Statistical Shape Model

Recognizing hand-drawn geometric shapes is a foundational sub-problem of sketch recognition, with applications in education, human-computer interaction, and diagram digitization. This paper presents the design, implementation, and evaluation of a desktop application that recognizes four basic hand-drawn geometric shapes, circle, square, rectangle, and triangle using a compact Convolutional Neural Network (CNN). A dataset of 2,000 labeled 28x28-pixel shape images was collected independently and released publicly. The classifier consists of three convolutional blocks (16, 32, and 64 filters) with max-pooling, an in-model data-augmentation stage (random horizontal flip, rotation, and zoom), a dropout-regularized dense layer of 128 units, and a 4-way linear output layer, totaling 97{,}956 trainable parameters. The network is trained with the Adam optimizer on a sparse categorical cross-entropy objective computed directly on logits. On an 80/20 train-validation split, the model achieves 94.80% training accuracy and 96.01% validation accuracy with a validation loss of 0.1437. A Tkinter-based graphical interface allows a user to draw a shape with the mouse and receive an immediate class prediction with a confidence score. We situate this system within the broader sketch and shape-recognition literature, compare its accuracy against related hand-drawn shape classification studies, and discuss the limitations inherent to a small, single-contributor dataset. The complete source code, trained model, and per-class datasets are released publicly to support reproducibility.

This work proposes a real-time 6 Degree-of-Freedom (6 DoF) tracking algorithm for monocular laparoscopic surgery. It provides alignment between intra-operative video and pre-operative data (e.g., CT). The 6 DoF tracking offers a solution for accurately locating the internal anatomy of the target organ despite the lack of tactile feedback and transparency. The ORB-SLAM2 framework is adopted and modified for prior-based 3D tracking with four major modifications. First, the primitive 3D shape is used for fast initialization of the ORB-SLAM2 monocular mode. Second, a pseudo-segmentation strategy is employed to separate the target organ from the background for tracking. Third, the 3D shape is incorporated as a geometric prior in its pose graph optimization. Fourth, the Multi-Scale Retinex with Chromaticity Preservation (MSRCP) algorithm is leveraged and modified for image enhancement in challenging illumination scenarios. In-vivo and ex-vivo experiments validate that LapaTrack-3D provides robust 3D tracking and effectively handles typical challenges such as poor illumination, fast motion, out-of-field-of-view scenarios, partial visibility, and ``organ-background'' relative motion. LapaTrack-3D achieves a processing rate of 13 Hz for 1280*720 pixel video.

Estimating the 3D center of mass of unknown objects is challenging when grasping is infeasible, geometry is irregular, or mass distribution is uneven. We present a force-based method that estimates CoM height and mass from a single sub-critical tipping experiment by a robot manipulator. The robot applies a quasistatic elevated push and retract motion, using force-angle measurements recorded during tipping to identify parameters from the object trajectory. Our proposed push-retract cycle mitigates frictional bias, enabling generalized fitting. We experimentally validate our method using a robot manipulator with a six-axis force torque sensor on varying types of objects without prior shape information and without specific models. We also propose a method to prevent toppling, keeping the object in a sub-critical tipping regime by leveraging a safety margin. In experimental studies, our method recovers mass, CoM height, and toppling angle with relative errors below 5.0 percent across all unknown objects. This work demonstrates reliable 3D inertial parameter estimation under proper safety thresholds in tipping. Our proposed method informs and enables reliable non-prehensile manipulation and robotic grasping of challenging objects that were previously infeasible.

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 a fully animatable 3D animal from a single image remains challenging because animation-ready assets require not only plausible geometry, but also a unified topology, editable appearance, and fur representations compatible with deformation and simulation. Existing image-to-3D approaches often rely on implicit or loosely structured representations that are difficult to rig or edit, while parametric animal models support animation but cannot capture detailed texture and fur appearance. We present AnimalLift, a framework for reconstructing structured, animation-compatible 3D animal assets with explicit fur from a single image. Our method lifts an input image into a shared canonical space with a consistent topology and UV parameterization across the dataset, enabling joint prediction of canonical geometry, texture, and fur in a unified feed-forward architecture. A key component of our representation is a UV-aligned fur map that encodes strand geometry in a surface-aligned canonical domain, allowing explicit fur reconstruction compatible with mesh deformation and fur simulation. To train the model, we introduce a procedural data generation pipeline that provides large-scale supervision with aligned geometry, texture, and fur across diverse animal species and appearances. Experiments on synthetic and real-world datasets demonstrate strong reconstruction quality and generalization across animal categories. Beyond reconstruction, our structured representation directly supports downstream applications including animation, pose transfer, fur editing, and simulation-compatible rendering.

Three-dimensional femoral reconstruction from radiographs supports surgical planning, implant sizing, and post-operative follow-up, but remains ill-posed as X-ray projections discard depth information. Existing methods often incorporate a 3D statistical shape model (SSM) as a shape prior to guide reconstructions toward anatomically plausible shapes, relying on iterative 3D-to-2D projection matching. Yet, these approaches are computationally expensive and constrain their SSM to a single dimensionality, leaving the statistical relationship between 2D observations and 3D geometry largely unexploited and unexplored. We instead propose a joint 2D-3D SSM that explicitly captures the co-variation between 2D and 3D segmentations in a shared latent space. During training, 2D and 3D segmentations are registered to a common 3D template and its corresponding 2D projections, and the resulting stationary velocity fields are jointly decomposed using principal component analysis (PCA). This joint modeling allows the 2D-to-3D mapping to be learned directly from data rather than computing correspondences at inference time. For unseen subjects, the 3D shape is recovered directly by lifting the 2D latent coordinates to the 3D PCA subspace, thereby eliminating the need for iterative 3D-to-2D projection. Experiments on NMDID demonstrate that the proposed joint 2D-3D SSM outperforms a widely-used 3D-only SSM baseline while achieving inference approximately 4 times faster, at under 3 seconds per subject. The code is available at: https://github.com/florence-dellaniello-picard/joint2d3d-ssm.

Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.

Accurate object detection in aerial and satellite imagery is dependent upon the bounding box representation. This is especially true for spatially oriented objects such as ships or aircrafts. Oriented Bounding Boxes (OBB) have a tighter fit and more robust non-max suppression compared to Horizontal Bounding Boxes (HBB), any current post-processing conversion from OBB to HBB either introduces excess empty and background space or removes data from the detection. This paper introduces a novel approach for a shape-aware OBB-to-HBB conversion for ship detection in remote sensing imagery. It leverages hull shape, hull fullness, and the bounding box orientation to produce a tighter axis-aligned HBB representation. The proposed method is benchmarked against three baselines methods for OBBto-HBB conversion, Outer HBB which uses minimum and maximum, Area Equivalent HBB and GBB Marginalized HBB.

Correspondence-based statistical shape modeling (SSM) is vital for population-level morphometric analysis, but conventional pipelines assume clean, fully registered surfaces. Real-world clinical photogrammetry scans are often noisy, partial, and cluttered, hindering the adoption of radiation-free surface imaging as a safe alternative to computed tomography (CT) for infant craniosynostosis. We present SCALP (Semi-supervised Correspondence via lAndmark Localization and sPectral warping), a two-stage framework that constructs consistent shape models directly from raw, imperfect surface scans. First, a semi-supervised Point Transformer leverages a small expert-annotated dataset alongside a large unlabeled cohort to accurately localize craniofacial landmarks with minimal annotation overhead. Second, these landmarks anchor a Laplace--Beltrami spectral deformation of an anatomical template, generating dense correspondences while naturally isolating the cranium from peripheral scanning clutter without manual preprocessing. Experiments on infant photogrammetry scans demonstrate that SCALP consistently outperforms state-of-the-art unsupervised point-cloud approaches, offering a clinically practical pathway toward objective, radiation-free head shape analysis.

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.

Glioma grading from tumor contours is often treated as a pixel problem even when the signal of interest is shape. We align closed contours with a functional shape-alignment framework, separate global deformation from residual Fourier shape, and organize these quantities as frequency-ordered tokens. In five-fold patient-disjoint cross-validation on BraTS~2020 tumor contours, with model selection performed using grouped inner validation, a compact multilayer perceptron (MLP) achieves the highest mean balanced accuracy at 71.5%, compared with 65.9% for ResNet-18 and 63.3% for ViT-Tiny. It also gives the highest mean low-grade glioma F1 at 54.9%. Its pooled out-of-fold balanced accuracy is 72.4% (patient-bootstrap 95% CI: 66.4--77.8%). The selected MLPs use 2.9k--117.3k parameters across folds, at least 46 times fewer than the pixel baselines. In a controlled noise-free simulation, shape-based models reach 56.3--71.5% balanced accuracy while the pixel models remain at 50.0--52.5%. This work demonstrates how incorporating a shape-based inductive bias at the representation level can improve interpretability and scalability while enabling substantial dimensionality reduction.

Recent radiance field methods represent scenes with 2D primitives that offer surface alignment and efficient rasterization, from Gaussian disks to triangles, yet all rely on convex boundaries: curved and concave structures demand excessive primitives. We introduce Deformable Triangle Splatting, which augments each triangle with $K$ control points per edge, each parameterized by a single learnable scalar displacement that shifts the boundary inward or outward, enabling non-convex shape representation while preserving the three base vertices that define the 3D plane. To render these non-convex primitives differentiably, we design a rasterization pipeline in the triangle's barycentric coordinate space, ensuring view-consistent rendering. A winding number test determines whether each pixel lies inside the deformed primitive, and a window function controlled by two learnable parameters, sharpness and corner smoothness, together with a per-primitive scalar opacity, produces the smooth opacity transition from interior to boundary. Validation is done in a variety of real-world scenes, outperforming recent works based on non-volumetric primitives in terms of visual quality and versatility while still achieving competitive rendering efficiency.

The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to the translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.

Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function. By replacing traditional multi-layer perceptrons (MLPs) with a parameterized primitive engine, Fluid-SDF reconstructs complex, non-convex topologies using strictly under 100 parameters, achieving comparable or superior intersection-over-union (mIoU) to standard neural baselines. Furthermore, we demonstrate that Fluid-SDF acts as a powerful geometric prior, inherently resisting high-frequency dataset noise where capacity-matched neural networks catastrophically overfit. Finally, unlike standard INRs, Fluid-SDF's explicit parameter space allows for direct, zero-shot user editing of local and global shape features without retraining. By bypassing expensive on-device gradient updates entirely, Fluid-SDF is uniquely suited for mobile AI, augmented reality, and resource-constrained embedded environments

3D scene graphs provide a hierarchical abstraction of environments by encoding spatial entities, such as objects and places, and their relationships. However, existing scene graph systems model object geometry coarsely, relying on partial point clouds or class-level CAD templates, which limits instance-specific shape detail. This paper presents Hydra++, a system-level investigation into how learning-based object shape estimators can be integrated into a hierarchical 3D scene graph pipeline. Hydra++ incorporates category-agnostic shape estimation and a reprojection-mask consistency check to reject degenerate predictions from partial observations or imprecise segmentation. In its default CRISP-based configuration, Hydra++ performs online scene graph construction; slower estimators such as SAM3D are evaluated as modular alternatives to demonstrate generalization-latency trade-offs. Furthermore, to address the challenges of sparse and noisy depth measurements in outdoor environments, Hydra++ supports a hybrid LiDAR-camera configuration for large-scale operation, improving scene-level reconstruction quality. Experiments in both simulation and real-world outdoor campus scenarios demonstrate that Hydra++ improves object- and scene-level reconstruction quality. Project page is available at https://hydra-plusplus.github.io/.

