Full Deformable Mesh State

Category-level object pose estimation seeks to recover a similarity transform $(R,t,s)$ for unseen instances without instance-specific CAD models. Most competitive methods are correspondence-based: prior-free variants regress canonical (NOCS) coordinates directly from local observations and implicitly memorize the canonical frame in the weights, which ties the parameters to category-typical orientations and hurts generalization under distribution shift; prior-based variants introduce a category prior but typically follow a serial deform-then-align pipeline, where underconstrained canonical completion can corrupt correspondences and induce error cascades in pose. We propose PriorPose, a reference-guided correspondence framework that keeps the category prior explicit and solves canonicalization and alignment jointly in a shared feature space. A reference-guided seeded transformer embeds the partial observation and the category prior as token sets and fuses them via geometry-aware seeds, from which the network jointly predicts a per-point NOCS field for visible points and a canonical deformation of the prior that reconstructs a full canonical instance, while a deep pose head regresses $(R,t,s)$ from the induced correspondences. A two-part shape consistency objective, with canonical-space and camera-space consistency losses, couples correspondence, deformation, and pose, reducing reliance on memorized canonical orientations and avoiding deform-then-align error cascades. Experiments on standard and larger-category benchmarks demonstrate that PriorPose sets new state-of-the-art results on most evaluated metrics, especially under strict pose thresholds, while remaining competitive on relaxed pose and IoU metrics and showing improved robustness under shape variation and domain shift.

Many scientific graphs attach several variables to each node, so a single scalar edge weight cannot describe direction-dependent interactions. We model each edge by a symmetric positive-definite (SPD) matrix and infer a posterior over matrix-valued graph geometries, which we call the Bayesian matrix-valued graph (BMVG). We ask how these interactions reconfigure across contexts: how large the change is and which multivariate directions strengthen or weaken. The geodesic distance induced by the affine-invariant Riemannian metric (AIRM) quantifies deformation magnitude and generalized eigenvalues resolve its signed directions.Against fused graphical lasso, Bayesian multiple-GGM, and common principal components, BMVG is competitive on global precision recovery while retaining identifiable matrix-valued edge structure and accurately recovering edge-level deformation directions. In controlled known-truth experiments, it resolves structural change with increasing sample size, including orientation changes that leave ordinary eigenvalues unchanged. In one year of Bay Area weather data, the geometry of 12-hour change reconfigures spatial coupling about as much as whole seasons differ. In TCGA-BRCA, estrogen-receptor (ER)-associated reconfiguration concentrates on specific gene-module pairs and persists under graph-scaffold sparsification and removal of subgroup mean differences. These results establish posterior matrix-valued edge geometry as a unified framework for quantifying and interpreting context-dependent multivariate reconfiguration.

Recent extensions of 3D Gaussian Splatting (3DGS) enable real-time novel view synthesis in dynamic scenes by learning time-conditioned Gaussian deformations. However, existing MLP-based methods typically estimate deformations independently at each timestamp, making them less robust to large or abrupt motions. To address this issue, we propose \textbf{EvoGS}, a 3DGS-based dynamic reconstruction framework that models Gaussian deformation as a temporal evolution process. EvoGS maintains persistent deformation states for each Gaussian, extrapolates future states from historical deformation states, and corrects the predictions with MLP-derived observations. The correction is adaptively weighted using a temporal residual memory and evolution statistics such as deformation velocity and trajectory deviation. To further improve reconstruction quality, EvoGS introduces deformation-aware densification. Clone and split operations are performed along corrected deformation directions, while an uncertainty-aware strategy suppresses densification for Gaussians with unstable deformation histories. Experiments show that EvoGS improves dynamic novel view synthesis quality and achieves competitive performance across benchmarks.

