TGA: True-to-Geometry Avatar Dynamic Reconstruction

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.

According 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.

Furthermore, to compensate during the rebuttal, we present our method’s visual effectiveness through comprehensive quantitative metrics and existing qualitative results:

1. 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.

2. Qualitative side: We will provide more detailed explanations of the visual examples already included in the main paper.

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Q1: Chromatic inconsistency problem in vanilla 3DGS and evaluations on Perspective-Aware Gaussian Transformation (PGT).

We 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.

• 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:

  Methods	GA	SF	Ours-	Ours	GA	SF	Ours-	Ours	GA	SF	Ours-	Ours	GA	SF	Ours-	Ours
  Subjects	#442	#442	#442	#442	#487	#487	#487	#487	#537	#537	#537	#537	Avg.V2	Avg.V2	Avg.V2	Avg.V2
  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
  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
  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

• Qualitative side: In the main paper, Fig. 6 presents the self-reenactment evaluation results.

  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.

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Q2: Low-quality RGB results with artifacts in Figure 6.

We 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).

We 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.

• Quantitative side: We conduct self-reenactment experiments on each individual subject:

  	#442-GA	#442-SF	#442-Ours	#487-GA	#487-SF	#487-Ours	#537-GA	#537-SF	#537-Ours	Avg.-GA	Avg.-SF	Avg.-Ours
  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
  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
  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

• 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.

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Q3: Insufficient figures or video results for dynamic avatars.

We 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.

Initially, 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.

• 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.

  	#442-GA	#442-SF	#442-Ours	#487-GA	#487-SF	#487-Ours	#537-GA	#537-SF	#537-Ours	Avg.-GA	Avg.-SF	Avg.-Ours
  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

• 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.

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Q4: Comparisons with the ray marching method.

Thank 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.

Furthermore, we evaluate avg. PSNR and SSIM between TGA with 3DGS-marcher[2] modified with FLAME-Gaussian deformation:

It can be seen that 3DGS-marcher[2] can converge earlier than GA and SurFhead, but it remains less suitable for dynamic avatar modeling.

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Q5: Related work section missing some papers and repeated references.

We appreciate the reviewer pointing this out. We will correct the duplicated citation and extend the related work section such as [2-6].

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Q6: Does in Eq. 6 swap the 3rd and 4th basis vectors?

No explicit swap of basis vectors is performed in Eq. 6.

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Q7: The geometry seems to be low-frequency after PGT.

Thank 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.

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Q8: More discussion about facial expressions.

Our 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.

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References

[1] Toward a practical perceptual video quality metric.

[2] Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?

[3] NPGA: Neural Parametric Gaussian Avatars.

[4] 3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting

[5] Gaussianhead: High-fidelity head avatars with learnable gaussian derivation.

[6] Headgas: Real-time animatable head avatars via 3d gaussian splatting.

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.

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Q1: Comparisons with these existing approaches about improvement over EWA splatting.

Thanks 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.

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Q2: Lack of experiments about fine-level details and general effectiveness on the proposed Perspective-Aware Gaussian Transformation (PGT).

We 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.

Specifically, 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.

Furthermore, 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.)

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Q3: Comparison with other methods in terms of reconstruction speed.

As noted in the original manuscript, the reconstruction speed comparison is presented in the "Inference" column of Tab. 1 and discussed in lines 294–296.

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Q4: Paper formatting concerns.

Thank you for spotting this. This issue may arise from a misreading of our figure annotations.

Specifically, 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. Regarding 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.

We believe this can address your concerns.

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References

[1] 3dgut: Enabling distorted cameras and secondary rays in gaussian splatting.

[2] Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?

Q3: Discussion on the enhancement of fine details such as hair and wrinkles.

We would like to discuss more about fine details such as hair and wrinkles.

From a theoretical perspective, as you insightfully mentioned, the proposed Perspective-Aware Gaussian Transformation (PGT) can reduce the approximation error inherent in EWA splatting.

• The vanilla EWA splatting avatar approach struggles with fine details such as hair strands and wrinkles because it flattens each 3D ellipsoid onto the image plane via a first-order affine approximation, ignoring depth-shear terms in perspective projection and typically deforming the covariance to an isotropic form. This oversmooths highly elongated Gaussians, causes neighboring strands to merge visually, and introduces frame-to-frame flicker due to inconsistent approximations.
• Our PGT adopts a full 4×4 homogeneous matrix H (Eq. 5), which embeds the 3D ellipsoid into projective space. The perspective divide projects the Gaussian onto the tangent plane, ensuring that its isocontours align with the true perspective distortion and effectively eliminating shear artifacts. Simultaneously, we apply a Jacobian matrix J (Eq. 4), derived from the first-order deformation of the associated triangle, to anisotropically stretch or compress the Gaussian. This preserves its principal axis alignment and provides more accurate coverage, which is especially important for highly elongated structures like hair strands or rapidly changing geometry, such as the inner mouth. This combined formulation elevates the projection error from second-order O(‖d‖²) in EWA to third-order O(‖d‖³) in PGT, where d represents the depth variation. This improvement suppresses first-order shear error terms and ensures that the screen-space ellipse of the projected Gaussian remains consistent with its true 3D orientation and shape, avoiding the typical “center-aligned but contour-drifting” artifacts of EWA.

