A fundamental challenge in artificial intelligence is the transformation of observations into explicit symbolic representations suitable for abstraction, interpretation, and reasoning. While modern AI systems achieve remarkable perceptual capabilities through large-scale statistical learning, the resulting knowledge is typically encoded within latent parameters that are difficult to inspect or manipulate analytically. Inspired by Neuro-Symbolic AI and theories of human abstraction, this paper investigates the formation of symbolic mathematical representations from geometric observations. We propose NeuSOGA (Neuro-Symbolic Geometric Abstraction), a framework that progressively transforms observations into topological abstractions, geometric abstractions, and ultimately symbolic mathematical representations. The architecture combines topology-guided structural discovery using Euclidean Distance Transforms, foundation-model perception using Segment Anything, adaptive multi-scale geometric abstraction, and symbolic synthesis through Implicit Area Splines. The resulting representation is an analytical implicit model supporting arbitrary-order smoothness, additive composition, and closed-form evaluation. Unlike neural latent encodings, the generated representation remains interpretable, editable, and mathematically explicit. Experiments on ModelNet40 point clouds, arbitrary-view projections, and segmented optical observations demonstrate that NeuSOGA transforms diverse observations into compact symbolic representations while preserving essential geometric and topological structure across sensing modalities and viewing directions. NeuSOGA provides an interpretable and explainable pathway from observation to symbol and establishes
Standard Transformers have proven effective in point cloud object classification, but their performance in dense prediction tasks within complex scenes is often hindered by weak prior assumptions. To address this challenge, we propose PCT-Prompt, a novel framework that enhances standard Transformers by introducing a prompt-guided feature branch to improve performance in dense prediction tasks. The standard Transformer branch leverages pre-trained models for global feature extraction from point cloud data, serving as the backbone for processing high-level features. Meanwhile, the prompt-guided feature branch consists of two key components: a fine-grained feature extraction block that captures multi-scale geometric features using geometry-sensitive abstraction layer, along with the PnP-3D layer to integrate local context with global regularization. The second component, the prompt-refined feature learning block generates prompt tokens, which are subsequently refined through cross-attention mechanisms. Additionally, we introduce a prompt drop mechanism that progressively removes prompt information across Transformer layers, balancing local details and global consistency. Experimental results on the ShapeNetPart, S3DIS, and DALES datasets demonstrate that PCT-Prompt significantly improves the adaptability of standard Transformers to dense prediction tasks, achieving strong performance in real-world scenarios.
Learning reliable correspondences between images and point clouds is fundamental for 2D-3D matching. Despite recent progress in detection-free methods, existing approaches primarily optimize matching within a single model and often struggle to maintain reliable correspondences under challenging conditions such as noisy inputs, low overlap, and ambiguous structures. In this work, we propose TeaMatch, a novel framework that introduces teachability as a criterion for cross-modal representation learning. We define teachability as the ability of a representation to be effectively recovered by weak learners under degraded inputs, reflecting its structural consistency and robustness. To this end, we construct a set of task-specific weak students that simulate common failure modes and train them to imitate the teacher on a training split while evaluating their recoverability on a disjoint meta split. The teacher is then optimized to improve the students' ability to recover reliable correspondences, guided by correspondence-level and geometry-aware constraints. Our framework can be seamlessly integrated into existing coarse-to-fine matching pipelines without additional inference cost. Extensive experiments demonstrate that TeaMatch improves matching robustness and achieves state-of-the-art performance on challenging 2D-3D matching benchmarks.
Research regarding the sign language recognition mostly relies on RGB images, whileas sign language datasets that provide depth images are limited. Point clouds obtained from depth images can be used for sign language recognition with neural networks like PointNet. In recent years, various neural networks are used for generating realistic depth images from monocular RGB images. In this work, synthetic depth images were created from RGB images using Depth Anything V2 network. For this purpose, three sign language datasets (Real-time ASL Fingerspelling, KArSL, AUTSL) which contain both RGB and depth images were used. Classification accuracies of the point cloud data created from both original and synthetic depth images using various PointNet architectures were measured for sign language recognition. From the original and synthetic point clouds, frame based, Point Gesture Map and Long Short Term Memory data models were used for classification and their performances were compared. In the results, both original and synthetic based data achieved acceptable performance in most models. In general, original depth based point cloud models performed better than synthetic ones, however in some models synthetic depth based models performed better than the originals.