Monocular UAV videos provide valuable observations for dynamic reconstruction of complex urban scenes. However, such scenes exhibit pronounced spatiotemporal heterogeneity: different regions follow distinct temporal activity patterns, while the motion states of some dynamic regions may further evolve over time. Although dynamic Gaussian methods based on decomposed shared spatiotemporal feature fields have achieved efficient and accurate reconstruction in object-centric or relatively compact scenes, their commonly adopted fixed plane-wise feature combination mechanisms are less suited to the heterogeneous local dynamics of UAV scenes, often leading to ghosting artifacts and blurred dynamic details. To address this challenge, we propose AdaAnchor4D, an adaptive anchor deformation framework for monocular UAV dynamic scene reconstruction. At its core, Anchor-Conditioned Feature Aggregation (ACFA) adaptively aggregates shared spatiotemporal features using anchor-specific aggregation embeddings and temporal information, allowing different local units to obtain dynamic representations tailored to their local and temporal states. Decoupled Local Geometry Deformation (DLGD) separates anchor-state deformation from local Gaussian geometry deformation, while Density-Adaptive Coordinate Warping (DACW) reparameterizes feature-query coordinates according to the axis-wise anchor distributions, alleviating the mismatch between non-uniform geometric sampling and uniform grid parameterization. Experiments on UAV-Arc4D, VisDrone, and UAVDT show that AdaAnchor4D achieves higher rendering quality than representative dynamic Gaussian methods while maintaining real-time rendering performance. The code will be made publicly available.

Dynamic scene reconstruction with 3D Gaussian Splatting requires a balance between fine-grained motion modeling, structural stability, and compact representation. Existing per-primitive methods provide flexible local deformation but often suffer from redundant primitive growth, while anchor-based methods improve spatial regularity at the cost of suppressing locally varying motion. To address these issues, we present GrainGS, a dynamic Gaussian framework that combines a hierarchical anchor scaffold with per-Gaussian deformation. A static warm-up stage first establishes a time-invariant canonical representation from observations across all timestamps. During joint training, a stop-gradient operation blocks the deformation-mediated gradient pathway to the canonical positions while preserving their direct refinement through the reconstruction objective. Each Gaussian then predicts independent temporal offsets for position, rotation, and scale, enabling detailed local motion within a structurally constrained scaffold. A canonical-residual appearance decomposition further models frame-dependent photometric changes without forcing them into geometric deformation. Experiments on synthetic monocular and real-world multiview benchmarks show that GrainGS achieves high reconstruction quality, real-time novel view synthesis, and compact storage. Under the synthetic benchmark setting, it reaches an average peak signal-to-noise ratio of 36.98 decibels, renders at 435.6 frames per second, and requires 4.67 megabytes of storage.

While Implicit Neural Representations (INRs) and dynamic 3D Gaussian Splatting (3DGS) achieve impressive results in video processing, they often fall short of producing representations that are easily editable. Recent methods address this by introducing complex spatial deformations or folded distributions, which constrain optimization and reduce flexibility for downstream editing. In this paper, we introduce TOM-GS, an editable video representation that forgoes complex deformations in favor of regular 3D Gaussians equipped with a continuous temporal opacity formulation. By assigning a learnable temporal mean and scale to the opacity of each Gaussian, our model enables static 3D spatial components to fade smoothly in and out of the scene. Grounded by robust, off-the-shelf pose estimation, our approach maintains a static spatial geometry that naturally supports a wide range of manual and physics-based edits. TOM-GS outperforms prior editable video representations in visual fidelity, while its reliance on standard 3D Gaussians ensures seamless compatibility with established 3D editing tools.

Surgical tissue retraction requires effective manipulation planning under partial and noisy perception. We study state estimation for deformable tissue retraction, where only sparse observations of the tissue surface are available at decision time. We propose a learned state estimator that reconstructs the full deformable mesh state from 40 noisy vertex observations. The estimator combines a multilayer perceptron with a low-dimensional PCA latent representation and is trained using geometry-aware regularization that encourages smooth and physically plausible deformations. We evaluate the approach in a 2D deformable sheet simulation using single-step and multi-step retraction planning. Results show that the learned estimator achieves 98.1% of oracle performance in multi-step retraction while supporting efficient inference. These results demonstrate that learned, geometry-regularized state estimation can support effective deformable manipulation under realistic perception constraints.

