Geometry in Style: 3D Stylization via Surface Normal Deformation

• Prior learning-based methods either make small surface changes or use expressive deformations that can destroy the base object’s identity.Source: §1 · p. 1
• Target normals and dARAP provide expressive mesh deformations that remain restrictive enough to preserve the input shape’s identity.Source: §1 · p. 2
• A text-to-image visual loss guides dARAP deformations toward prompt styles across shapes without dedicated 3D supervision data.Source: §1 · p. 2
• Stylizations span fine details and low-frequency changes, retain structural features, and better match target styles with lower surface distortion than recent deformation techniques.Source: §1 · p. 2, Figure 2 · p. 2

2.1. Classical Deformation Representations

• 2.1. Classical Deformation Representations: Differential deformation methods encode local quantities and recover vertex positions through a global least-squares solve; ARAP regularizes local changes toward rigidity.Source: §2.1 · pp. 2–3
• 2.1. Classical Deformation Representations: Normal-driven stylization has used geometric templates, whereas text prompts allow semantic styles and different treatment of parts sharing the same source normal.Source: §2.1 · p. 3

2.2. Neural Shape Manipulation

• 2.2. Neural Shape Manipulation: Text2Mesh uses style prompts, while Geometry in Style instead rotates surface normals and recovers an identity-preserving deformation with dARAP.Source: §2.2 · pp. 3–4
• 2.2. Neural Shape Manipulation: Neural Jacobian Fields recover vertices from face-local transforms with a differentiable Poisson solve, and dARAP uses a similar solver with ARAP regularization.Source: §2.2 · p. 4
• 2.2. Neural Shape Manipulation: TextDeformer and MeshUp optimize Jacobians and add an identity loss, while Geometry in Style’s deformation is more contained by construction.Source: §2.2 · p. 4

3. Method

• The method optimizes per-vertex target normals, then uses one differentiable local–global dARAP step to produce a mesh styled toward the text prompt.The single step condenses the repeated alternating iterations used by classical ARAP.Source: §3 · p. 4

3.1. Local Rotations from Normals

• Each vertex’s Procrustes rotation fits its edge neighborhood and source normal toward the target normal, retaining local rigidity without a separate identity loss.The edge neighborhood regularizes the rotation alongside the normal match.Source: §3.1 · pp. 4–5

3.2. Global Solve from Local Rotations

• With rotations fixed, dARAP finds vertex positions through linear least squares, yielding a cotangent-Laplacian Poisson equation that can be solved differentiably and efficiently.The equation uses the cotangent Laplacian.Source: §3.2 · p. 5

3.3. Optimization Using a Semantic Visual Loss

• A differentiable rasterizer renders multiple views, which Cascaded Score Distillation using DeepFloyd IF stages 1 and 2 uses as semantic visual guidance.The visual loss is guided by a pretrained text-to-image diffusion model.Source: §3.3 · p. 5

4.1. Properties of Geometry in Style

• Open-vocabulary prompts produce detailed, part-aware styles across varied shapes, including local geometric details, silhouette changes, and shared LEGO-like stylization across different inputs.Examples include style-specific vase and chair geometry, and LEGO stylization across chairs, animals, and vases.Source: §4.1 · p. 6, Figure 6 · p. 6
• Stylization can be confined to a selected region by fixing rotations outside it, with detailed local changes and no observed boundary artifacts.The reported inset localizes deformation to the head while retaining detail appropriate for the rest of the body.Source: §4.1 · p. 6
• The method retains identity cues including animal poses, facial features, body proportions, and chair parts while applying the requested style.Figure 7 illustrates preserved pose characteristics such as limb positioning and head angle.Source: §4.1 · p. 6, Figure 7 · p. 7
• The authors attribute pronounced yet identity-preserving stylizations to target normals and dARAP’s local rotation fitting, which favors local rigid changes over scaling or shearing.The formulation is described as avoiding the need for an extra identity-regularization loss on local transforms.Source: §4.1 · p. 6
• After optimization, changing λ when reapplying saved normals adjusts stylization strength; larger λ sharpens geometry, while lower λ keeps normals closer to the original.An inference λ larger than the optimization value can produce more salient yet still sensible stylization.Source: §4.1 · p. 7, Figure 8 · p. 7

4.2. Evaluation

• Compared with TextDeformer and MeshUp, the method achieves the target style with fewer artifacts and better preservation of source features and proportions.TextDeformer distorts surfaces and poses; MeshUp can produce weaker textures, proportion changes, a crushed head, or duplicate features.Source: §4.2 · p. 7

4.3. Limitations

• The cotangent Laplacian works only on manifold meshes and is sensitive to triangle aspect ratios, and deformed meshes can self-intersect; remeshing and λ adjustment offer mitigations.The authors remesh inputs for cotangent-Laplacian behavior, and report that adjusting λ can somewhat mitigate self-intersections.Source: §4.3 · pp. 7–8

4.2. Evaluation

• The method’s triangle-area ratio is closer to 1 with lower standard deviation than MeshUp and TextDeformer, and it achieves better CLIP similarity to the prompt.Table 1 summarizes the triangle-area comparison; CLIP similarity is evaluated on the same shapes in supplementary material.Source: §4.2 · p. 7, Table 1 · p. 8

