Deformable Shape Reconstruction

Dynamic endoscopic reconstruction is fundamental to robotic surgery and computer-assisted interventions. While 3D Gaussian Splatting (3DGS) realises real-time rendering, its application to deformable intraoperative environments remains constrained by spurious geometry and varying illuminations. To address these limitations, we introduce EndoPrior-GS, a novel pipeline that explicitly couples frame-extracted vision heuristics and estimated depth maps. EndoPrior-GS derives a joint texture prior from a tool-filtered valid tissue mask, a non-specular photometric filter, and anatomical structural salience, yielding a probability map that guides primitive initialisation and subsequent density control. The prior is further extended to the temporal domain through a texture-aware term that dynamically weighs pairwise primitive contributions during training. We conduct extensive experiments on benchmark datasets EndoNeRF and SCARED, and the obtained results show that our method EndoPrior-GS reduces Flow Error by 27.7% and 25.8% over the representative approaches while preserving competitive rendering quality and real-time rendering speed. Our project website is available at https://jiaqi-huang-77.github.io/EndoPrior-GS/.

Reconstructing simulation-ready 3D scenes from real-world observations enables robotics, gaming, and immersive applications, yet existing methods largely assume rigid objects. This leaves an important gap for deformables, whose simulation-ready geometry depends on dimensionality (curves, surfaces, or volumes) and whose behavior may require models beyond elasticity. We present CoDimRecon, an agentic framework that reconstructs editable scenes containing rigid, articulated, and deformable objects from multi-view RGB observations. Scene-level geometric priors ground scale and layout, while object-level generated meshes guide the agent toward detailed, compact geometry; articulated rigid objects are decomposed into movable parts with explicit joints. For deformables, category-wise agent sessions reconstruct curves as centerlines with radii, surfaces as manifold shells with thickness, and volumes as watertight solids for volumetric meshing. Reusable simulator skills initialize compatible physical models and parameters, while agent-guided behavioral tests expose mismatches and trigger targeted revisions of motion, geometry, numerics, or material modeling. On evaluated Replica and ScanNet++ scenes, CoDimRecon achieves competitive compositional reconstruction accuracy while additionally producing deformable assets for rod, shell, and solid simulation. We further demonstrate robot interactions across all three representations, including a controlled paper-folding case in which behavioral testing motivates plastic bending.

Estimating deformable object states remains a fundamental challenge in robotics and simulation. We propose a novel factor graph-based framework for probabilistic mesh state estimation of deformable objects. The method directly updates a tetrahedral mesh, a rich and physically-grounded representation of an environment, by combining physics priors, noisy sensor measurements, and temporal smoothness constraints within a unified probabilistic formulation. The estimation problem is posed as a nonlinear least-squares optimization and solved using Levenberg-Marquardt. Ex vivo central-airway obstruction experiments and simulations on deforming cube models demonstrate reliable and accurate reconstruction under both rigid motion and deformation, highlighting the potential of this probabilistic approach for principled, measurement-driven mesh state estimation in deformable object reconstruction.

Manipulating deformable objects (DOs) is challenging due to their high-dimensional state space, underactuated dynamics, and partial observability. In this paper, we propose cRVAE, a lightweight conditional recurrent variational autoencoder that estimates the full DO state from only partial corner-node observations during inference. The resulting model is used as the forward model in a receding-horizon optimal control framework for obstacle-aware collaborative DO manipulation. In simulation on rope and fabric, cRVAE estimates the full DO state from the available corner-node measurements alone, matching the accuracy of a parameter-identified XPBD model. At inference it uses no physical parameters as model inputs and performs no online parameter identification. It also runs approximately 350 times faster on the rope and over 1500 times faster on the fabric per forward pass, keeping horizon-based planning within the 100 ms control budget where XPBD exceeds it already at short horizons. Full-shape estimation from corner sensing at in-loop speed is what makes the model deployable on hardware, which we demonstrate on a Unitree Go2 robot.