Mesh deformation, the process of altering the vertex positions of a 3D mesh while preserving its topological structure, is a cornerstone of computer graphics. Despite the recent emergence of numerous text-guided 3D mesh deformation methods, deforming an initial mesh into one that both adheres to text prompts and preserves its pose remains challenging. This paper proposes PoseAlign, which decomposes text-guided mesh deformation into two stages: global pose scaling and local detail sculpting. Specifically, in the first stage, we introduce the Laplacian as a differentiable mesh representation to enable more efficient yet smoother global deformation. Then, we propose a novel pose-aligned SDS loss by adapting score distillation sampling (SDS) with an attention-sharing mechanism, which sculptures fine-grained geometric details for the deformed mesh while preserving its original pose. PoseAlign significantly enhances the controllability of the overall deformation process, achieving a favorable balance between pose preservation and text alignment. Experiments demonstrate the competitive advantages of our method in text alignment and mesh quality. Code is available at: https://cousingrade6.github.io/PoseAlign

Gaussian splatting is the current state-of-the-art for dense, deformable 3D anatomy reconstruction in robot-assisted minimally invasive surgery (RAMIS); however, most pipelines are offline and depend on accurate camera trajectory priors (often from robotic kinematics), limiting applicability when priors are missing or noisy. To address these limitations, we propose Track2Map, an online 3D Gaussian Splatting pipeline that jointly optimizes camera trajectory and 3D deformable scene representation directly from surgical video. Track2Map is therefore capable of robust 3D reconstructions when camera trajectory priors are either absent or noisy, and due to its online nature it effectively works as a Simultaneous Localisation and Mapping (SLAM) method. To stabilize optimization in the presence of tissue motion and ambiguous visual cues, we introduce a track-anchored deformation initialization using dense 2D point tracks. Track statistics are further utilized to disentangle camera motion from scene deformation by detecting static camera periods and reducing drift during incremental mapping. Experiments on StereoMIS show improved reconstruction quality and camera trajectory against competing SLAM methods, as well as compared to non-SLAM methods that utilize camera trajectory priors. The code is available at https://track2map.github.io/.

Dynamic scene reconstruction remains challenging due to the heterogeneous and spatially varying nature of real-world motion. Although recent 3D Gaussian Splatting methods have introduced diverse deformation formulations for dynamic novel view synthesis, each method typically relies on a single deformation model within its representation, which limits robustness across diverse dynamic scenarios. In this work, we study a fundamental problem-multi-deformation modeling for dynamic 3D Gaussian representations-under two distinct integration constraints that differ in when and how multiple deformation experts interact during training. From a Mixture-of-Experts (MoE) perspective, we view multi-deformation modeling as the problem of combining multiple specialized deformation models within a unified 3D representation. We first introduce Mixture of Deformation Experts (MoDE), which integrates multiple deformation experts directly into the deformable Gaussian Splatting pipeline through joint optimization. In MoDE, experts operate on a shared canonical Gaussian representation, enabling multi-deformation modeling without introducing additional training stages or modifying the original optimization schedule. In contrast, we further present Mixture of Experts for Dynamic Gaussian Splatting (MoE-GS) under a different integration constraint, where deformation experts are optimized independently and combined through a separate routing stage. As a result, expert interaction occurs over non-canonical Gaussian representations after individual optimization. Together, these two approaches provide alternative strategies for multi-deformation modeling, clarifying how integration constraints shape the design and behavior of deformation experts in dynamic 3D Gaussian representations. Our code is available at: https://github.com/cvsp-lab/MoE-GS-studio.

Generating realistic human avatars in complex motions--such as clothing dynamics--requires modeling of global and local deformations which remains challenging in monocular settings. We address this problem by leveraging neural Jacobian fields (NJFs) for representing semi-rigid deformations. We train self-supervised neural networks for predicting Jacobian matrices that give the pose-dependent deformations, by solving a Poisson equation. However, monocular input presents several difficulties such as self-occluded regions and invisible surfaces. To address these issues, we introduce three key components: a constrained Poisson solver, signed distance-based Jacobian regularization, and a deformation-guided residual flow loss, which together suppress boundary artifacts, recover frequently occluded regions such as armpits and thighs, and enforce temporal consistency during motion. Experiments on benchmark and in-the-wild videos demonstrate that our method generates temporally stable and geometrically coherent avatars, outperforming state-of-the-art approaches.