Accurate modeling of dental crown morphology is fundamental for diagnosis, orthodontic planning, and computer-aided restoration design. However, datasets suitable for training such models are typically limited in size. We present ToothForge, a deep spectral generative framework that models dental crown geometries from compact, intrinsic representations. By operating in the spectral domain, ToothForge learns a latent manifold of 3D tooth shapes through synchronized spectral embeddings, ensuring consistent modeling across samples with varying connectivity. Spectral synchronization mitigates the instability of Laplace-Beltrami eigenbases and enables efficient learning in a low-dimensional space. The framework is thoroughly evaluated through robustness analysis, ablation studies, and benchmarking against PCA-based statistical shape models and point-based generative frameworks. Results show that synchronized spectral modeling achieves reconstruction and generative performance comparable to or exceeding spatial approaches, while maintaining compactness and geometric interpretability. Together, the compact synchronized coefficients and low-dimensional learning space make the framework particularly suitable for limited datasets, as often encountered in dental and medical domains, and applicable in real-world scenarios where guaranteeing consistent connectivity across shapes from various clinics is unrealistic.

Computational models of the human heart are widely used to study electromechanical and fluid-dynamical cardiac function and to support applications such as in silico clinical trials. However, most studies remain limited to single or patient-specific anatomies, restricting the inclusion of population-level variability required for uncertainty quantification. A key challenge is translating medical-image segmentations, which may contain artifacts, mesh defects or disjoint domains, into topologically coherent geometries suitable for multiphysics simulations. In this work, we present a semi-automatic pipeline that converts CT-based segmentations into simulation-ready cardiac meshes within a few minutes while preserving anatomical and topological consistency. Building on modern deep learning segmentation methods, the framework incorporates a template-based registration stage to regularize artifacts and enforce mesh-quality constraints. A Chamfer-distance morphing strategy deforms a high-quality template toward each segmented heart, matching individual chambers while preserving topology. The resulting meshes are watertight, isotopological, and endowed with consistent point-to-point correspondence. The pipeline is validated on 58 healthy cardiac CT scans, including all cardiac chambers and proximal vessel segments. The resulting meshes can be represented in a unified shape space, enabling the construction of a statistical shape model of the heart and major vessels. Principal Component Analysis shows that a low-dimensional latent space efficiently captures population variability, while Gaussian Mixture Modeling enables synthetic anatomy generation. Overall, the proposed framework (released open-source) provides a pathway from raw segmentations to simulation-ready cardiac geometries, enabling anatomically consistent virtual cohorts for large-scale in silico studies.

Accurate volume and surface area estimation is critical for diverse applications, from marine ecology to medical diagnostics. However, existing methods often suffer from high computational costs and poor performance with sparse and noisy data. We propose a fully feed-forward framework that regresses scale-normalized volume and surface area and their associated uncertainties directly from multi-view images. By fusing 3D point cloud reconstructions with view-aligned 2D features through a graph-based decoder, our model bypasses iterative optimization, ensuring exceptional scalability and rapid inference. Experimental results demonstrate that our approach outperforms state-of-the-art methods, particularly when operating with a low number of input images. Validated across coral monitoring, dietary analysis, and anthropometry, our proposed framework provides a robust, adaptable solution for quantitative shape analysis. This architecture provides a high-speed, scalable alternative for precise geometric estimation from visual data, maintaining high performance even in resource-constrained or sparse-view scenarios.

Recent work motivates moving large language model (LLM) evaluation from mean-based to tail-aware metrics, including conditional value-at-risk and tail-index estimates of reward-model error. We ask whether the canonical extreme-value-theory tail-index parameter, which isolates how heavy a tail is from how large the tail mass is, adds discriminative information beyond the mean and a standard tail-magnitude statistic in LLM evaluation. We pre-register a protocol covering admissibility, goodness-of-fit, threshold-stability, and effect-size requirements for any positive tail-shape claim. The protocol is the contribution of this paper; the empirical study below is a demonstration of what its gates catch. Applied to a standard LLM toxicity-evaluation setup under two structurally different scorer families, the protocol catches three distinct modes of false positives that a naive analysis would have published, and rejects the headline tail-shape claim on both scorers. We conclude that tail-shape estimation in the LLM toxicity-evaluation setups we examined is more fragile than the recent literature suggests, and recommend the protocol as a starting point for tail-index claims in similar setups.

Precise biomedical image segmentation is crucial for clinical diagnosis. Geometric cues (e.g., boundary, shape, and topology) can improve structural consistency, yet most are task-specific and lack a unified geometric foundation that generalizes across organs and modalities. We are motivated by the observation that several medical segmentation targets can be approximated as globally near-convex shapes. A convex region is one in which any two interior points can be connected by a line segment entirely contained within the region. In practice, medical targets may exhibit small local concavities or boundary irregularities; we refer to such globally convex-like shapes as near-convex. Motivated by this, we derive Hadwiger Shape Priors from Hadwiger's theorem as an interpretable global regularizer using three 2D measures: area A, perimeter P, and Euler characteristic chi, enabling transfer across organs and modalities. However, because medical datasets are shape-heterogeneous, enforcing near-convex priors uniformly can over-regularize non-convex anatomy with significant concavities, washing out concavities and fine details and degrading segmentation accuracy. To address this challenge, we propose Conflict-Aware Objective Balancing (CAOB), which integrates shape priors with segmentation in a gradient-aware manner. For each prior, CAOB removes only the gradient component that conflicts with segmentation while preserving the remaining aligned component, and adaptively regulates objective influences to prevent prior dominance. This enables stable use of shape priors on shape-heterogeneous data without erasing genuine concavities or fine structural details. We call this plug-and-play framework HadBalance.