From an experimental perspective, wrinkles are well reconstructed, as shown in the extracted meshes in Figs 5, 7, and 8 of the original manuscript. In particular, Fig. 8 highlights that, compared to the version without the homogeneous PGT, our full model is able to finely capture the eyelid folds, mouth corner creases, and nearby nasolabial wrinkles, and the rendering evaluation is shown in Q2 (general effectiveness on the proposed PGT) of our rebuttal. Similarly, hair regions can also benefit from our method's ability to capture subtle chromatic variations, thanks to the PGT module. However, accurate modeling of hair remains inherently more challenging due to its translucent appearance and non-rigid motion. When the hair is relatively matte and free of strong specular highlights, our method is able to approximate the overall hair structure and flow direction as illustrated in Fig. 5. Nevertheless, individual hair strands still pose challenges as illustrated in Fig. 5. Gaussian primitives in these regions may suffer from unstable coverage or opacity inconsistencies under changing viewpoints.

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Q4: Comparisons with neural rendering or radiance field-based methods (e.g., INSTA [1], DELTA [2], SCARF [3]).

We have demonstrated comparisons with radiance field-based methods NHA and NPHM in the Fig. 5 and Fig. 7 of the original manuscript. We would like to clarify why we initially did not include results or comparisons with INSTA [1], DELTA [2], and SCARF [3]:

• INSTA primarily utilizes the tracked FLAME mesh as a geometric prior for rendering, but it does not explicitly optimize or refine the tracked mesh itself. While our method also uses the improved tracked mesh by VHAP for initialization, the final extracted surface is not derived from it directly. Instead, we reconstruct the mesh based on the learned opacity fields of the dynamic Gaussian primitives, which allows us to enhance the fine-level details of the initial mesh.
• DELTA and SCARF mainly focus on animating full-body avatars and garments from monocular video. Since our method targets facial geometry reconstruction under multi-view settings, we consider that comparing to body-centric monocular methods might not be entirely fair or aligned in scope. However, we did perform evaluations on the Multiface dataset and observed that DELAT and SCARF achieved lower quantitative results that other radiance field-based baselines such as NHA and NPHM.

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References

[1] Instant volumetric head avatars.

[2] Learning disentangled avatars with hybrid 3d representations.

[3] Capturing and animation of body and clothing from monocular video.

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.

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Q1: The limitations and further discussions of TGA.

Thank you for spotting this. We will further include this discussion and visual examples in the supplemental material.

• Discussion of limitations and failure cases.

  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.

  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.

• Discussion of the 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 offer significant benefits across various applications, including virtual reality, augmented reality, and the entertainment industry.

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Q2: Lack of Statistical Analysis.

Thank 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.

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Q3: Discussion on computational costs or memory overheads.

Thank 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.

The 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.

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Q4: How does TGA handle more diverse data?

Thank you for this insightful question. We will include this in the final version of the supplementary material.

• Sparse-view or monocular scenarios.

  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.

  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.

  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.

  Views	16	6	3	1
  PSNR↑	31.37	29.86	27.49	24.95
  SSIM↑	0.952	0.932	0.923	0.898
  LPIPS↓	0.060	0.074	0.113	0.146

• Low-light scenarios.

  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.

• Atypical head topology.

  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.

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.

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Q1: Generalization in sparse-view scenarios.

We 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.

Specifically, 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.

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.

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Q2: 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 Gaussians and reuses triangulations when no significant local deformation is detected.

We 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.

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Q3: Analysis on appearance and texture quality.

To assess mesh-based rendering quality, we evaluate the frontal view of four subjects (#104, #264, #302, and #140) from Fig. 5, summarized below.

Currently, 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.

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Q4: Requirements for the input video.

Thank you for spotting this. We will further include the requirements in the final version of the main paper. We 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.

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Q5: Discussions on variations in lighting conditions.

Thank 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. Lighting 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.

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.

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Q1: Additional qualitative results.

We 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.

To 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.

• Novel-view synthesis.

  We conduct novel-view synthesis experiments and achieve the best results among all compared methods.

  Methods	GA	SF	Ours	GA	SF	Ours	GA	SF	Ours	GA	SF	Ours
  Subjects	#442	#442	#442	#487	#487	#487	#537	#537	#537	Avg.V2	Avg.V2	Avg.V2
  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
  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
  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

• Self-reenactment.

  We conduct self-reenactment experiments, and our method consistently outperforms prior methods in terms of PSNR, SSIM, and LPIPS.

  Methods	GA	SF	Ours	GA	SF	Ours	GA	SF	Ours	GA	SF	Ours
  Subjects	#442	#442	#442	#487	#487	#487	#537	#537	#537	Avg.V2	Avg.V2	Avg.V2
  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
  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
  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

• Temporal consistency.

  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.

  	#442-GA	#442-SF	#442-Ours	#487-GA	#487-SF	#487-Ours	#537-GA	#537-SF	#537-Ours	Avg.-GA	Avg.-SF	Avg.-Ours
  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

Additionally, 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.

We 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.

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Q2: No evaluation on photometric metrics (PSNR / SSIM / LPIPS).

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.

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.)

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Q3: What cannot be modeled with the new formulation?

We 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. Specifically, 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. Eye 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.

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Q4: Impact of the focal length.

Thank 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.

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Q5: Discussion of failure cases.

We will include this discussion and visual examples in the supplemental material.

One 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.

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.

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Q6: Discussion of the societal impact.

We will include this discussion in the supplemental material.

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.

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Q7: Variable definitions and minor issues (figure cropping, capitalization, citations).

Thank you for pointing this out. We will correct them in the final manuscript.

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Reference

[1] Toward a practical perceptual video quality metric.

[2] FaceTalk: Audio-Driven Motion Diffusion for Neural Parametric Head Models.