Aiming at the problem that obstacle avoidance flexibility and formation integrity are difficult to coexist in multi-UAV formation motion in complex obstacle environments , and that the traditional artificial potential field (APF) method easily falls into local optima, a cooperative obstacle avoidance algorithm for multi-UAV formations integrating BI-APF-RRT and affine transformation is proposed. First, abandoning the traditional APF centroid path planning method , a goal-biased Bidirectional Artificial Potential Field method RRT (BI-APF-RRT) algorithm is adopted to conduct global collision-free path planning for the centroid of the leader formation. By introducing an improved artificial potential field and cubic B-spline interpolation, the smoothness and rapid convergence of the global path are ensured. Secondly, using the generated global path as the guiding trajectory for the formation's centroid , combined with an affine transformation matrix (including non-uniform scaling and rotation) , the formation can adaptively deform based on the distance to obstacles while moving along the optimal path. Finally, the followers track the leaders through a distributed control law , enabling the entire formation to safely cross complex obstacle areas without disassembling.

Modeling dynamic facial expressions using 3D Gaussian representations remains challenging due to their unstructured nature. Conventional Gaussian avatar pipelines require extensive multiview and sequential expression data, limiting scalability and accessibility. In this work, we introduce Self-Adaptive Gaussian Expression (SAGE), a framework for self-learning expression-induced Gaussian deformations that enables high-fidelity, animatable avatars from minimal input data. Our method jointly optimizes 2D Gaussian surfels and a Signed Distance Field (SDF) to enforce compact, surface-aligned Gaussian distributions, while a self-supervised expression learning phase replaces long training sequences with geometric and appearance consistency constraints. This design allows flexible deployment across multiple reconstruction regimes: in the multiview setting, only a single frame (timestep) is required instead of thousands; in the monocular setting, only head rotations are needed without expression sequences; and in the one-shot setting, no pretraining or priors are necessary. Experiments demonstrate that our approach achieves reconstruction and animation quality comparable to state-of-the-art methods, while reducing data requirements by several orders of magnitude. Our results highlight the potential of self-supervised Gaussian deformation learning as a step toward accessible, data-efficient avatar creation.

Understanding dynamic 3D environments is essential for safe autonomous driving, particularly when reasoning about human-centric, nonrigid agents. However, existing weakly supervised occupancy prediction frameworks predominantly assume rigid-body motion and rely on simple frame-to-frame offsets, limiting their ability to capture fine-grained deformations and maintain temporal coherence. To address this issue, we propose DeGO, a deformable Gaussian occupancy framework that unifies decoupled Gaussian deformation with factorized 4D foundation-model distillation. DeGO disentangles rigid and nonrigid motion, enabling each Gaussian primitive to evolve through both deformation and offset-based updates. In parallel, a factorized 4D distillation strategy transfers cross-camera and cross-frame knowledge from the VGGT foundation model, producing foundation-aligned features that enhance temporal consistency. Experiments on the Occ3D-NuScenes benchmark demonstrate that our method achieves state-of-the-art performance under weak supervision, delivering 13.5% gains on human-centric instances and 10.9% overall improvements. These results highlight the effectiveness of deformation-aware and foundation-guided occupancy modeling for dynamic scene understanding. The code is publicly available: https://github.com/vita-epfl/DeGO