This paper introduces ARAPDiffusion, a latent diffusion model to learn the underlying continuous shape space of a deformation shape collection. The key innovation is in injecting the as-rigid-as-possible (ARAP) deformation model as regularization losses into latent diffusion (LD), releasing the requirement of having abundant 3D training data for learning generative models. In contrast to the standard LD, we show how the ARAP model can be used to improve both the encoder/decoder and the LD model. The training procedure alternates between using the synthetic distribution defined by the LD model to develop a regularization loss that enhances the shape encoder/decoder and using the shape decoder to develop a regularization loss to improve the LD model. We also show the benefit of the LD paradigm in combining a representation-free LD process and an implicit shape decoder that is applicable to unorganized point clouds. The experimental results of unconditional and conditional shape generation demonstrate the advantages of ARAPDiffusion over baseline approaches.

Generalized segmentation of medical images prevents performance degradation when different imaging devices and clinical protocols are used across multiple domains. The Whitening Transform-based Probabilistic Shape Regularization Extractor (WT-PSE), published in IEEE Transactions on Medical Imaging in 2024, addresses this challenge by employing feature decorrelation and Wasserstein distance-based knowledge distillation to achieve robust cross-domain segmentation. This study systematically examines improvements to the WT-PSE learning framework. Four limitations in the original implementation are identified: limited training augmentations that fail to simulate real scanner variations, reliance on per-pixel binary cross-entropy loss that is sensitive to edge noise, the absence of a scheduled loss weighting strategy that may destabilize early training, and the lack of ablation switches for controlled scientific comparison. To address these issues, we propose four enhancements: (1) domain-adaptive augmentation including random erasing, gamma correction, and salt-and-pepper noise; (2) a hybrid BCE and Dice loss function for improved edge-aware segmentation under noisy conditions; (3) a curriculum-based Dice weight scheduling strategy; and (4) command-line control flags for systematic ablation studies. Experiments on the fundus optic disc segmentation benchmark demonstrate that the improved pipeline achieves a final epoch optic-disc Dice score of 0.956 and an ASD score of 13.31, outperforming the baseline epoch-5 Dice score of 0.939. These results indicate that training-level improvements can provide consistent performance gains without modifying the underlying WT-PSE architecture.

Robotics manipulation usually assumes that the shape and pose of the object are known to the robot prior to motion planning. However, precise geometric information is not always available in practice, and pose inference suffers from sensor uncertainties and view occlusion. In this work, we propose a unified model-based geometric framework integrating robotic haptic perception, modeling, and manipulation planning. Our novelties involve: \textit{i)} Introducing Bayesian Optimization (BO) to guide the haptic exploration for object shape inference, where superellipses are used to approximate geometric boundary; \textit{ii)} Adaptive formulation of manipulation potential encoding object geometry for quasi-static robot-object interaction; \textit{iii)} Proposing an online Ordinary Differential Equation (ODE) for real-time pose inference based on model prediction and tactile feedback. We deploy our system on a 2D robotic sorting task, and vary object geometries to validate the robustness and generalizability of our framework in both simulation and a real-world multi-arm setup.

Reported retrieval scores for training-free shape descriptors conflate local signal design, normalization, aggregation, codebook fitting, and metric choices, making isolated component evaluation difficult. This paper reframes descriptor evaluation as a {\em protocol audit}. We introduce Diffused Geodesic Moments (DGM), a seed-conditioned descriptor that computes sparse implicit heat responses, converts them to distance-like fields, and summarizes each vertex by low-order moments across seeds and scales. DGM is used both as a practical non-spectral baseline and as an instrument for isolating protocol effects. On the registered FAUST benchmark split (FAUST-Reg) and the TOSCA shape collection, aggregation-matched experiments show that an independent Geometric Moment Shape Descriptor baseline built on Heat Kernel Signature features (GMSD-HKS) obtains the highest scores in this implementation ($0.621/0.820$ and $0.865/0.963$ mean average precision (mAP)/top-1), Wave Kernel Signature (WKS) remains a strong classical signal, and DGM is useful mainly when sparse solves, non-spectral deployment, or symmetry-informative seed frames are priorities. The broader finding is methodological: the input field and aggregation protocol can dominate the moment formula. The paper contributes a reproducible protocol-cascade analysis, a cross-shape alignment diagnostic for functional-map compatibility, and concrete recommendations for designing and reporting training-free shape descriptors.

Real-time anomaly segmentation demands both high recall and efficient low-precision inference. We study the three-way interaction of model architecture, model scale, and FP4 quantization-aware training (QAT) recipe on a recall-critical brain tumor segmentation task, evaluating multiple architectures, scales, and QAT recipes under a unified protocol. We find that architecture choice has the largest impact on quantization robustness, with attention-based architectures showing remarkable resilience to recipe choice while CNN degrades under gradient-quantizing recipes at larger scales. At low capacity, FP4 can discretize softmax attention, but advanced QAT recipes prevent this collapse. At larger scales, advanced recipes mitigate gradient quantization noise that degrades CNN quality. Five-fold patient-level cross-validation confirms these findings are robust to data partition. Our results show that the Swin Transformer is robust to QAT recipe choice across all scales, making it the recommended architecture for FP4-quantized anomaly segmentation.