Dense 3D sensors in various real-world fields produce point clouds that are geometrically redundant for real-time processing. In this paper, we propose an efficient and scalable learning-based anisotropic surface approximation framework, HD-PEA, that operates directly on unstructured point clouds, integrating anisotropic optimization into reconstruction to produce compact, geometry-aligned surface representations with higher fidelity, fewer elements, and improved numerical stability compared to isotropic and adaptive meshes. Firstly, we develop a novel learning-based high-dimensional (high-d) Euclidean point embedding method to map the input point clouds into a high-d manifold embedding space. For handling large-scale point clouds without retraining and fine-tuning, a patch-based meta-embedding scheme is designed during the inference stage. Then, we develop a new tangent subspace estimation for the high-d embedding manifold approximation and anisotropic manifold reconstruction in high-d space. The main contribution of this work is to propose a scalable deep learning framework and a variety of datasets for constructing a high-d Euclidean point embedding space aimed to 3D anisotropic surface mesh approximation and Riemannian curvature tensor estimation from point clouds. We extensively evaluate our method against state-of-the-art surface reconstruction approaches using several datasets, such as Thingi10K dataset, AIM@SHAPE and Stanford 3D Scanning Repository, ScanNet dataset, and further demonstrate its generalization and usability on diverse unseen shapes and applications from these datasets.
Sangmin Hong, Daniel Sungho Jung, Heewon Kim +1cs.CV
Point clouds are one of the most fundamental and widely used 3D representations, serving as the most basic geometric representation of 3D shapes. Nevertheless, most existing 3D printing pipelines require a watertight mesh as input, preventing the direct use of point clouds for fabrication. A common workaround is to reconstruct meshes from point clouds; however, the resulting meshes often contain geometric artifacts, such as incorrect faces or topological inconsistencies, that are difficult to repair and may lead to printing failures. To overcome these limitations, we propose PrintAnything, a novel framework that learns to produce executable 3D printing G-code directly from 3D point clouds without requiring mesh reconstruction. To enable point clouds to serve as direct input for slice-wise toolpath generation, we introduce a slice-wise point projection strategy that transforms unstructured 3D point clouds into slice-aligned 2D representations consistent with layer-by-layer nature of fused deposition modeling in 3D printing. To eliminate mesh dependency and provide a unified representation that bridges point clouds and G-code, we propose Geometric plan (G-plan) map, a compact 2D representation composed of occupancy, region, and flow maps that encode the geometric and extrusion properties required for toolpath synthesis in 3D printing. As a result, our proposed method accurately generates printable G-code directly from point clouds, enabling a practical and fully mesh-free pipeline for 3D printing. The code is publicly available at \href{https://github.com/Sangminhong/PrintAnything}{https://github.com/Sangminhong/PrintAnything}.
Modeling continuous object deformation is important for many computer vision and robotics tasks, such as manipulation and simulation. Existing approaches rely on learning-based methods or physics simulators to model shape deformations. However, these approaches either use discrete time steps or are too computationally intensive for real-time applications. We present ODeform, a novel extension of Neural Ordinary Differential Equations to continuous 4D dynamics of deformable objects in 3D space. Our method transforms 3D point clouds and physical conditions (like material properties) into a unified latent space. By solving the resulting ordinary differential equations over time, we model deformations as continuous flows within this learned embedding, eliminating the need for discrete time steps while maintaining computational efficiency. We evaluate our approach on unseen physical parameter configurations, showing improved motion prediction accuracy over baseline methods. Our experiments further demonstrate a successful transfer to real 3D captured objects with novel shapes, along with effective interpolation and extrapolation of the learned dynamics. Our code and data will be made publicly available.
Nicole Feng, Ioannis Gkioulekas, Keenan Cranecs.GR cs.CV
We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points - simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.
Stephan Nebiker, Micha Tschanz, Nando Amport +1cs.CV
Tree growth determines how much CO2 is sequestered from the atmosphere and temporarily stored in woody biomass. At the same time tree growth is affected by increasing temperatures, more frequent drought periods, late frosts and other extreme events associated with climate change. While continuous measurements of radial (secondary) tree growth using dendrometers are well established, monitoring of shoot elongation (primary growth) has largely been neglected because suitable measurement techniques are lacking. As a result, the effects of climate change on primary tree growth remain insufficiently understood. This work aims at reconstructing native deciduous trees in 3D as a basis for measuring and monitoring shoot elongation over entire tree canopies. Here we explored the use of low-cost UAV photogrammetry and of a multi-camera CraneCam system under real-world conditions. Data were collected in two study areas over an entire growing season. We present sensor evaluations, photogrammetric data acquisition and processing strategies. A special focus is placed on the analysis of the resulting photogrammetric 3D point clouds in terms of accuracy, resolution and completeness. Results demonstrate 3D point accuracies of 5-6 mm for entire trees using consumer-grade UAVs weighing less than 250 g and a 3D reconstruction completeness between 92% and 98% depending on the UAV type. The paper introduces a novel 3Dprinted ground-truth branch to evaluate the capability to reconstructing fine-detail structures such as thin tree shoots. Finally, we discuss operational challenges and initial experiments towards a skeletonization of entire trees based on photogrammetric point clouds.