Learning deformable 3D object models from single-view in-the-wild images has enabled impressive 3D shape reconstruction without supervision. However, it remains unclear whether these models capture the semantic structure required for downstream tasks. We find that existing deformable reconstruction approaches, despite producing visually plausible geometry, yield unstable correspondences across instances and perform poorly on semantic correspondence benchmarks. We introduce SEMAGIC, a framework for learning semantically consistent deformable 3D representations from single-view in-the-wild images. Rather than treating reconstruction as the end goal, SEMAGIC uses deformable modeling as a mechanism to discover category-level correspondences. Each category is represented by a canonical template mesh and a learned deformation field, functioning similarly to an autoencoder that reconstructs instance geometry from image features, enabling vertices to maintain consistent semantic meaning across instances. Semantic consistency is enforced during training through (i) a feature-level consistency loss aligning semantic features between canonical and deformed meshes, and (ii) vertex-index-conditioned deformation that preserves semantic correspondence across instances. By explicitly coupling geometric deformation with semantic alignment, SEMAGIC produces representations that maintain stable part correspondences across intra-category variation. Experiments demonstrate that SEMAGIC improves semantic correspondence of deformable models by +14.7 PCK@0.1 on SPair-71k, establishing deformable models as effective semantic 3D representations.

Existing Gaussian avatar methods typically parameterize geometry on a body-template surface, which entangles the avatar's representation space with the template's deformation space and limits the capture of layered, off-body, and non-rigid clothing geometry. We present PiG-Avatar, which addresses this limitation by using the parametric body model solely for kinematic transport, while representing the avatar as Gaussians anchored in a volumetric canonical space governed by a continuous neural field. This decouples representation from template topology, avoiding the geometric constraints of surface-based parameterizations. Kinematic coherence is maintained through 3D barycentric anchor transport, which guides motion without constraining geometry and allows anchors to deviate freely from the template surface, yielding dense, stable temporal surface correspondences by construction. To make this unconstrained formulation tractable, we introduce dual-level spatially coherent optimization, combining Sobolev-preconditioned neural-field updates with a novel KNN-based preconditioning of canonical anchor geometry. Together, these mechanisms induce an emergent self-organization of anchor density: anchors migrate toward regions of high curvature, appearance variation, and non-coherent motion without explicit heuristics. As a result, complex clothing geometry and layered surfaces emerge as natural, high-fidelity outputs. This single representation further supports hierarchical reconstruction across multiple levels of detail, with coarse-level supervision propagating to finer levels through the shared field and coupled anchor graph. On established benchmarks featuring subjects with complex clothing and challenging non-rigid motion, PiG-Avatar achieves state-of-the-art rendering quality, generalizes robustly to imperfect body model initialization, and renders in real time across all detail levels.

We present FrameTwin, a curve-anchored Gaussian alignment framework that uses sparse-view images to close the control loop for adaptive wireframe 3D printing. Our key idea is to capture the deformation of thin wireframe structures from sparse-view images using Gaussian kernels anchored to parametric curves, yielding a compact and geometry-aware encoding that explicitly captures strut topology. Driven by a differentiable rendering pipeline, FrameTwin estimates a neural deformation field that aligns the partially printed target model with the deformed structure observed during fabrication, where the optimized curve-Gaussian representation serves as a digital twin of the evolving wireframe. Unlike general Gaussian-splatting approaches, our formulation constrains kernel placement along parametric curves, substantially reducing the ambiguity inherent in sparse-view observations of thin structures. The resultant deformation-field alignment enforces global consistency across all struts. By using the estimated deformation field to blend the distorted printed geometry with the remaining unprinted geometry, FrameTwin enables adaptive updates to future printing trajectories. We demonstrate that FrameTwin can robustly capture and compensate for deformation in wireframe models fabricated using a robotized 3D printing system.

Reconstructing dynamic 3D scenes from blurry monocular videos is challenging as motion-induced blur entangles object motion and geometry, hindering geometric consistency. We present Kinematics-GS, a kinematics-aware framework that models blur as motion-aligned deformation and introduces a kinematic prior to reparameterize Gaussian shapes along motion trajectories, thereby mitigating degenerate shape collapse without auxiliary motion supervision. To stabilize optimization, we decompose scenes into dynamic and static components using temporal deformation variance and employ a coarse-to-fine deformation strategy to capture both global motion and fine-grained details. We also introduce a challenging real-world dataset of deformable and elastic objects exhibiting non-rigid motion with spatially non-uniform motion blur that obscures geometric cues. Extensive experiments on real-world benchmarks with realistic motion blur demonstrate that Kinematics-GS outperforms prior methods by a clear margin in monocular dynamic scene reconstruction, highlighting its effectiveness in handling complex and non-rigid motion scenarios.