Reconstructing objects with mechanical properties from video observations enables physically consistent dynamic prediction, benefiting robotics planning and interaction. Existing spring--mass based physical driven reconstruction approaches offer efficient and differentiable physical reconstruction, but they typically rely on axial springs alone. Such formulations oversimplify the underlying structural mechanics and can become mechanically under-constrained when the physical graph is coarsened, limiting their ability to preserve stable local deformation. We present BendTwin, a bending-aware differentiable spring--mass framework for video-based reconstruction and future prediction of deformable objects. BendTwin introduces bending stiffness and damping over local surface triplets, penalizing deviations from rest angles and regularizing higher-order deformation. These bending constraints improve mechanical stability while preserving the simplicity of spring--mass system. Experiments show that BendTwin consistently outperforms the axial-only PhysTwin baseline. Ablation studies further demonstrate that the bending constraints maintain system stability across different downsampling ratios and consistently improve upon the original PhysTwin formulation. Overall, BendTwin provides an effective approach for constructing mechanically faithful digital twins from sparse-view RGB-D videos.

Single-image 3D hand avatar reconstruction is fundamentally ill-posed and particularly challenging due to limited visual evidence under severe self-occlusion and the complex pose-dependent deformation of highly articulated hands. Existing methods predominantly rely on implicit NeRF-style representations, whose volumetric fitting is computationally expensive and often struggles to preserve fine-grained hand details. In this work, we present OASIS, a tailored 3D Gaussian Splatting framework for single-image hand avatar reconstruction. To faithfully encode sparse image-specific appearance cues in single-view reconstruction, we construct geometry-aligned visual evidence tokens by explicitly aligning input image observations with 3D hand geometry and context-adaptively tokenizing the resulting visual evidence. Since severe self-occlusion makes the reliability of image evidence inherently visibility-dependent, we introduce a visibility-conditioned point-image attention to reliably transfer visual evidence to geometric tokens, yielding occlusion-aware Gaussian features for faithful and robust reconstruction. To further capture non-rigid deformation of articulated hands, we introduce a Feature-on-Mesh representation to enable Gaussian deformation to be guided by local surface stretching. Under this framework, we adopt a one-shot adaptation scheme that learns a shared hand prior from multi-identity training data and then fits it to a target image for target-specific reconstruction. Extensive experiments show that OASIS outperforms existing baselines in both visual fidelity and efficiency across challenging poses and in-the-wild scenarios, and further demonstrates strong versatility in downstream applications such as text-to-avatar generation and texture editing.

Curved tactile fingertips for dexterous manipulation must resolve fine contact geometry, distinguish normal and tangential loads, and capture transient signals. Existing curved vision-based tactile sensors struggle to combine accurate 3D reconstruction, three-axis force estimation, and high-speed processing in a compact form. This article presents FasTac, a curved vision-based tactile sensor integrating multispectral photometric stereo, dynamic-convolution force estimation, and hardware acceleration on a field-programmable gate array (FPGA). Single-image-sensor simultaneous multispectral imaging provides spatially aligned observations for robust surface normal estimation, followed by boundary-prior fast Poisson depth reconstruction. HyperForce uses position-aware dynamic convolution to model the spatially nonuniform mechanical response of curved elastomers and estimate three-axis forces. The complete image-to-normal-force pipeline is deployed on an FPGA. Experiments show that near-infrared (NIR) illumination and the boundary prior decrease depth mean absolute error (MAE) from 0.2730 mm to 0.0415 mm; HyperForce achieves normalized mean absolute error (NMAE) values of 2.74% and 2.39% for normal and shear forces, respectively; and FPGA deployment shortens processing latency from 3.26 ms on the GPU to 1.09 ms. Multi-object reconstruction, feedback grasping, and vibration measurement validate fine geometric perception, stable force feedback, and dynamic contact sensing.

Estimating the full shape of a deformable object is especially challenging when vision is unavailable: in the dark, inside an opaque bag, behind the manipulating hand, or under heavy self-occlusion. Touch is the natural sensor in these settings, but touches are sparse and local. We present a single topology-agnostic estimator that reconstructs the full mesh of a deformable object from only a few touches and no vision, using one permutation-invariant cross-attention architecture that handles a 1D rope, a 2D cloth, and a 3D volumetric soft body. The learned estimator reduces reconstruction error by roughly two-thirds relative to non-learned geometric mesh completion and a Gaussian-process surface baseline, and it outperforms a simpler global-pool set encoder, with the gap growing as more touches are observed. We then show that the estimator's deep-ensemble uncertainty can be used to learn where to touch next, which lowers error further and beats both random touching and a Gaussian-process active baseline at sparse budgets. This gain is modest on average but grows with self-occlusion and on the error tail. When vision is also available, where to touch barely matters, motivating the vision-free setting we study.