The problem of object pose and shape estimation has seen key advancements lately. Encoder-decoder (e.g., SAM3D, LRM, CRISP) and diffusion-based models (e.g., InstantMesh, Zero123, SceneComplete) have shown category-agnostic shape encoding capacity and open-set generalizability. In this work, we ask the question: Are the object pose and shape estimation methods mature enough, such that when used with antipodal grasp sampling, can outperform the end-to-end grasp synthesis methods? We explore this question in detail by scoping our study to parallel jaw grippers, 7-DoF grasps, and single-view RGB(-D) image as input. We implement and compare a state-of-the-art, end-to-end grasp synthesis method and three modular methods, which first estimate the object pose and shape for all objects in the scene, and generate grasps using antipodal sampling. We observe that the modular methods outperform the end-to-end method in all our experiments. The modular methods are able to synthesize plenty of grasps, even for small objects, where the end-to-end methods fail. The effectiveness of the modular methods is contingent on the accuracy of the pose and shape estimation, and suffers partial degradation in cluttered scenes - a limitation of the existing pose and shape estimation methods. We also analyze the failure modes and run-times for the three modular methods, which use two different ways of object pose and shape estimation: one based on an encoder-decoder model, while another a diffusion model. Finally, we demonstrate that the single-view object pose and shape estimation methods can be augmented with vision-language models to yield language-conditioned grasps from just single-view RGB-D image as input. We notice comparable performance to the state-of-the-art LERF-TOGO baseline.

Advancements in 3D curve skeletonization are accelerating progress across a wide range of applications. However, developing robust skeletonization algorithms that capture intricate object details remains challenging. Skeletonization via Local Separators (LS) offers an efficient graph-based approach but suffers from representation inaccuracies due to its discrete nature. To address this, we introduce CSCD, a novel framework for Curve Skeletonization in the Continuous Domain, generalizing LS to manifolds. Specifically, we present two realizations: CSCD-M for meshes and CSCD-PC for point clouds. CSCD-M leverages the intrinsic triangulation of a mesh for resilience to noise and improved topological preservation, while CSCD-PC employs tufted Laplacians for enhanced robustness. To our knowledge, CSCD-M is the first intrinsic method for curve skeletonization. Our results show CSCD-M matches LS performance across diverse meshes and outperforms LS (TOG'21) on benchmarks like Thingi10k dataset. CSCD-PC qualitatively outperforms CoverageAxis++ (Eurographics'24) and EPCS (CAG'23). Finally, we demonstrate the efficacy of CSCD in a few downstream tasks: object classification, shape segmentation, identifying handles, tunnels, and constrictions in objects. Project Website: https://cscd-skel.pages.dev

Amodal instance segmentation aims to predict the complete object mask including occluded regions that lack pixel-level observations and must be inferred with the aid of shape priors. Existing methods acquire shape priors through fixed-capacity encoding spaces or expensive generative models, and inject them uniformly across all spatial positions without adapting to the varying prior demand between visible and occluded regions. In this paper, we propose a gated reliability-adaptive shape prior framework, which introduces a shape prior memory module that combines learnable prototypes via cross-attention to produce instance-adaptive shape priors through weighted prototype combination rather than generation. A spatial adaptive reliability gate then employs the signed distance field of the visible mask to modulate injection intensity at each position according to its occlusion depth, preserving reliable features in visible regions while directing shape compensation toward occluded areas. Experiments on two mainstream amodal instance segmentation benchmarks demonstrate that the proposed method outperforms existing approaches under multiple evaluation settings, improving the mean intersection-over-union over occluded regions by over 11 percentage points on one of the two benchmarks under the standard setting, while using approximately one-third of the total parameters. Linear probing analysis further reveals that the visible-mask cross-attention module implicitly encodes occlusion geometry into visual token representations, explaining the effectiveness of the proposed module decomposition.

Discovering shapelets -- i.e., discriminative temporal patterns within time series -- has been widely studied to address the inherent complexity of time-series classification (TSC) and to make model decision-making processes more transparent. However, existing methods primarily focus on population-level shapelets optimized across the entire dataset, which leads to two fundamental limitations: (i) population-level patterns often misalign with instance-specific features, resulting in suboptimal performance and potentially misleading interpretations, and (ii) most methods treat shapelets as independent entities, overlooking important temporal dependencies and interactions among multiple patterns. To address these limitations, we propose INSHAPE, an interpretable TSC framework that discovers variable-length, discriminative temporal patterns specific to each time series. INSHAPE identifies these patterns as non-overlapping segments and models their temporal dependencies, thereby providing clear instance-level interpretations while achieving strong predictive performance. Furthermore, INSHAPE bridges local and global interpretability through a bottom-up approach, aggregating instance-level shapelets into prototypical (population-level) shapelets. Extensive experiments on 128 UCR and 30 UEA benchmark datasets show that INSHAPE consistently outperforms state-of-the-art shapelet-based methods while providing more intuitive and interpretable insights.