Scalable Vector Graphics (SVG) animation generation is pivotal for professional design due to their structural editability and resolution independence. However, this task remains challenging as it requires bridging discrete code representations with continuous visual dynamics. Existing optimization-based methods often destroy topological consistency, while general-purpose LLMs rely on rigid CSS/SMIL transformations, failing to model geometry-level non-rigid deformations. To address these limitations, we present VAnim, the first LLM-based framework for open-domain text-to-SVG animation. We reconceptualize animation not as sequence generation, but as Sparse State Updates (SSU) on a persistent SVG DOM tree. This paradigm compresses sequence length by over 9.8x while preserving the SVG DOM structure and non-participating elements by construction. To enable precise control, we propose an Identification-First Motion Planning mechanism that grounds textual instructions in explicit visual entities. Furthermore, to overcome the non-differentiable nature of SVG rendering, we employ Rendering-Aware Reinforcement Learning via Group Relative Policy Optimization (GRPO). By leveraging a hybrid reward from a state-of-the-art video perception encoder, we align discrete code updates with high-fidelity visual feedback. We also introduce SVGAnim-134k, the first benchmark for vector animation. Extensive experiments demonstrate that VAnim significantly outperforms state-of-the-art baselines in semantic alignment and structural validity, with additional appendix metrics further validating motion quality and identity preservation.

Despite advances in dexterous hand manipulation, robotic hand design is still largely decoupled from task-driven evaluation and control, limiting systematic optimization. Existing robotic hand co-design approaches are often limited in scope, optimizing a small subset of design parameters. We introduce a comprehensive parametric framework for robotic hand generation that unifies palm structure, finger kinematics, fingertip geometry, and fine-scale surface curvatures within a single design space. Fine geometric features are introduced through parametric surface deformation kernels that directly influence contact interactions. We validate the framework on design optimization in grasp stability tasks in simulation and real-world dynamic scenarios. Our framework produces simulation- and fabrication-ready hand models and will be released as open-source to enable rapid design iteration for dexterous hand co-design optimization frameworks and cross-embodiment policy training and control research.

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely unexamined. In this paper, we present a stability evaluation framework that probes parametric projections with Gaussian perturbations around selected anchor points and assesses how neighborhoods deform in the 2D embedding. Our approach combines quantitative measures of mean displacement, bias, and nearest-anchor assignment error with per-anchor visualizations of displacement vectors, local PCA ellipsoids, and Voronoi misassignment for detailed inspection. We demonstrate the framework's effectiveness on UMAP- and t-SNE-based neural projectors of varying network sizes and study the effect of Jacobian regularization as a gradient-based robustness strategy. We apply our framework to the MNIST and Fashion-MNIST datasets. The results show that our framework identifies unstable projection regions invisible to reconstruction error or neighborhood-preservation metrics.

We propose a compositional method for constructing a complete 3D head avatar from a single image. Prior one-shot holistic approaches frequently fail to produce realistic hair dynamics during animation, largely due to inadequate decoupling of hair from the facial region, resulting in entangled geometry and unnatural deformations. Our method explicitly decouples hair from the face, modeling these components using distinct deformation paradigms while integrating them into a unified rendering pipeline. Furthermore, by leveraging image-to-3D lifting techniques, we preserve fine-grained textures from the input image to the greatest extent possible, effectively mitigating the common issue of high-frequency information loss in generalized models. Specifically, given a frontal portrait image, we first perform hair removal to obtain a bald image. Both the original image and the bald image are then lifted to dense, detail-rich 3D Gaussian Splatting (3DGS) representations. For the bald 3DGS, we rig it to a FLAME mesh via non-rigid registration with a prior model, enabling natural deformation that follows the mesh triangles during animation. For the hair component, we employ semantic label supervision combined with a boundary-aware reassignment strategy to extract a clean and isolated set of hair Gaussians. To control hair deformation, we introduce a cage structure that supports Position-Based Dynamics (PBD) simulation, allowing realistic and physically plausible transformations of the hair Gaussian primitives under head motion, gravity, and inertial effects. Striking qualitative results, including dynamic animations under diverse head motions, gravity effects, and expressions, showcase substantially more realistic hair behavior alongside faithfully preserved facial details, outperforming state-of-the-art one-shot methods in perceptual realism.

