacobian-guided 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-art performance in dynamic avatar reconstruction. Future work will explore its extension to relighting, full-body modeling and real-time applications.

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.20250484786), the Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, and the Fundamental Research Funds for the Central Universities.

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A Theoretical Analysis

A.1 Homogeneous Projection and Perspective-Aware Transformation.

Let C ( p ) ∈ R 3 be the rendered color at pixel p = ( x, y ) obtained by compositing of K Gaussians,

where ϕ ∗ k denotes the normalized projected deviation of Gaussian k in image space. Denote the full perspective Jacobian J persp ∈ R 2 × 3 by

and the affine approximation by J aff = diag( f/Z, f/Z, 0) that drops the shear terms. Let ∇ p C and ˜ ∇ p C be the image-space gradients computed with J persp and J aff, respectively. Then, for any camera pose where at least one off-diagonal entry of J persp is non-zero (i.e. any non-frontal view):

where J ∆ = J persp -J aff contains only the shear components, and S k is a symmetric positive matrix that depends on α k , D k , and the transmittance of the front Gaussians. Consequently ∥∇ p C ∥ 2 > ∥ ˜ ∇ p C ∥ 2 ; i.e. the homogeneous-projection renderer is strictly more view-sensitive than its affine counterpart.

Proof. For brevity, write T k -1 = ∏ j<k (1 -A j ) and note that 0 < T k -1 ≤ 1 . By direct differentiation we have

All dependence on the projection model is confined to ∇ p ϕ ∗ k . With either Jacobian choice it can be expressed as a linear map acting on the shear term J ∆ :

Substituting in ∇ p C and expanding ∥∇ p C ∥ 2 2 yields

̸

The cross-term in the inner product vanishes because J ∆ contains only off-diagonal elements while ˜ ∇ p C depends exclusively on J aff (diagonal). Hence the second equality in (4) follows, and the Frobenius-norm term is strictly positive whenever J ∆ = 0 .

Implication. Because facial albedo varies weakly, rendering fidelity primarily depends on how strongly the visibility term responds to slight shifts in viewpoint or shape. As shown in Sec. A.1, the homogeneous-projection formulation amplifies this response, leading to higher sensitivity to view changes and thus improved reproduction of fine-scale, view-dependent facial appearance.

B Algorithm

B.1 Pivot and Filter Hopping Points.

Here, we represent the proposed algorithm for Pivot and Filter Hopping Points in Sec. 3.3.2.

̸

̸

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 [33], where one frame is sampled every 5-8 frames for visualization.

210

460

175

304

306

104

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

210

175

460

218

460

D More Discussion

D.1 Impact of the focal length.

Shorter focal lengths (i.e., wider fields of 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.

D.2 Generalization in sparse-view scenarios.

TGAis primarily designed for multi-view dynamic reconstruction, but it 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-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 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.

Specifically, the proposed BVH pivoting mechanism is designed to support long-range consistency. It incrementally tracks topological variations in 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

We further compare TGA with existing approaches 3DGUT [72, 73] and 3DGS-marcher [74] about improvement over EWA splatting, modified with FLAME-based mesh-Gaussian deformation. The quantitative results show that our method achieves superior performance in the scope of dynamic avatar reconstruction .

F Future Work

Our current work primarily focuses on dynamic reconstruction under controlled indoor lighting and does not explicitly support lighting variations. Lighting changes can indeed affect 3DGS-based methods due to their reliance on photometric consistency. In future work, we plan to 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 in-the-wild scenarios with improved photometric robustness and relightability.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\n**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.\n\nQUESTIONS:\n1) Does $J$ in Eq. 6 swap the 3rd and 4th basis vectors?\n2) Why are there no supplemental videos attached?\n\nLIMITATIONS:\n1) 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.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\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).\n\nQUESTIONS:\nPlease refer to the \"Weakness\" section.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths：\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.\n\nQUESTIONS:\n1.\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?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\n**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.\n\nQUESTIONS:\n1. 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?\n\nLIMITATIONS:\nOne 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.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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.\n\nQUESTIONS:\n- 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?\n\nLIMITATIONS:\nThere 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.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-10"}