GeoAvatar: Adaptive 3D Avatars & Mobility

• GeoAvatar is a multifaceted term that encompasses adaptive 3D head avatar generation using geometrical Gaussian splatting and a pseudo personal mobility generator.
• The 3D head avatar approach employs explicit Gaussian representations rigged to 3DMM faces, leveraging adaptive pre-allocation and anatomically informed mouth modeling to balance reconstruction and animation.
• Benchmark results demonstrate GeoAvatar’s strong identity preservation and performance, establishing it as a key reference in geometry-aware avatar research and related mobility analysis.

GeoAvatar denotes multiple distinct research uses in recent arXiv literature. In computer graphics and vision, it names “Adaptive Geometrical Gaussian Splatting for 3D Head Avatar,” a 3D Gaussian Splatting framework for 3D head avatar generation that seeks to balance identity-preserving reconstruction with animation under novel poses and expressions. In a separate mobility-analysis line, GeoAvatar is an individual-based generator of pseudo personal mobility. The surrounding avatar literature also uses “GeoAvatar” as a shorthand for geometry-aware avatar systems, so the term is context dependent rather than uniquely tied to a single formulation (Moon et al., 24 Jul 2025, Li et al., 2023, Zhang et al., 19 Aug 2025).

1. Nomenclature and scope

In the current literature, the name “GeoAvatar” is not monosemous. The table below summarizes the two titled arXiv works that explicitly use the name.

Usage	arXiv id	Brief description
“GeoAvatar: Adaptive Geometrical Gaussian Splatting for 3D Head Avatar”	(Moon et al., 24 Jul 2025)	3D head avatar generation with adaptive geometrical Gaussian Splatting
“Learning to Generate Pseudo Personal Mobility”	(Li et al., 2023)	pseudo personal mobility generator named GeoAvatar

Within avatar research, the head-avatar sense is the one tied to adaptive geometrical Gaussian Splatting. That work addresses a specific failure mode in prior 3D Gaussian-splatting avatars: uniform regularization across facial regions, which can either allow offsets to grow too large in well-fitted regions or deny sufficient flexibility in poorly fitted regions such as scalp, ears, neck, and bangs (Moon et al., 24 Jul 2025).

Adjacent papers broaden the term’s semantic field. Several later descriptions use “GeoAvatar” as a category label for geometry-aware avatar methods rather than as a single proper noun. This suggests a secondary usage in which “GeoAvatar” functions as a shorthand for geometry-centric avatar modeling built around explicit geometry, 3DMM priors, SDFs, or mesh-/Gaussian-bound representations (Budria et al., 2024, Lee et al., 30 Mar 2026, Zhang et al., 2023).

2. Representation in the 3D head-avatar formulation

In the head-avatar formulation, GeoAvatar defines a rigged Gaussian representation bound to a 3DMM face. A Gaussian is written as

$$\mathcal{G} = \{\boldsymbol{\mu}, r, s, c, \alpha\},$$

where $\boldsymbol{\mu}\in\mathbb{R}^{3}$ is the local mean, $r\in\mathbb{R}^{4}$ is the rotation quaternion, $s\in\mathbb{R}^{3}$ is the scale, $c\in\mathbb{R}^{3}$ is the color, and $\alpha$ is the opacity. For regularization, the local mean $\boldsymbol{\mu}=(x,y,z)$ is converted to spherical coordinates with radius $r$ and angles $\theta$ and $\varphi$ (Moon et al., 24 Jul 2025).

The representation is rigged to facial triangles through a face-conditioned transformation. With facial features rotation $\boldsymbol{\mu}\in\mathbb{R}^{3}$0, center $\boldsymbol{\mu}\in\mathbb{R}^{3}$1, and scale $\boldsymbol{\mu}\in\mathbb{R}^{3}$2, the local-to-global mapping is

$\boldsymbol{\mu}\in\mathbb{R}^{3}$3

This makes Gaussian motion explicitly dependent on the deformed 3DMM face, rather than free-floating in world space (Moon et al., 24 Jul 2025).

For rendering, GeoAvatar uses the 3DGS renderer. The completed description supplied with the paper gives the standard Gaussian density

$\boldsymbol{\mu}\in\mathbb{R}^{3}$4

the projected screen-space Gaussian

$\boldsymbol{\mu}\in\mathbb{R}^{3}$5

with

$\boldsymbol{\mu}\in\mathbb{R}^{3}$6

and the front-to-back compositing rule

$\boldsymbol{\mu}\in\mathbb{R}^{3}$7

The significance of this formulation is that geometry, appearance, and rigging are all explicit, which makes the method directly comparable to other mesh-bound or 3DMM-guided Gaussian avatars (Moon et al., 24 Jul 2025).

