GaussianMorphing: Mesh-Guided 3D Morphing

• GaussianMorphing is a hybrid framework that uses mesh-guided 3D Gaussian Splatting to achieve continuous semantic-aware 3D shape and texture morphing.
• It binds 3D Gaussians to mesh faces, enforcing topological coherence and regularized deformation through ARAP constraints and geodesic distortion loss.
• The method overcomes limitations of 2D and NeRF approaches by ensuring multi-view consistency, detailed texture preservation, and unsupervised semantic correspondence.

Searching arXiv for the primary paper and closely related work on Gaussian-based morphing, 3D Gaussian Splatting morphing, and broader Gaussian morphing formulations. GaussianMorphing most commonly denotes a mesh-guided 3D Gaussian Splatting framework for semantic-aware 3D shape and texture morphing from multi-view images. In its primary formulation, source and target objects are first reconstructed as 3D Gaussian Splatting models and then converted into meshes that act as a topological scaffold; 3D Gaussians are anchored to mesh faces, semantic correspondence is inferred without labeled matches, and a time-dependent deformation field drives a continuous morph sequence whose geometry, appearance, and semantic structure remain coupled throughout interpolation (Li et al., 2 Oct 2025).

1. Problem setting and conceptual scope

GaussianMorphing addresses the problem of generating a temporally continuous 3D morph sequence from multi-view images of a source object and a target object. The intended output is not merely an image-space interpolation, but a 3D representation that changes geometry smoothly, preserves and interpolates texture realistically, and respects semantic structure such as head-to-head or leg-to-leg transitions (Li et al., 2 Oct 2025).

The framework is motivated by several limitations in earlier families of methods. Purely 2D image morphing approaches operate in image space and have difficulty maintaining multi-view consistency. NeRF-based and related “2.5D” approaches provide implicit geometry but lack strong geometric priors and explicit topology. Classical mesh morphing typically assumes input meshes of high quality, often focuses on untextured geometry, and does not directly couple shape and appearance. Point-cloud or Gaussian-only morphing lacks connectivity, which makes semantic correspondence and coherent deformation difficult and can induce tearing, fragmentation, and inconsistent motion (Li et al., 2 Oct 2025).

Within this design space, GaussianMorphing makes a specific architectural choice: it uses 3D Gaussian Splatting for high-fidelity geometry and appearance modeling, but performs morphing in the mesh domain. The mesh supplies adjacency, topology, and geodesic structure; the Gaussians preserve detailed appearance and are advected by mesh deformation rather than optimized as independent trajectories. This hybridization is the central idea of the method (Li et al., 2 Oct 2025).

2. Mesh-guided representation and Gaussian binding

The framework begins by reconstructing, for each object, a 3D Gaussian Splatting model whose primitives are

$g = (\mu_g, \Sigma_g, \alpha_g, \mathbf{sh}_g),$

where $\mu_g \in \mathbb{R}^3$ is the 3D center, $\Sigma_g$ is the covariance, $\alpha_g$ is the opacity, and $\mathbf{sh}_g$ denotes spherical harmonics coefficients for view-dependent color (Li et al., 2 Oct 2025).

A mesh is then reconstructed from the Gaussian representation using methods such as SuGaR and Gaussian Frosting with Poisson surface reconstruction. The resulting triangular mesh is not an auxiliary visualization; it is the structural substrate of the morph. Each Gaussian is attached to a triangle face $f=(V_1,V_2,V_3)$ through barycentric coordinates and a normal offset:

$$\mu_g = w_1 V_1 + w_2 V_2 + w_3 V_3 + d \cdot \mathbf{n}_f.$$

Here $\mathbf{n}_f$ is the face normal and $(w_1,w_2,w_3)$ are barycentric weights (Li et al., 2 Oct 2025).

This binding has several consequences. First, it imposes topological coherence: Gaussians move with their supporting surface patch rather than drifting independently. Second, it regularizes deformation implicitly, because trajectories are determined by mesh vertex motion rather than per-Gaussian displacements. Third, it keeps geometry and appearance aligned, since the appearance encoded in the Gaussians remains tied to specific surface locations (Li et al., 2 Oct 2025).

Under deformation, the Gaussian centers inherit the mesh motion:

$$\mu_g(t) = w_1 V_1(t) + w_2 V_2(t) + w_3 V_3(t) + d \cdot \mathbf{n}_f(t).$$

The paper also states that covariances and colors are kept tied to the local surface. This suggests that the method treats the mesh as the carrier of geometric continuity, while the Gaussians function as a high-fidelity rendering layer whose motion is induced rather than independently parameterized (Li et al., 2 Oct 2025).

3. Unsupervised semantic correspondence and the morphing field

Semantic correspondence is learned on the meshes rather than directly on the Gaussian sets. A 5-layer Graph Convolutional Network extracts per-vertex features using mesh connectivity as a prior. From these features, a probabilistic source-to-target correspondence matrix $\mu_g \in \mathbb{R}^3$0 is defined by a softmax over cosine similarities:

$\mu_g \in \mathbb{R}^3$1

where $\mu_g \in \mathbb{R}^3$2 is the cosine similarity between learned features of source vertex $\mu_g \in \mathbb{R}^3$3 and target vertex $\mu_g \in \mathbb{R}^3$4 (Li et al., 2 Oct 2025).