Convexity is a fundamental geometric prior that underlies many natural and man-made structures, yet remains challenging to impose effectively in end-to-end trainable segmentation networks. We revisit convexity from a functional perspective and propose a unified, threshold-free convexity prior based on the quasi-concavity of the network's output mask function u. Instead of constraining a single binary segmentation, we require all super-level sets of u to be convex, transforming global shape constraints into local, differentiable inequalities on u and its derivatives. From this principle, we derive zero, first, and second-order characterizations, yielding respectively a local midpoint convexification algorithm, a gradient-based condition linked to supporting hyperplanes, and a sufficient second-order inequality expressed as a quadratic form on the tangent plane. The first and second-order formulations produce a compact convolutional loss that can be densely applied across the image without thresholding. Our quasi-concavity losses integrate seamlessly with modern segmentation networks via the proposed convex gradient projection module (CGPM). They consistently enforce convexity and improve shape regularity across multiple datasets, outperforming networks tailored for retinal segmentation and surpassing previous shape-aware methods. Remarkably, our analysis unifies a wide spectrum of previous convex shape models, from discrete 1-0-1 line constraints and graph-cuts convexity formulations to curvature or signed distance Laplacian based level-set priors, within a single continuous and differentiable framework.

Infrared object detection is crucial for perception in autonomous driving and surveillance but remains vulnerable to physical adversarial attacks. Unlike in the RGB domain, where attacks rely on color texture, infrared attacks must manipulate thermal signatures, making the geometry shape of heat-blocking materials the primary adversarial information carrier. Current shape-based methods suffer from a fundamental trade-off between representational capability and optimization power, limiting their attack effectiveness.In this work, we overcome this dilemma by introducing learnable Fourier shapes to the infrared domain. We utilize an end-to-end differentiable framework where a compact set of Fourier coefficients, defining the shape boundary, is analytically mapped to a pixel-space mask via the winding number theorem. This enables efficient gradient-based optimization to generate potent shapes that cause human targets to evade detection. Extensive digital and physical experiments provide a comprehensive evaluation and validate our superior performance. Our resulting physical patch achieves striking robustness, successfully evading detectors across diverse distances, angles, poses, and individuals, and achieves over 88% attack success rate at distances greater than 25m (conf.=0.5). Code is available at https://github.com/Yongyx99/Fourier-shape-attack.

Accurate estimation of plant skeletal structures (e.g., branching structures) from images is essential for smart agriculture and plant science. Unlike human skeletons with fixed topology, plant skeleton estimation presents a unique challenge, i.e., estimating arbitrary tree graphs from images. To address this problem, we introduce PlantPose, a universal plant skeleton estimator via tree-constrained graph generation. PlantPose combines learning-based graph generation with traditional graph algorithms to enforce tree constraints during the training loop. To enhance the model's generalization capability, we curate a large and diverse dataset comprising real-world and synthetic plant images, along with simplified representations (e.g., sketches and abstract drawings). This dataset enables the generalized model to adapt to diverse input styles and categories of plant images while preserving topological consistency. Our approach demonstrates robust and accurate plant skeleton estimation across multiple domains, including previously unseen out-of-domain scenarios. Further analyses highlight the method's strengths and limitations in handling complex, heterogeneous data distributions. All implementations and datasets are available at https://github.com/huntorochi/PlantPose/.

Hyperdimensional (HD) computing offers an attractive alternative to deep networks for edge learning due to its simplicity, fast prototype-based inference, and compatibility with online updates. However, standard pixel-based HD encoders are brittle: small distribution shifts such as rotation, noise, or occlusion can drastically reduce accuracy. We extract discrete topological primitives-most notably holes-from binarized shapes and pair them with rotation/translation/scale (RTS)-invariant shape signatures. Our method constructs RTS-stable descriptors for (i) the outer shape using a spatial-pyramid variant of Zernike moments and (ii) each hole using an intrinsic Fourier descriptor of its radial signature together with RTS-canonical relative geometry. Each primitive is mapped to a bipolar hypervector via randomized projection and role binding, and variable-cardinality hole sets are aggregated by permutation-invariant bundling to form a single image hypervector. To avoid over-weighting any cue, we learn nonnegative reliability weights for the Zernike and hole channels on a validation set via late fusion of cosine similarities. Experiments on MNIST and EMNIST under controlled corruptions (rotation, Gaussian noise, salt-and-pepper, cutout, zoom) show that Topology-guided HD computing substantially improves robustness compared with a naive HD baseline, maintaining high accuracy across multiple corruption families and benefiting from lightweight online training. Compared with a compact CNN trained on clean data, our method achieves competitive clean accuracy while offering markedly stronger robustness to several pixel-level corruptions, demonstrating that explicit topological structure is a practical route to robust HD representations. The code is provided at https://github.com/arpan-kusari/Topological-HDC.

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

High-dimensional point cloud data arise across many scientific domains, especially single-cell biology. The shapes or topologies of these datasets determine the types of information that can be extracted. For example, clustered data supports cell-type identification, trajectory structures support transition analysis, and archetypal structures capture continua of cellular behaviors. Existing analysis pipelines often assume a specific shape. The standard Seurat pipeline combines UMAP visualization with Louvain clustering and therefore assumes clustered data, while tools such as Monocle and SPADE assume tree-like structures, and flow-based models such as MIOFlow and Conditional Flow Matching target trajectories. Choosing which pipeline to apply is therefore often left to bioinformaticians who visually inspect datasets before selecting an analysis strategy. With the rise of agentic AI scientists, automating shape detection is increasingly important for selecting downstream analysis pipelines. To address this problem, we introduce scShapeBench, a benchmark dataset for shape detection containing both synthetic and expert-annotated single-cell datasets. Synthetic datasets are sampled from ground-truth skeleton graphs with controlled variance. Real single-cell datasets are curated from diverse sources and annotated by experts into four categories: clusters, single trajectory, multi-branching, and archetypal. We additionally introduce scReebTower, a baseline method that uses diffusion geometry to extract Reeb graphs and connect visualization with pipeline selection. We provide topology-aware evaluation metrics and compare scReebTower against PAGA and Mapper on synthetic and real data. Our results indicate that scReebTower outperforms existing baselines. Overall, our contributions span benchmarks, evaluation metrics, and a baseline for automated shape detection in single-cell data.