3. Adaptive pre-allocation, mouth modeling, and rigging regularization

GeoAvatar’s central innovation is the Adaptive Pre-allocation Stage, or APS. APS performs an unsupervised segmentation of FLAME faces into rigid faces $\boldsymbol{\mu}\in\mathbb{R}^{3}$8 and flexible faces $\boldsymbol{\mu}\in\mathbb{R}^{3}$9, while mouth-added faces form $r\in\mathbb{R}^{4}$0. The criterion is a part-wise local mean distance computed over bound Gaussians. For FLAME semantic part $r\in\mathbb{R}^{4}$1,

$r\in\mathbb{R}^{4}$2

After an initial optimization stage, the mean over parts becomes $r\in\mathbb{R}^{4}$3; parts below it are assigned to $r\in\mathbb{R}^{4}$4, and parts above it are assigned to $r\in\mathbb{R}^{4}$5 (Moon et al., 24 Jul 2025).

The purpose of APS is region-wise adaptive regularization. In well-fitted regions such as face and lips, GeoAvatar tightens the rigging correspondence. In poorly fitted regions such as scalp, ears, neck, and bangs, it permits looser offsets. This directly targets the failure mode of uniform regularization described by the paper (Moon et al., 24 Jul 2025).

A second contribution is anatomically grounded mouth modeling. GeoAvatar augments FLAME with a mouth structure including frontal and molar teeth, palate, and floor. It then splits the mouth vertices into upper and lower parts:

$r\in\mathbb{R}^{4}$6

Each offset is predicted by an MLP conditioned on FLAME expression $r\in\mathbb{R}^{4}$7, pose $r\in\mathbb{R}^{4}$8, and a positional encoding of frame index $r\in\mathbb{R}^{4}$9:

$s\in\mathbb{R}^{3}$0

At inference, $s\in\mathbb{R}^{3}$1 (Moon et al., 24 Jul 2025).

The rigging regularizer operates on the spherical local mean. Region-specific radial penalties are

$s\in\mathbb{R}^{3}$2

with $s\in\mathbb{R}^{3}$3, $s\in\mathbb{R}^{3}$4, and $s\in\mathbb{R}^{3}$5. When the radial offset exceeds the rigid threshold, a polar-angle constraint is activated:

$s\in\mathbb{R}^{3}$6

The full rigging term is

$s\in\mathbb{R}^{3}$7

The stated purpose of the angle term is to prevent binding leakage into neighboring faces when radial offsets become large (Moon et al., 24 Jul 2025).

4. Objective, training pipeline, datasets, and empirical results

GeoAvatar uses a photometric objective of the 3DGS-with-D-SSIM type:

$s\in\mathbb{R}^{3}$8

and the full training loss is

$s\in\mathbb{R}^{3}$9

APS warmup runs for $c\in\mathbb{R}^{3}$0 iterations, and total training uses $c\in\mathbb{R}^{3}$1 iterations. The method uses SH degree $c\in\mathbb{R}^{3}$2 in the monocular setting, follows GaussianAvatars’ densification strategy, and is reported on a single RTX 3090 with training time $c\in\mathbb{R}^{3}$3 hours and inference speed $c\in\mathbb{R}^{3}$4 FPS (Moon et al., 24 Jul 2025).

The paper also introduces DynamicFace, a high-expressivity monocular video dataset. It contains 10 identities, about 2–3 minutes per subject, 20 expression categories, 3840×2160 resolution, and totals about 32.25 minutes and about 18.92 GB. Nine subjects were captured using Sony AX700 with a chroma-key background, and one subject used iPhone 14 with a normal background (Moon et al., 24 Jul 2025).

The quantitative results reported by the paper are summarized below.

Evaluation setting	Reported result	Context
SplattingAvatar monocular benchmark	MSE $c\in\mathbb{R}^{3}$5, PSNR $c\in\mathbb{R}^{3}$6, SSIM $c\in\mathbb{R}^{3}$7, LPIPS $c\in\mathbb{R}^{3}$8	best among listed baselines
DynamicFace monocular benchmark	MSE $c\in\mathbb{R}^{3}$9, PSNR $\alpha$0, SSIM $\alpha$1, LPIPS $\alpha$2	best among listed baselines
NeRSemble multi-view comparison	MSE $\alpha$3 vs $\alpha$4, PSNR $\alpha$5 vs $\alpha$6, SSIM $\alpha$7 vs $\alpha$8, LPIPS $\alpha$9 vs $\boldsymbol{\mu}=(x,y,z)$0	GeoAvatar 1-view vs GaussianAvatars 16-views

The cross-reenactment metrics reported by the paper are cosine-similarity scores of $\boldsymbol{\mu}=(x,y,z)$1 for identity preservation and $\boldsymbol{\mu}=(x,y,z)$2 for expression, both listed as best. The ablation sequence A→E adds APS, FLAME mouth modification, part-wise mouth deformation, and $\boldsymbol{\mu}=(x,y,z)$3; LPIPS improves from $\boldsymbol{\mu}=(x,y,z)$4 to $\boldsymbol{\mu}=(x,y,z)$5, and the qualitative discussion attributes sharper accessories and hair to APS, more stable mouth interiors to the mouth structure and part-wise deformation, and fewer residual rigging artifacts to the angle regularizer (Moon et al., 24 Jul 2025).