We propose Skelebones, a Scaffold-Skin Rigging System built on three steps: (1) Bones compress temporally consistent Gaussian or mesh sequences into free-form bones with smooth skinning weights, approximating non-rigid deformations via linear blend skinning (LBS); (2) Skeleton extracts the Mean Curvature Skeleton (MCS) from the canonical shape and temporally refines its topology and kinematics into a compact skeletal structure; and (3) Binding connects the skeleton and bones through non-parametric Partwise Motion Matching (PartMM), which synthesizes novel bone motions by matching, retrieving, and blending existing ones. Together, these steps compress the dynamics of 4D shapes into compact skelebones that are simultaneously controllable and expressive. The resulting representation is category-agnostic, meaning template-free; motion-adaptive, with dynamic topology; and topology-correct, with a skeleton consistent with the surface geometry. PartMM requires no learning. We validate our method on both synthetic and real-world datasets, achieving substantial reanimation improvements on unseen poses: a 17.3 dB PSNR gain over LBS on DNA-Rendering and a 45.6 dB gain over Bag-of-Bones on ActorsHQ, while preserving high rendering fidelity for characters with complex non-rigid dynamics. PartMM generalizes robustly to both Gaussian and mesh representations, excelling in low-data regimes of approximately 1,000 frames, with a 48.4 RMSE improvement over LBS and improvements of more than 20 over GRU- and MLP-based methods. Code will be publicly released at https://cookmaker.cn/gaussianimate/.

Shape optimisation of thin-shell structures requires a flexible, differentiable geometric representation suitable for gradient-based optimisation. We propose a neural parametric geometry representation (NRep) for shells based on a neural network with periodic activation functions. The NRep is defined using a multi-layer perceptron (MLP), which maps the parametric coordinates of mid-surface vertices to their physical coordinates. A structural compliance optimisation problem is posed to optimise the shape of a thin-shell parameterised by the NRep subject to a volume constraint, with the network parameters as design variables. The resulting shape optimisation problem is solved using a gradient-based optimisation algorithm. Benchmark examples with classical solutions and comparisons with the free-form deformation method demonstrate that the proposed NRep is capable of representing shell geometries with local geometric features using a small set of network parameters. The robustness of the approach has been demonstrated with different initial geometries, boundary conditions and neural network hyperparameters. The approach also exhibits potential for complex lattice-skin structures, owing to the compact and expressive geometry representation afforded by the NRep.

Deformable scenes violate the rigidity assumptions underpinning classical visual--inertial odometry (VIO), often leading to over-fitting to local non-rigid motion or to severe camera pose drift when deformation dominates visual parallax. In this paper, we introduce DefVINS, the first visual-inertial odometry pipeline designed to operate in deformable environments. Our approach models the odometry state by decomposing it into a rigid, IMU-anchored component and a non-rigid scene warp represented by an embedded deformation graph. As a second contribution, we present VIMandala, the first benchmark containing real images and ground-truth camera poses for visual-inertial odometry in deformable scenes. In addition, we augment the synthetic Drunkard's benchmark with simulated inertial measurements to further evaluate our pipeline under controlled conditions. We also provide an observability analysis of the visual-inertial deformable odometry problem, characterizing how inertial measurements constrain camera motion and render otherwise unobservable modes identifiable in the presence of deformation. This analysis motivates the use of IMU anchoring and leads to a conditioning-based activation strategy that avoids ill-posed updates under poor excitation. Experimental results on both the synthetic Drunkard's and our real VIMandala benchmarks show that DefVINS outperforms rigid visual--inertial and non-rigid visual odometry baselines. Our source code and data will be released upon acceptance.