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/.

Superquadrics have proven to provide a compact, geometrically meaningful representation for 3D objects. However, existing methods suffer from limited reconstruction accuracy, are restricted to rigid primitives, and lack robustness to partial point clouds. In this work, we present SuperFlex, an enhanced framework that expands the expressive power and applicability of superquadric decompositions. First, we introduce a novel loss formulation which significantly improves reconstruction accuracy. Second, we include bending and tapering deformations, enabling high-fidelity representation of curved and asymmetric geometries. Finally, we leverage these high-quality decompositions as supervision to train a model that is robust to partial real-world point clouds. Experiments demonstrate substantial improvements in reconstruction accuracy over both optimization- and learning-based baselines while maintaining a highly compact primitive representation.

We introduce \textbf{OVOW}, the first training-free system that reconstructs \emph{instance-level, simulation-ready} 4D mesh scenes from a single monocular video. Recent 4D reconstruction achieves impressive rendering quality, but its outputs (\eg, implicit fields, Gaussian primitives, or point clouds) lack the watertight topology, instance separation, and standardized physical interfaces required by physics simulators and embodied AI. OVOW closes this gap with a four-stage pipeline: a vision-language model discovers, labels, and motion-classifies all instances; category-aware reconstruction yields per-instance meshes for rigid objects and topology-consistent mesh sequences for deformable ones; an iterative render-match-optimize procedure recovers metric scale and 6-DoF pose trajectories; and physics-grounded assembly enforces ground contact and inter-object support. Crucially, we model all motion, rigid and non-rigid, through direct vertex deformation without category-specific priors or skeleton rigging, producing watertight mesh scenes ready for downstream physics simulation and editing. We further establish the first benchmark for \emph{structured Video-to-4D} evaluation, with metrics for geometric correctness, instance separation, and physical plausibility beyond visual fidelity; the same pipeline doubles as a scalable engine for \emph{synthesizing} paired video-to-4D simulation data for future 4D world models and embodied AI. Across two synthetic benchmarks (static and 4D), OVOW attains the best overall layout and geometry accuracy and the lowest photometric and semantic error among all baselines, and on monocular video runs one to two orders of magnitude faster than the baselines, while downstream physics simulation confirms its physical stability.

Gaussian splatting (GS) has garnered significant attention in VR/AR and digital content creation due to its explicit parameterization and efficient rendering capabilities. However, existing GS-based methods for deformable objects face two key limitations: (i) illumination is erroneously baked into textures, causing physically inconsistent responses under dynamic deformations and lighting changes; (ii) snapshot-based reconstruction restricts post-reconstruction material editing. To address these challenges, we propose Deformable and Relightable GS (DR-GS), a unified Gaussian framework that integrates physically-based inverse rendering, relighting, and deformation-aware manipulation. Through explicitly disentangling geometry, illumination, and material representations, DR-GS overcomes the limitations of static snapshots, resolving unrealistic appearance under varying conditions while enabling post-reconstruction parameter editing. Extensive experiments show that DR-GS achieves leading visual quality across static reconstruction, dynamic deformation, and relighting, reliably preserving reflections and specular highlights on glossy surfaces. It further establishes a fully decoupled geometry-illumination-material pipeline, enabling high-quality 3D asset creation and comprehensive post-editing.

Reconstructing dynamic non-rigid objects from monocular video requires integrating visual cues from direct observations with data-driven priors over geometry and appearance. Prior approaches either learn to directly predict 4D representations from visual input or initialize a 3D representation that is subsequently deformed and refined based on video evidence. However, the former are constrained by the scarcity of 4D training data, while the latter leverage priors only for the initial reconstruction and rely solely on video supervision thereafter; neither handles complex in-the-wild scenarios with large deformations and occlusions well. We present Lift4D, a test-time optimization framework that addresses both limitations. First, we adapt an existing single-view 3D reconstruction model to yield temporally consistent per-frame predictions via causal latent conditioning, providing a coherent initialization for a deformable 3D Gaussian Splatting representation. We then ``sculpt'' this representation to match the input video through an occlusion-aware optimization that faithfully recovers visible surface details while completing unobserved regions using a view-conditioned diffusion prior. We demonstrate that Lift4D clearly improves over prior 4D reconstruction methods, particularly on challenging in-the-wild sequences with severe occlusions and non-rigid motion.