The soft target position for a source vertex is $\mu_g \in \mathbb{R}^3$5, and the semantic displacement is therefore

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

A neural morphing field $\mu_g \in \mathbb{R}^3$7 then produces a time-dependent displacement:

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

This is explicitly non-linear interpolation rather than simple linear blending between source and target vertex positions (Li et al., 2 Oct 2025).

The correspondence learning is constrained by mesh topology through approximate geodesics. The method constructs both an adjacency graph and a KNN graph, combines them into a hybrid adjacency structure, and then computes geodesic distances by Dijkstra’s algorithm:

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

These geodesics enter the geodesic distortion loss

$\Sigma_g$0

which encourages mapped target geodesic distances to match source geodesic distances and thereby preserves intrinsic geometry (Li et al., 2 Oct 2025).

An endpoint constraint is imposed by the alignment loss

$\Sigma_g$1

Together, $\Sigma_g$2 and $\Sigma_g$3 define an unsupervised but geometry-respecting semantic correspondence mechanism. The framework does not require labeled correspondences or pre-defined homeomorphic mappings as input; the correspondence emerges from mesh topology, learned features, and deformation objectives (Li et al., 2 Oct 2025).

4. Deformation regularization, texture preservation, and optimization

GaussianMorphing describes its trajectories as physically plausible, but in this formulation that plausibility is enforced through deformation regularization rather than explicit simulation. The central term is an As-Rigid-As-Possible objective:

$\Sigma_g$4

where $\Sigma_g$5 is the mesh at time $\Sigma_g$6 and $\Sigma_g$7 is the standard ARAP energy between nearby temporal states. This penalizes non-rigid shearing between adjacent time samples and promotes locally rigid, temporally smooth motion (Li et al., 2 Oct 2025).

Texture preservation is handled through a geodesic-aware color smoothness loss. Vertex colors are initialized by averaging the colors of bound Gaussians, with spherical harmonics evaluated from a canonical direction, and neighboring vertices are coupled by

$\Sigma_g$8

The geodesic weighting makes the constraint intrinsic to the surface rather than purely Euclidean, and it is intended to prevent texture fragmentation and abrupt local color transitions during morphing (Li et al., 2 Oct 2025).

The full training objective is

$\Sigma_g$9

The optimized variables are the GCN parameters, the morphing flow network $\alpha_g$0, and, through its feature-based definition, the correspondence matrix $\alpha_g$1. Training is performed for 500–1000 iterations per object pair, while generating a full high-resolution morph sequence takes about 2 minutes after training. Reconstruction of the hybrid mesh–Gaussian representation from images takes about 1 hour for a typical mesh of roughly 12k faces on a single NVIDIA RTX A6000 (Li et al., 2 Oct 2025).

A common misunderstanding is to view the method as direct Gaussian-to-Gaussian matching. The formulation in fact avoids that. The mesh carries correspondence and deformation; the Gaussians are bound to the mesh and rendered through 3DGS. Another common misunderstanding is to equate the phrase physically plausible with explicit mechanics. In GaussianMorphing, that phrase refers to ARAP-regularized point trajectories rather than to a simulator-based constitutive model (Li et al., 2 Oct 2025).

5. TexMorph benchmark, empirical performance, and ablations

The framework is evaluated on TexMorph, a benchmark for texture-rich 3D morphing from multi-view images. TexMorph includes synthetic objects rendered in Blender, real-world scanned objects such as Google Scanned Objects, and in-the-wild objects captured with mobile phones, spanning over ten categories including animals, fruits, furniture, and vehicles (Li et al., 2 Oct 2025).

Three metrics are introduced. Structural Stability uses the MSE between actual SSIM trajectories and ideal linear SSIM trajectories from source to target. Color Consistency uses CIELAB color difference,

$\alpha_g$2

aggregated into $\alpha_g$3. Edge Integrity measures edge fragmentation as the number of connected Canny edge components minus background. Lower values are უკეთter for all three metrics (Li et al., 2 Oct 2025).

Method	MSE(SSIM) ↓	Other metrics ↓
DiffMorpher	0.19	$\alpha_g$4 105; EI 97
MorphFlow	0.17	$\alpha_g$5 8.23; EI 33.6
Neuromorph	0.13	$\alpha_g$6 /; EI 13.0
FreeMorph	0.20	$\alpha_g$7 13.0; EI 21.6
GaussianMorphing	0.11	$\alpha_g$8 6.40; EI 9.0

On the proposed TexMorph benchmark, GaussianMorphing substantially outperforms prior 2D/3D methods, reducing color consistency error ($\alpha_g$9) by 22.2% and EI by 26.2% (Li et al., 2 Oct 2025).