Deep generative models provide flexible frameworks for modeling complex, structured data such as images, videos, 3D objects, and texts. However, when applied to sequences of human skeletons, standard variational autoencoders (VAEs) often allocate substantial capacity to nuisance factors-such as camera orientation, subject scale, viewpoint, and execution speed-rather than the intrinsic geometry of shapes and their motion. We propose the Elastic Shape - Variational Autoencoder (ES-VAE), a geometry-aware generative model for skeletal trajectories that leverages the transported square-root velocity field (TSRVF) representation on Kendall's shape manifold. This representation inherently removes rigid translations, rotations, and global scaling of shapes, and temporal rate variability of sequences, isolating the underlying shape dynamics. The ES-VAE encoder maps skeletal sequences to a low-dimensional latent space incorporating the Riemannian logarithm map, while the decoder reconstructs sequences using the corresponding exponential map. We demonstrate the effectiveness of ES-VAE on two datasets. First, we analyze skeletal gait cycles to predict clinical mobility scores and classify subjects into healthy and post-stroke groups. Second, we evaluate action recognition on the NTU RGB+D dataset. Across both settings, ES-VAE consistently outperforms standard VAEs and a range of sequence modeling baselines, including temporal convolutional networks, transformers, and graph convolutional networks. More broadly, ES-VAE provides a principled framework for learning generative models of longitudinal data on pose shape manifolds, offering improved latent representation and downstream performance compared to existing deep learning approaches.

Humans grasp unfamiliar objects by combining an initial visual estimate with tactile and proprioceptive feedback during interaction. We present ShapeGrasp, a robotic implementation of this approach. The proposed method is an iterative grasp-and-complete pipeline that couples implicit surface visuo-haptic shape completion (creation of full 3D shape from partial information) with physics-based grasp planning. From a single RGB-D view, ShapeGrasp infers a complete shape (point cloud or triangular mesh), generates candidate grasps via rigid-body simulation, and executes the best feasible grasp. Each grasp attempt yields additional geometric constraints -- tactile surface contacts and space occupied by the gripper body -- which are fused to update the object shape. Failures trigger pose re-estimation and regrasping using the refined shape. We evaluate ShapeGrasp in the real world using two different robots and grippers. To the best of our knowledge, this is the first approach that updates shape representations following a real-world grasp. We achieved superior results over baselines for both grippers (grasp success rate of 84% with a three-finger gripper and 91% with a two-finger gripper), while improving the 3D shape reconstruction quality in all evaluation metrics used.

Articulation modeling aims to infer movable parts and their motion parameters for a 3D object, enabling interactive animation, simulation, and shape editing. In this paper, we present Sketch2Arti, the first sketch-based articulation modeling system for CAD objects. Our key observation is that designers naturally communicate articulation intent through lightweight sketches (e.g., arrows and strokes) that indicate how parts should move, yet translating such sketches into articulated 3D models remains largely manual. Sketch2Arti bridges this gap by enabling users to specify articulation through simple 2D sketches drawn from a chosen viewpoint. Given a CAD model and user sketches, our approach automatically discovers the corresponding movable parts and predicts their motion parameters, allowing iterative modeling of multiple articulations on complex objects with fine-grained control. Importantly, Sketch2Arti is trained in a category-agnostic manner without requiring object category information, leading to strong generalization to diverse objects beyond existing articulation datasets. Moreover, for shell models lacking interior structures, Sketch2Arti supports controllable internal completion guided by user sketches, generating plausible internal components consistent with the existing geometry and predicted motion constraints. Comprehensive experiments and user evaluations demonstrate the effectiveness, controllability, and generalization of Sketch2Arti. The code, dataset, and the prototype system are at https://arlo-yang.github.io/Sketch2Arti.

Object recognition (OR) in humans relies heavily on shape cues and the ability to recognize objects across varying 3D viewpoints. Unlike humans, deep networks often rely on non-shape cues such as texture and background, leading to vulnerabilities in generalization and robustness. To address this gap, we introduce ShapeY, a novel and principled benchmarking framework designed to evaluate shape-based recognition capability in OR systems. ShapeY comprises 68,200 grayscale images of 200 3D objects rendered from multiple viewpoints and optionally subjected to non-shape ``appearance'' changes. Using a nearest-neighbor matching task, ShapeY specifically probes the fine-grained structure of an OR system's embedding space by evaluating whether object views are clustered by 3D shape similarity across varying 3D viewpoints and other non-shape changes. ShapeY provides a suite of quantitative and qualitative performance readouts, including error rate graphs, viewpoint tuning curves, histograms of positive and negative matching scores, and grids showing ordered best matches, which together offer a comprehensive evaluation of an OR system's shape understanding capability. Testing of 321 pre-trained networks with diverse architectures reveals significant challenges in achieving robust shape-based recognition: even state-of-the-art models struggle to generalize consistently across 3D viewpoint and appearance changes, and are prone to infrequent but egregious matches of objects of obviously completely different shape. ShapeY establishes a principled framework for advancing artificial vision systems toward human-like shape recognition capabilities, emphasizing the importance of disentangled and invariant object encodings.