Humans naturally understand object physics through everyday interactions, but faithfully predicting complex deformable dynamics, such as elastic materials and fabrics, remains a major challenge for computer vision and robotics. We present EgoPhys, a framework that constructs deformable physical digital twins from egocentric RGB-only video using generalizable priors. EgoPhys overcomes the limitations of existing methods to enable controllable deformable digital twin generation from egocentric videos by distilling per-object inverse-physics solutions into a compact codebook, enabling prediction of dense spring stiffness fields for unseen objects without per-spring test-time optimization. Trained with generalizable priors from diverse egocentric interactions, EgoPhys outperforms baselines in reconstruction, future prediction, and zero-shot generalization. To support training and evaluation, we curate an egocentric interaction dataset covering diverse deformable objects, scenes, and manipulation styles. We deploy EgoPhys on a real xArm6 robot, demonstrating that a digital twin initialized from a single egocentric human play video can serve as an internal world representation to aid in deformable-object planning, highlighting egocentric RGB observations as a scalable path toward real-to-sim pipelines.

3D reconstruction could improve colonoscopy by estimating mucosal coverage and alerting clinicians to missed regions during screening. However, algorithm development is limited as no current datasets provide both a realistic in vivo appearance and dense, time-resolved 3D ground truth, especially under non-rigid deformation. We present C3VD-DEFCOL, a framework and dataset for evaluating deformable colonoscopy reconstruction with paired geometry and realistic texture. Starting from C3VD/C3VDv2 colon meshes and camera trajectories, we generate controlled deformations of the colon surface, including peristaltic waves and centerline motion, and render per-frame depth, surface normals, optical flow, camera poses, and time-stamped 3D meshes. We then use the rendered geometry, primarily depth, to condition an LTX-2.3-based sim-to-real translation model that produces RGB clips with in vivo-like mucosal color, texture, vasculature, and specular appearance while preserving the underlying 3D scene structure. The resulting dataset contains 110 videos from 11 unique colon mesh geometries, with varying camera trajectories, appearances, and parameterized deformation regimes, including three peristaltic severity levels that serve as controlled evaluation axes. We evaluate the generated videos using appearance realism, geometric consistency, and temporal consistency metrics, and use the paired ground truth to benchmark the downstream task of pose estimation in deformable 3D reconstruction. Our experiments show how pose estimation error increases with increasing deformation severity, providing a controlled stress test that is not possible with existing in vivo datasets. Overall, C3VD-DEFCOL is designed as a reproducible, quantitative evaluation platform for testing deformable 3D reconstruction algorithms, with the goal of reducing the domain gap between synthetic datasets and in vivo colonoscopy.

Existing inverse physics methods recover physical parameters from multi-view videos, where geometric constraints across views resolve scale and 3D structure. In monocular settings, however, such constraints are absent, leading to severe scale ambiguity, inaccurate geometry, and weak coupling between appearance optimization and physical simulation. To address these challenges, we propose MonoPhysics, a framework for monocular inverse physics estimation of deformable objects that jointly optimizes geometry, appearance, and physical parameters using a differentiable simulator and 3D Gaussian Splatting. Our key contribution is removing the multi-view capture requirement of existing methods, a necessary step toward handling in-the-wild video. MonoPhysics introduces three visual-physical bridges: scene re-parameterization, physics-aware geometry refinement, and a differentiable position map. We evaluate on Vid2Sim, real-world captures, and a new dataset of elastic and plasticine objects that we introduce. MonoPhysics outperforms monocular baselines in future prediction and recovers Young's modulus on Vid2Sim with accuracy comparable to a multi-view baseline. Code and data are available at https://daniel03c1.github.io/MonoPhysics/.