Qualitatively, the paper attributes the gains to the joint preservation of topology, semantics, and appearance. It reports that MorphFlow tends toward linear color interpolation and oversmoothing, DiffMorpher often fails in geometry and color alignment on cross-category pairs, FreeMorph can introduce strong artifacts such as oversaturation or incorrect textures, and NeuroMorph can struggle with coarse or fragmented meshes because its geodesic computation relies purely on mesh adjacency. GaussianMorphing is reported to preserve fine-grained textures such as fur and patterns while producing coherent transitions even for non-isometric deformations (Li et al., 2 Oct 2025).

The ablation results isolate the role of each structural component. Removing mesh guidance and morphing directly on points or Gaussians produces severe structural incoherence, with EI = 34.3 instead of 9.0, MSE(SSIM) = 0.34 instead of 0.11, and user preference 0.02 versus 0.98 for the full model. Removing the color smoothness term increases MSE(SSIM) to 0.22. Removing the geodesic distortion term leads to unrealistic geometric distortions, including distorted legs in the reported examples. A user study with 54 participants found that over 80% preferred GaussianMorphing overall, with especially strong preference on texture consistency and edge continuity (Li et al., 2 Oct 2025).

6. Related formulations and broader usage of the term

Although the name GaussianMorphing is attached most directly to the mesh-guided 3DGS framework above, the broader literature uses closely related ideas for several distinct classes of problems.

One neighboring line of work treats Gaussian-scene morphing as a continuous deformation field over space. "FLOWING: Implicit Neural Flows for Structure-Preserving Morphing" models morphing as a differential flow and applies it directly to Gaussian Splatting scenes by transporting Gaussian centers with a 3D flow, linearly time-weighting opacities, and taking the union of warped source and target Gaussian sets. It does not require explicit Gaussian-to-Gaussian correspondence and instead relies on 3D landmark correspondences such as FLAME landmarks (Bizzi et al., 10 Oct 2025).

A different line introduces explicit mechanics. "PhysMorph-GS: Differentiable Shape Morphing via Joint Optimization of Physics and Rendering Objectives" couples differentiable MPM to dense 3D Gaussians through a deformation-aware upsampling bridge from sparse particle states $\mathbf{sh}_g$0 to Gaussian means and covariances. In that setting, image-space losses on silhouette and depth backpropagate to deformation gradients and particle positions, and the paper describes about a 2.5 percent Chamfer-distance reduction for its depth-supervised variant relative to the physics-only baseline (Song et al., 21 Nov 2025). This is conceptually distinct from GaussianMorphing in the mesh-guided 3DGS sense: the former is simulation-driven, whereas the latter uses ARAP and geodesic regularization without an explicit material model.

Dynamic and controllable Gaussian representations supply additional neighboring formulations. "Animatable 3D Gaussian: Fast and High-Quality Reconstruction of Multiple Human Avatars" binds Gaussians to a skeleton in canonical space and deforms their centers and orientations by linear blend skinning, with hash-encoded fields for displacement, spherical harmonics, and ambient occlusion (Liu et al., 2023). "DragGaussian: Enabling Drag-style Manipulation on 3D Gaussian Representation" performs local drag-based editing of 3D Gaussian objects through multi-view diffusion guidance and subsequent 3D Gaussian optimization (Shen et al., 2024). "InfoGaussian: Structure-Aware Dynamic Gaussians through Lightweight Information Shaping" shapes the tangent space of a motion network so that Gaussians belonging to the same object move in resonance under perturbations, yielding object-level compositional control (Zhang et al., 2024). "3D Gaussian Model for Animation and Texturing" binds Gaussians in texture space to a proxy mesh through implicit shell mapping, enabling animation and texture transfer without animated training data (Wang et al., 2024). "Morpheus: Text-Driven 3D Gaussian Splat Shape and Color Stylization" stylizes RGBD renderings and then re-optimizes a 3DGS model, thereby morphing both geometry and appearance under text control (Wynn et al., 3 Mar 2025).

The phrase can also appear in broader historical or probabilistic senses that are not specific to 3D Gaussian Splatting. "Gaussian Process Morphable Models" models deformation fields as Gaussian processes and can be read as a continuous analogue of PCA-based statistical shape models (Lüthi et al., 2016). "Non-iterative Gaussianization" uses the phrase in the sense of mapping an arbitrary continuous multivariate distribution to a multivariate Gaussian through marginal Gaussianization and re-ranking (Rui et al., 2022). "IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Models" performs image morphing by interpolating in a Gaussian latent space and text embedding space inside a latent diffusion model (Yang et al., 2023). These uses are related at the level of Gaussian priors or Gaussian latent geometry, but they are not the same task as semantic-aware 3D shape and texture morphing from multi-view images.

In that wider context, GaussianMorphing in the narrow, current 3DGS sense is best understood as a hybrid paradigm: 3D Gaussians provide explicit appearance and renderability, meshes provide topology and intrinsic geometry, and semantic morphing is obtained by learning correspondence and deformation on the mesh while keeping the Gaussian layer bound to that evolving surface (Li et al., 2 Oct 2025).