• Target-normal deformations recover detailed stylizations while adhering to the input geometry, and the paper reports clean style matching with lower surface distortion than recent deformation techniques.The comparison is qualitative in the supplied passages.Source: §5 · p. 8, Figure 9 · p. 8
• The method preserves semantic correspondence between source and deformed vertices, visualized using the source shape’s wave kernel signature.Source: Figure 10 · p. 8
• dARAP is a differentiable layer for target-normal mesh deformation, and good results in the neural pipeline require only one step rather than iterating ARAP to convergence.The authors suggest iterative target-normal updates may avoid repeated local and global ARAP steps within a forward pass.Source: §5 · p. 8
• dARAP may also serve geometry tasks beyond stylization, including parameterization, re-posing, collisions, and editing.Source: §5 · p. 8
• The method preserves topology, while adding explicit parts or changing topology is left for future work.Source: §5 · p. 8
• The method may produce self-intersections; decreasing λ after optimization can alleviate them with only a mild reduction in stylistic surface detail.The figure also contrasts MeshUp’s warped lamp structure and weaker pineapple texture.Source: Figure 11 · p. 8

A. Additional Qualitative Results

• In additional comparisons, Geometry in Style matches the racer-bunny, pagoda, and cybernetic-glove prompts while retaining source identity and proportions.TextDeformer produces artifacts on the pagoda, while MeshUp changes the pagoda’s source shape beyond recognition.Source: A. Additional Qualitative Results · p. 13
• A person mesh retains its slender proportions across three style prompts, and additional tests pair select SMAL quadruped meshes with diverse prompts.Source: A. Additional Qualitative Results · p. 13

B. CLIP Similarity to Prompt

• The method achieves better CLIP similarity to the style prompt than TextDeformer and MeshUp on the evaluated 20-shape set.Evaluation used 16 views per mesh.Source: Table 2 · p. 13, B. CLIP Similarity to Prompt · p. 13

C. Ablations

• The comparison with MeshUp and TextDeformer shows cases where baselines miss the target style or lose source identity, while Geometry in Style preserves identity while matching style.Source: Figure 12 · p. 13
• The same mesh can be deformed toward different text-specified styles.Source: Figure 13 · p. 14
• The Procrustes solve preserves source identity across λ settings, whereas directly predicting rotations can severely alter the shape.The rotation ablation identifies direct rotation prediction without identity regularization as insufficiently restrictive.Source: C. Ablations · pp. 13–14, Figure 14 · p. 14
• For λ = 8 and λ = 10, the dog remains recognizable; λ = 8 better preserves the front-leg pose, while λ = 10 produces stronger sphinx-like feet.The main results use λ = 8 as a balance of identity preservation and stylization strength, though it can be tuned per mesh.Source: C. Ablations · p. 14

D.1. Method

• The section introduces SDS as a way to optimize deformation parameters, including target normals, against a pretrained 2D diffusion model.The method overview frames Cascaded Score Distillation as the guidance extension used in the paper.Source: §D.1 · p. 14
• Score Distillation Sampling optimizes target normals using the L2 difference between noise added to a rendered image and noise predicted by a denoising U-Net.The image and text condition the diffusion model, and the target-normal gradients can omit U-Net gradients for efficient computation.Source: §D.1 · p. 14
• Cascaded Score Distillation adds guidance from super-resolution models to the base diffusion model, supporting finer stylistic details.The described stages use upsampled and previous-stage images as inputs to a high-resolution module.Source: §D.1 · p. 14
• The target-normal gradients are backpropagated through the differentiable pipeline, and the final guidance combines SDS and CSD gradients with user-defined weights.Source: §D.1 · pp. 14–15

D.2. Configuration Details

• CSD uses one upscaling stage of DeepFloyd IF, with the second-stage weight ramped to 0.3 and the SDS weight fixed at 1.0.The second-stage weight ramps from 0 to 0.2 over 1000 epochs, then from 0.2 to 0.3 over 750 epochs.Source: §D.2 · p. 15
• The view batches contain eight randomly sampled views, and classifier-free guidance is set to 100.The guidance weight follows MeshUp [41].Source: §D.2 · p. 15
• Each batch of rendered views supplies the CSD loss; the method backpropagates and updates the deformation twice before recomputing and rerendering the shape.The passage reports that this update scheme empirically leads to sharper deformations.Source: §D.2 · p. 15
• Views cover a 0°–360° azimuth range and a 0°–60° elevation range, with 30° elevation for tall, slim shapes and a fixed 60° field of view.Camera distance is 2.5–3.0 for most shapes and 1.4–2.6 for tall, slim shapes.Source: §D.2 · p. 15

E. Additional Quantitative Evaluation Details

• For comparison, source meshes are normalized to a side-2 cube centered at the origin, and deformed meshes are rescaled to match the source bounding-box diagonal.This matches the normalization scheme used before and after deformation in MeshUp and this method.Source: E. Additional Quantitative Evaluation… · p. 15
• After normalization, face-area ratios reflect both localized face distortion and global rescaling caused by changes in bounding-box extent.A deformation that enlarges the bounding box can yield ratios below 1 after rescaling, even without substantial localized distortion; the converse can also occur.Source: E. Additional Quantitative Evaluation… · p. 15
• In contrast to TextDeformer [26] and MeshUp [41], our method’s face-area-ratio distribution is cleanly located around 1, indicating better triangle-area and bounding-box preservation compared with those methods.Source: E. Additional Quantitative Evaluation… · p. 16

F. Running Time

• With dARAP’s local step included, its local-global runtime is comparable to an NJF Poisson solve.The prose also describes the two methods as comparable overall in runtime.Source: F. Running Time · p. 16, Table 3 · p. 16
• Runtime measurements average 10 runs on a GTX 1660Ti GPU using a mesh with 20,708 faces and 10,356 vertices, excluding both methods’ precomputations.Source: F. Running Time · p. 16
• 0.0507s versus 0.0755s average: dARAP’s vertex-based global solve is faster than NJF’s face-Jacobian-based solve.The comparison excludes precomputations; the table describes the methods’ combined runtimes as on par.Source: Table 3 · p. 16, F. Running Time · p. 16