Monocular 3D shape recovery is fundamental to geometric understanding, yet achieving robust generalization across arbitrary viewpoints and unseen object categories remains a significant challenge. In this paper, we present a generalizable deformation learning framework that reconstructs 3D objects by explicitly deforming a category-level shape template to match the target observation. To address complex shape variations between the template and the target, we introduce a geometry-guided feature modeling mechanism. This process first enriches foundation features with template topology to yield a geometry-aware representation, which is then explicitly correlated with the target observation to guide precise deformation. Furthermore, to bridge the disparity between the fixed template and arbitrary target views, we propose a view-adaptive feature aggregation module. This module leverages multi-view template features and their corresponding camera poses to enrich the canonical template representation, ensuring robust feature alignment regardless of the target's perspective. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods in handling large shape variations and diverse viewpoints, exhibiting strong generalization to novel categories and effectively supporting downstream real-world dexterous robotic manipulation tasks. Project homepage: https://GODeform.github.io/

This study addresses the partial-to-complete geometry reconstruction of deformable objects (DOs) from point-cloud observations toward precise DO manipulation. Recent DO reconstruction approaches often adopt implicit neural representations (INRs) to model continuous surfaces as well as capture structural variability. However, these methods typically rely on object-specific shape priors that improve training stability and limit generalization. To figure it out, we introduce ParCo-SDF, a two-stage partial-to-complete signed distance field (SDF) reconstruction framework consisting of temporal geometry encoding followed by FiLM-conditioned SDF prediction. The temporal encoder captures structural similarity across DO sequence, enabling prior-free stable training. FiLM-based conditioning preserves reconstruction expressivity while reducing network complexity. We evaluate the proposed method against a state-of-the-art DO surface reconstruction baseline on a rubber band manipulation dataset, demonstrating robust and high-fidelity reconstruction under severe occlusions.

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 [email protected] on SPair-71k, establishing deformable models as effective semantic 3D representations.

While existing methods for reconstructing hand-object interactions have made impressive progress, they either focus on rigid or part-wise rigid objects-limiting their ability to model real-world objects (e.g., cloth, stuffed animals) that exhibit highly non-rigid deformations-or model deformable objects without full 3D hand reconstruction. To bridge this gap, we present PhysHanDI (Physics-based Reconstruction of Hand and Deformable Object Interactions), a framework that enables full 3D reconstruction of both interacting hands and non-rigid objects. Our key idea is to physically simulate object deformations driven by forces induced from densely reconstructed 3D hand motions, ensuring that the reconstructed object dynamics are both physically plausible and coherent with the interacting hand movements. Furthermore, we demonstrate that such simulation of object deformations can, in turn, refine and improve hand reconstruction via inverse physics. In experiments, PhysHanDI outperforms the state-of-the-art baseline across reconstruction and future prediction.

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.

Reliable real-time 3D shape sensing is essential for robust control and interpretation of deformable systems during motion. Existing vision-based approaches require line-of-sight and complex instrumentation, limiting operation in occluded and space-constrained settings. Here, we introduce a scalable, skin-like sensor that reconstructs its continuous 3D deformation in real time from distributed strain measurements. The device embeds a 2D array of mirror-stacked, printed oxidized eutectic gallium-indium (o-EGaIn) strain gauges within an elastomeric film to measure off-neutral-axis strains. Combined with a mechanics-informed observation model and a fast optimization routine, the system estimates local curvature, elongation, offset, and orientation under concurrent stretching, bending, and indentation, enabling reconstruction of complex surfaces. A 5-by-5 array with a 12 mm pitch achieves a mean surface reconstruction error of 0.62 mm with 0.1s latency across all tested scenarios. When conforming to complex surfaces, the sensor provides fast 3D shape mapping of the underlying geometry. Demonstrations involving palm gesturing, finger indentation, and contact-induced balloon deformation highlight utility for epidermal motion tracking, haptic interaction, and intraoperative monitoring.

We introduce MeshLAM, a feed-forward framework for one-shot animatable mesh head reconstruction that generates high-fidelity, animatable 3D head avatars from a single image. Unlike previous work that relies on time-consuming test-time optimization or extensive multi-view data, our method produces complete mesh representations with inherent animatability from a single image in a single forward pass. Our approach employs a dual shape and texture map architecture that simultaneously processes mesh vertices and texture map with extracted image features from a shared transformer backbone, allowing for coherent shape carving and appearance modeling. To prevent mesh collapse and ensure topological integrity during feed-forward deformation, we propose an iterative GRU-based decoding mechanism with progressive geometry deformation and texture refinement, coupled with a novel reprojection-based texture guidance mechanism that anchors appearance learning to the input image. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in reconstruction quality, animation capability, and computational efficiency. Project page at https://meshlam.github.io.

