Interaction Mesh-Based Retargeting

• Interaction mesh-based retargeting is a computational framework that employs geometric meshes and structured graphs to transfer spatial and spatio-temporal features between domains with differing morphologies.
• It utilizes methods such as Laplacian deformation energy, edge-vertex consistency, and hierarchical optimization to minimize distortions and maintain high-fidelity interactions.
• Applications span robotics, animation, and dexterous manipulation, where contact-aware retargeting supports real-time performance and precise semantic mapping.

Interaction Mesh-Based Retargeting

Interaction mesh-based retargeting encompasses a family of computational frameworks that leverage mesh, graph, or geometric interaction structures to transfer spatial or spatio-temporal information between domains of disparate morphology, topology, scale, or embodiment. Such techniques explicitly model relationships—distances, contacts, deformations, or high-level semantics—between distinguished mesh components or landmarks, thereby robustly preserving interaction fidelity under retargeting. Recent research establishes interaction mesh paradigms as critical foundations for high-fidelity retargeting in character animation, robotics, anthropomorphic hand-object manipulation, and contact-aware visual content transformation.

1. Theoretical Foundations and Types of Interaction Meshes

Interaction meshes generalize the notion of a mesh from dense spatial discretizations (as in geometry processing) to structured, often sparse, graphs capturing crucial pairwise or local geometric relationships. Canonical instantiations include:

• Landmark Interaction Mesh/Graph: Landmarks placed on key anatomical, object, or environmental features are connected via Delaunay tetrahedralization or heuristic edges; edge weights can be proximity- or semantics-driven, facilitating the encoding of both intra-agent and inter-agent (or agent-object) constraints (Zhang et al., 2023, Yang et al., 30 Sep 2025).
• Dense Meshes with Semantic Sensors: Semantically consistent sensors (SCS) probe and anchor corresponding features across diverse mesh topologies, forming a basis for dense or sparsified pairwise relation graphs as in the Dense Mesh Interaction (DMI) field (Ye et al., 2024).
• Key-Vertex and Atlas-Based Meshes: Editors pre-define mesh points (“key vertices” or atlas landmarks) capturing parts critical for semantic or contact preservation, with correspondences mapped across mesh domains by optimal transport, geodesic, or atlas parameterizations (Cheynel et al., 28 Feb 2025, Lakshmipathy et al., 2024).

This geometric graph structure is the substrate on which energy functions, loss terms, or reward signals are defined and minimized/maximized to drive retargeting.

2. Core Mathematical Formulations

Interaction mesh-based retargeting standardizes the encoding of semantic and physical relationships by employing mesh-based constraint energies or fields. The primary classes are:

• Laplacian Deformation Energy: Minimizes the distortion in mesh Laplacian coordinates between source and target, measured as $E_L = \sum_{i}\|L(p_i^{src})-L(p_i^{tgt}(q))\|^2$, providing invariance to global affine deformations and robustness under nonisometric mappings (Yang et al., 30 Sep 2025).
• Edge- and Vertex-Wise Consistency: Enforces the preservation or meaningful adaptation of pairwise distances/orientations. In DMI-based frameworks, pairwise vectors $\mathbf{d}^{t,i,j}$ between SCS probes are aligned via cosine similarity or distance losses, upweighted for physically interacting regions (Ye et al., 2024).
• Contact Semantics and Penetration Metrics: Employs explicit measurement and penalties for intersection volumes, signed penetration, and sliding, encoding contact formation, persistence, and semantics (Cheynel et al., 28 Feb 2025).
• Hierarchical and Multi-resolution Mesh Losses: Combines retargeting losses, rigid-edge consistency, and skinning similarity in a coarse-to-fine mesh refinement framework to preserve both global and local motion (Wang et al., 2023).

Tabulated Example (formulations):

Energy/Loss Type	Mathematical Form	Mesh Structure
Laplacian deformation (Yang et al., 30 Sep 2025)	$E_L = \sum_{i}\|L(p_i^{src})-L(p_i^{tgt}(q))\|^2$	Volumetric interaction mesh
DMI field alignment (Ye et al., 2024)	$\mathcal{L}_{dmi} = ...$ (cosine loss over DMI field)	SCS-based dense interaction graph
Non-isometric matching (Lakshmipathy et al., 2024)	$$E_{total} = E_{data} + E_{contact} + E_{smooth} + E_{reg}$$	Correspondence/atlas-based mesh

Significance: These choices enable statistical or optimal transport of locally- or globally-anchored spatial interactions during morphologically challenging retargeting.

3. Algorithmic Frameworks and Optimization Pipelines

Contemporary pipelines employing interaction mesh-based retargeting share several structural elements but differ in problem domain and optimization motifs:

• Contact-Aware Hand/Object Retargeting: Atlas-driven non-isometric shape matching (log-exp maps on geodesic landmarks) paired with per-frame inverse kinematics optimizes joint parameters to preserve contact and marker alignment (Lakshmipathy et al., 2024).
• Humanoid/Robot Imitation and Augmentation: Delaunay-based volumetric meshes combine Laplacian preservation with per-frame SQP-style constrained optimization over robot configuration, including kinematic, contact, and non-penetration constraints, often augmented for data diversity (Yang et al., 30 Sep 2025).
• Animation and Motion Transfer: Key-vertex embeddings drive the construction of low-dimensional motion descriptors (distance, direction, penetration, height, sliding), with optimization targeting their per-pair or per-vertex matching, extended adaptively via proximity-driven weighting for contact-rich retargeting (Cheynel et al., 28 Feb 2025).
• Dense Geometric Interaction: Networks such as MeshRet hybridize dense SCS interaction fields with transformer architectures and multi-level PointNet aggregation, supervised by DMI alignment, end-effector orientation, and adversarial losses to guarantee semantic and contact preservation (Ye et al., 2024).
• Skeleton-Free Coarse-to-Fine Refinement: Hierarchical mesh coarsening (QEM) supports incremental, part-level deformation via layered retargeting modules, each integrating pose encoding, skinning prediction, and residual correction (Wang et al., 2023).