5. Position within geometry-aware avatar research

GeoAvatar belongs to a broader class of geometry-aware avatar systems that couple explicit geometry control with learned appearance. Earlier work such as OmniAvatar formulates controllable 3D head synthesis around a semantic SDF conditioned on FLAME shape, expression, and articulated neck/jaw poses, then uses an EG3D backbone to synthesize canonical heads and a volumetric correspondence map to render them in observation space (Xu et al., 2023). AvatarGen extends a similar geometry-aware logic to clothed full-body generation from 2D images, using SMPL-guided canonicalization, an SDF representation, and a deformation network for pose-dependent non-rigid dynamics (Zhang et al., 2022).

Within explicit Gaussian head avatars, GGAvatar introduces a Neutral Gaussian Initialization Module and a Geometry Morph Adjuster. Its neutral initialization pairs Gaussians with a deformable FLAME triangular mesh and uses adaptive density control, while the Geometry Morph Adjuster introduces per-Gaussian deformation bases in global space learned from a multi-resolution tri-plane and compact latent expression/pose features (Li et al., 2024). DipGuava shifts emphasis toward disentanglement: it separates a geometry-driven base appearance from personalized residual details and applies dynamic appearance fusion after residual geometric deformation, all from monocular video (Lee et al., 30 Mar 2026).

Later head-avatar work further subdivides the design space. EAvatar is a 3DGS-based framework for head reconstruction that is expression-aware and deformation-aware; it uses sparse expression control via key Gaussians, Gaussian-kernel propagation to neighbors, deformation-aware splitting, and generative geometry priors for identity-aware SDF initialization (Zhang et al., 19 Aug 2025). InstantGeoAvatar targets animatable clothed humans from monocular video with a hash-grid SDF and a geometry-aware smooth surface regularization that penalizes normal variation along rays, aiming for fast training in about five to ten minutes (Budria et al., 2024). GETAvatar operates at full-body generative scale and directly produces explicit textured 3D meshes extracted via DMTet, supervised in part by normal maps rendered from 3D scans and rendered with rasterization rather than volumetric ray marching (Zhang et al., 2023).

This suggests that “geometry-aware avatar” research has diversified into at least three technical lineages: mesh-/3DMM-bound Gaussian splatting, canonical SDF-based rendering, and explicit mesh generation. GeoAvatar is situated in the first lineage and is specifically distinguished by APS, anatomically extended mouth modeling, and spherical-coordinate rigging regularization.

6. Reception, benchmark status, and the unrelated mobility GeoAvatar

Later papers treat GeoAvatar as a strong per-subject 3DGS baseline. SpatialAvatar-0 explicitly places GeoAvatar among per-subject 3DGS refiners on the SplattingAvatar monocular benchmark and reports that its own refined model achieves PSNR $\boldsymbol{\mu}=(x,y,z)$6 versus GeoAvatar $\boldsymbol{\mu}=(x,y,z)$7, SSIM $\boldsymbol{\mu}=(x,y,z)$8 versus $\boldsymbol{\mu}=(x,y,z)$9, MSE $r$0 of $r$1 versus $r$2, and LPIPS $r$3 of $r$4 versus $r$5. The same paper reports $r$6K iterations per subject for SpatialAvatar-0 versus $r$7K for GeoAvatar, about $r$8 minutes versus about $r$9 hours on RTX 3090, and $\theta$0 FPS versus $\theta$1 FPS at $\theta$2 resolution (Wang et al., 14 Jun 2026). In that benchmark-specific sense, GeoAvatar functions as a reference point for later layout-preserving refinement methods.

Outside computer graphics, GeoAvatar names an unrelated mobility generator. “Learning to Generate Pseudo Personal Mobility” describes GeoAvatar as an individual-based generator of pseudo personal mobility that learns “life patterns,” uses a reliable labeler for demographic characteristics, applies a Bayesian approach for spatial choices, and reconstructs activity-location sequences through Graph-Walk With a Guide. Reported results include an MAE of $\theta$3 for aggregated average activity probabilities versus FEM $\theta$4, hourly-distribution Jensen-Shannon divergence of $\theta$5 versus FEM $\theta$6, and Tokyo grid-population $\theta$7 of $\theta$8 for GT1 versus GeoAvatar compared with $\theta$9 for GT1 versus FEM and $\varphi$0 for GT1 versus TimeGeo (Li et al., 2023).

A common misconception is therefore that “GeoAvatar” refers to a single unified method. The literature does not support that reading. In graphics, the term usually points to the adaptive geometrical Gaussian-splatting head-avatar method or to a broader geometry-aware-avatar category; in mobility analysis, it refers to a privacy-preserving synthetic mobility generator. The intended meaning must be inferred from domain, benchmark, and citation context.