Accurate reconstruction and tracking of dynamic human faces from image sequences is challenging because non-rigid deformations, expression changes, and viewpoint variations occur simultaneously, creating significant ambiguity in geometry and correspondence estimation. We present a unified method for high-fidelity 4D facial reconstruction based on canonical facial point prediction, a representation that assigns each pixel a normalized facial coordinate in a shared canonical space. This formulation transforms dense tracking and dynamic reconstruction into a canonical reconstruction problem, enabling temporally consistent geometry and reliable correspondences within a single feed-forward model. By jointly predicting depth and canonical coordinates, our method enables accurate depth estimation, temporally stable reconstruction, dense 3D geometry, and robust facial point tracking within a single architecture. We implement this formulation using a transformer-based model that jointly predicts depth and canonical facial coordinates, trained using multi-view geometry data that non-rigidly warps into the canonical space. Extensive experiments on image and video benchmarks demonstrate state-of-the-art performance across reconstruction and tracking tasks, achieving approximately 3$\times$ lower correspondence error and faster inference than prior dynamic reconstruction methods, while improving depth accuracy by 16%. These results highlight canonical facial point prediction as an effective foundation for unified feed-forward 4D facial reconstruction.

Reconstructing the three-dimensional (3D) geometry of object surfaces is essential for robot perception, yet vision-based approaches degrade under low illumination or occlusion. This limitation motivates the design of a proprioceptive membrane that conforms to the surface of interest and infers 3D geometry by reconstructing its own deformation. Conventional deformation-aware membranes typically rely on resistive, capacitive, or magneto-sensitive mechanisms, but can suffer from structural complexity, limited compliance during large-scale deformation, and susceptibility to electromagnetic interference. This work presents a soft, flexible, and stretchable proprioceptive silicone membrane based on optical waveguide sensing. The membrane integrates edge-mounted LEDs and centrally-distributed photodiodes (PDs) within a multilayer elastomeric composite. Rich deformation-dependent light-intensity signals are decoded by a data-driven model to recover the membrane geometry. Real-time reconstruction is demonstrated on a customized 140 mm square membrane at an end-to-end update rate of 90 Hz, achieving an average reconstruction error of 1.307 mm for out-of-plane deformation of up to 25 mm. The proposed sensor also demonstrates accurate reconstruction under large in-plane deformation, achieving reliable shape recovery up to 75% strain with an average Chamfer distance of 1.214 mm. The proposed framework provides a scalable, robust, and low-profile solution for global shape perception in deformable robotic systems.

Tissue deformation recovery based on stereo endoscopic images is crucial for tool-tissue interaction analysis and benefits surgical navigation and autonomous soft tissue manipulation. Previous research suffers from the problems raised from camera motion, occlusion, large tissue deformation, lack of tissue-specific biomechanical priors, and reliance on offline processing. Unlike previous studies where the tissue geometry and deformation are represented by 3D points and displacements, the proposed method models tissue geometry as the 3D point and derivative map and tissue deformation as the 3D displacement and local deformation map. For a single surface point, 6 parameters are used to describe its rigid motion and 3 parameters for its local deformation. The method is formulated under the camera-centric setting, where all motions are regarded as the scene motion with respect to the camera. Inter-frame alignment is realized by optimizing the inter-frame deformation, making it unnecessary to estimate camera pose. The concept of the canonical map is introduced to optimize tissue geometry and deformation in an online approach. Quantitative and qualitative experiments were conducted using in vivo and ex vivo laparoscopic datasets. With the inputs of depth and optical flow, the method stably models tissue geometry and deformation even when the tissue is partially occluded or moving outside the field of view. Results show that the 3D reconstruction accuracy in the non-occluded and occluded areas reaches 0.37$\pm$0.27 mm and 0.39$\pm$0.21 mm in terms of surface distance, respectively. The method can also estimate surface strain distribution during various manipulations as an extra modality for mechanical-based analysis.