Expressive Human Pose and Shape Estimation (EHPS) plays a crucial role in various AR/VR applications and has witnessed significant progress in recent years. However, current state-of-the-art methods still struggle with accurate parameter estimation for facial and hand regions and exhibit limited generalization to wild images. To address these challenges, we present CoEvoer, a novel one-stage synergistic cross-dependency transformer framework tailored for upper-body EHPS. CoEvoer enables explicit feature-level interaction across different body parts, allowing for mutual enhancement through contextual information exchange. Specifically, larger and more easily estimated regions such as the torso provide global semantics and positional priors to guide the estimation of finer, more complex regions like the face and hands. Conversely, the localized details captured in facial and hand regions help refine and calibrate adjacent body parts. To the best of our knowledge, CoEvoer is the first framework designed specifically for upper-body EHPS, with the goal of capturing the strong coupling and semantic dependencies among the face, hands, and torso through joint parameter regression. Extensive experiments demonstrate that CoEvoer achieves state-of-the-art performance on upper-body benchmarks and exhibits strong generalization capability even on unseen wild images.

This study presents a Shape from Shading (SfS) framework to enhance sub-metre resolution lunar digital elevation models (DEMs) using imagery from the Orbiter High Resolution Camera (OHRC) aboard Chandrayaan-2. The framework applies SfS to an independent OHRC image of the same region, enabling SfS not just as a refinement tool, but as a source of new topographic data, unconstrained by stereo baseline limitations. The method is applied across three lunar sites, including the Cyrillus crater, the Vikram landing region, and the lunar south pole (Mons Mouton), with a systematic three-stage parameter sweep on the SfS smoothness weight. Results show measurable topographic enhancement, particularly in surface slope statistics, revealing fine-scale crater morphology previously unresolved. A limiting case is also characterized, where large pitch angle separation between the shading image and stereo pair reduces SfS sensitivity, and partial footprint coverage of the shading image is identified as a factor influencing spatially variable enhancement quality.

Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strength of both paradigms by estimating the coefficients of a low-dimensional Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector directly amenable to model-based control, while retaining the modularity, probabilistic treatment and computational efficiency of factor graph inference. The proposed method is evaluated in simulation on a 0.4 m long tendon-driven continuum robot under three measurement configurations, achieving mean position errors below 2 mm for all three scenarios and demonstrating a sixfold reduction in orientation error compared to a Gaussian process regression baseline when only position measurements are available.

Given a demonstration, a robot should be able to generalize a skill to any object it encounters-but existing approaches to skill transfer often fail to adapt to objects with unfamiliar shapes. Motivated by examples of improved transfer from compositional modeling, we propose a method for improving transfer by decomposing objects into their constituent semantic parts. We leverage data-efficient generative shape models to accurately transfer interaction points from the parts of a demonstration object to a novel object. We autonomously construct an objective to optimize the alignment of those points on skill-relevant object parts. Our method generalizes to a wider range of object geometries than existing work, and achieves successful one-shot transfer for a range of skills and objects from a single demonstration, in both simulated and real environments.

Parametric 3D human models such as SMPL have driven significant advances in human pose and shape estimation, yet their simplified kinematics limit biomechanical realism. The recently proposed SKEL model addresses this limitation by re-rigging SMPL with an anatomically accurate skeleton. However, estimating SKEL parameters directly remains challenging due to limited training data, perspective ambiguities, and the inherent complexity of human articulation. We introduce SKEL-CF, a coarse-to-fine framework for SKEL parameter estimation. SKEL-CF employs a transformer-based encoder-decoder architecture, where the encoder predicts coarse camera and SKEL parameters, and the decoder progressively refines them in successive layers. To ensure anatomically consistent supervision, we convert the existing SMPL-based dataset 4DHuman into a SKEL-aligned version, 4DHuman-SKEL, providing high-quality training data for SKEL estimation. In addition, to mitigate depth and scale ambiguities, we explicitly incorporate camera modeling into the SKEL-CF pipeline and demonstrate its importance across diverse viewpoints. Extensive experiments validate the effectiveness of the proposed design. On the challenging MOYO dataset, SKEL-CF achieves 85.0 MPJPE / 51.4 PA-MPJPE, significantly outperforming the previous SKEL-based state-of-the-art HSMR (104.5 / 79.6). These results establish SKEL-CF as a scalable and anatomically faithful framework for human motion analysis, facilitating the use of computer vision techniques in biomechanics-related analysis. Our implementation is available on the project page: https://pokerman8.github.io/SKEL-CF/.

Maintaining proper form while exercising is important for preventing injuries and maximizing muscle mass gains. Detecting errors in workout form naturally requires estimating human's body pose. However, off-the-shelf pose estimators struggle to perform well on the videos recorded in gym scenarios due to factors such as camera angles, occlusion from gym equipment, illumination, and clothing. To aggravate the problem, the errors to be detected in the workouts are very subtle. To that end, we propose to learn exercise-oriented image and video representations from unlabeled samples such that a small dataset annotated by experts suffices for supervised error detection. In particular, our domain knowledge-informed self-supervised approaches (pose contrastive learning and motion disentangling) exploit the harmonic motion of the exercise actions, and capitalize on the large variances in camera angles, clothes, and illumination to learn powerful representations. To facilitate our self-supervised pretraining, and supervised finetuning, we curated a new exercise dataset, Fitness-AQA (https://github.com/ParitoshParmar/Fitness-AQA), comprising of three exercises: BackSquat, BarbellRow, and OverheadPress. It has been annotated by expert trainers for multiple crucial and typically occurring exercise errors. Experimental results show that our self-supervised representations outperform off-the-shelf 2D- and 3D-pose estimators and several other baselines. We also show that our approaches can be applied to other domains/tasks such as pose estimation and dive quality assessment.