These optimization architectures are chosen according to application requirements (feasibility/on-device, real-time constraints, user interaction).

4. Applications and Domains

Interaction mesh-based retargeting has demonstrated state-of-the-art performance across a diverse set of domains:

• Robotics and Loco-manipulation: Human motions are retargeted to robots with substantially different embodiments, enabling physically plausible trajectory generation, successful RL policy training, and real-zero-shot sim-to-real transfer (Yang et al., 30 Sep 2025).
• Contact-Rich Dexterous Manipulation: In hand-object retargeting, the mesh-based frameworks support dense contact transfer across heteromorphic hands, supporting object substitution, cross-morphology manipulation, and low intersection/contact errors (Lakshmipathy et al., 2024).
• Multi-character and Multi-object Animation: Motion retargeting among multiple agents (human-human, human-object) leverages interaction-graph rewards within deep RL, yielding controllers that preserve complex, spatially extended interaction patterns without manual reannotation (Zhang et al., 2023).
• Real-time, Contact-aware Character Animation: Compact key-vertex descriptors and proximity-based adaptive weighting enable fast optimization cycles with semantic and physical contact preservation in challenging, highly non-isometric retargeting (Cheynel et al., 28 Feb 2025).
• Dense Geometric Contact for Skinned Models: Dense interaction perception using SCS allows for direct, topology-invariant preservation of both contact and non-contact interactions across highly diverse mesh domains (Ye et al., 2024).

The impact spans offline data generation for policy learning, interactive animation tools, and real-time deployment in graphics engines and robotic platforms.

5. Comparative Evaluation and Performance Metrics

Evaluation of interaction mesh-based retargeting frameworks systematically quantifies aspects such as contact preservation, penetration avoidance, semantic fidelity, and physical plausibility:

• Penetration and Intersection Volumes: Percentage of mesh or hand volume involved in object, self, or environment intersection; top-performing methods consistently reduce these to below 2% for object, 1% for self, and 0.5% for table intersections (Lakshmipathy et al., 2024).
• Contact Preservation Scores: Fraction of contact duration or contact-point consistency achieved relative to reference motions, often exceeding previous methods by substantial margins in user/metric studies (Yang et al., 30 Sep 2025, Cheynel et al., 28 Feb 2025).
• Edge/Vertex Distance Error: RMSE or per-frame error in pairwise distance over interaction mesh edges, reflecting physical and semantic alignment (Zhang et al., 2023, Ye et al., 2024).
• Retargeting Smoothness and Jerk: Third-difference (jerk) metrics, with mesh-driven optimizations reducing jerk by an order of magnitude relative to baseline kinematic copy methods (Cheynel et al., 28 Feb 2025).
• User Study Preferences: Categorical preference ratings establish the superiority of frameworks that embed explicit interaction criteria (Ye et al., 2024, Cheynel et al., 28 Feb 2025).

A plausible implication is that framework choice can be guided empirically by the specific contact and smoothness requirements of the application.

6. Extensions, Limitations, and Research Outlook

Several extensions solidify the versatility of the interaction mesh paradigm:

• Multi-character and Non-flat Terrain Generalization: Embeddings can stack key-vertices per character and adapt descriptor construction for interacting agents, with ground-facing descriptors modulated for arbitrary height fields (Cheynel et al., 28 Feb 2025).
• Conflict Diagnosis and Interactive Reweighting: Optimization conflict among geometric or semantic constraints can be detected via cosine similarity of loss gradients; manual slider-based resolution is enabled (Cheynel et al., 28 Feb 2025).
• Augmentation and Robustness: Automatic data augmentation via mesh perturbation in pose, shape, or environment, as well as encoder designs invariant to mesh topology, supports transfer and deployment at scale (Yang et al., 30 Sep 2025, Ye et al., 2024).
• Computational Scalability: Dense correspondence and Laplacian/atlas computations remain the primary computational bottleneck; ongoing research is expected to focus on analytical Jacobians and GPU acceleration for real-time, large-batch retargeting (Lakshmipathy et al., 2024).

Notable limitations are evident in scenarios with extreme mesh divergence, highly cluttered interactions exceeding mesh capacity, or lack of semantic anchors in uniform regions. Nonetheless, interaction mesh-based retargeting represents a unifying abstraction, underlying a broad spectrum of contemporary approaches to high-fidelity, semantics-preserving motion and content transfer (Yang et al., 30 Sep 2025, Ye et al., 2024, Cheynel et al., 28 Feb 2025, Wang et al., 2023, Lakshmipathy et al., 2024, Zhang et al., 2023).