Interactive 3D segmentation aims to extract object masks in point clouds with minimal user clicks. Despite recent progress, most existing approaches still struggle with (i) coarse voxel resolution that blurs fine boundaries under limited clicks and (ii) hard false positives caused by confusing background structures. These issues are exacerbated by density and scale shifts across datasets (e.g., dense RGB-D reconstructions vs. sparse LiDAR scans), where fixed refinement heuristics and purely click-driven decoding generalize poorly. To address them, we propose NegROI -- a novel transformer-based interactive framework that couples click-centric multi-resolution refinement with scene-conditioned negative prompts. Given a coarse voxel prediction, it refines only a local Region Of Interest (ROI) around the current click on a finer grid and fuses refined logits back to the coarse mask. To improve robustness and efficiency, we introduce uncertainty-driven selective refinement that prioritizes ambiguous regions. Meanwhile, we model hard background patterns via a set of scene-conditioned negative prompts obtained by cross-attention over scene tokens. We further stabilize these prompts with a diversity regularizer. Finally, we propose boundary-aware hard negative mining to supervise negative-prompt attention toward boundary-proximal, high-confidence false positives. Our experiments on common benchmark datasets (i.e., ScanNet, S3DIS, and KITTI) demonstrate improved click efficiency and reduced false positives, with stronger cross-dataset robustness than the state-of-the-art baselines.
Functional maps are the cornerstone of recent non-rigid 3D shape matching methods due to their efficiency and performance. However, existing methods struggle with challenging scenarios, such as partiality, topological noise, and raw point clouds. A primary bottleneck is that significant intrinsic distortion prevents truncated spectral bases from being accurately aligned via linear transformations (i.e., functional maps). To address this, we introduce a hyper-network that predicts non-linear neural functional maps (NFM), learned in an unsupervised manner, to better align spectral bases. Specifically, we model the NFM as an MLP with skip-connection to refine standard FM and employ a hyper-network to predict its weights, conditioned on standard FM. Our framework is trained using a novel unsupervised spectral alignment loss. Experiments demonstrate that our approach can be seamlessly integrated into state-of-the-art unsupervised deep functional map pipelines, substantially improving matching accuracy in demanding scenarios.
Detecting and localizing defects in 3D point clouds is challenging because abnormal samples are scarce and diverse, while training is often limited to normal data. We propose Anomaly Factory 3D (AF3AD), a modular framework that synthesizes diverse pseudo-anomalies from normal point clouds to expand the training data for unsupervised 3D anomaly detection methods that rely on pseudo-anomalies. AF3AD uses a center-conditioned parametric deformation model defined in local PCA frames, with kernel-controlled spatial falloff, anisotropy, directional gating, and normal/tangential displacement fields, enabling a broad set of geometric defect presets. We demonstrate its ease-of-use and effectiveness by integrating AF3AD with an offset-prediction detector and a reconstruction-based anomaly detection method, showing that AF3AD transfers across detection paradigms. Experiments on AnomalyShapeNet and Real3D-AD show consistent improvements in object- and point-level detection and localization, supported by ablations on preset groups and robustness under noise. AF3AD is designed as a standalone synthesis tool to facilitate adoption across different 3D anomaly detection paradigms. Code is available at github.com/vpc-ccg/AF3AD.
Object pose estimation is crucial to many industrial applications, with one example being automated spray painting using a robot. However, confidentiality concerns often limit access to high-quality 3D models, posing a significant challenge for point-cloud-based pose estimation. In such scenarios, rotational symmetry, a readily accessible characteristic of many industrial objects, can provide valuable prior information to facilitate pose estimation.In this paper, we propose a method that leverages the rotational symmetry commonly found in industrial objects to address the challenge caused by the absence of 3D models. The object pose is jointly estimated with point cloud refinement through an iterative optimization process. This optimization relies on a rotational symmetry constraint loss. To construct this loss, each 3D point is rotated according to the currently estimated pose, and multiple correspondences are identified using nearest-neighbor search by exploiting the rotational symmetry property. These correspondences are then used to compute the rotational symmetry constraint loss, which iteratively refines both the pose and the point cloud.By explicitly incorporating rotational symmetry into the optimization process, the proposed method achieves robust pose estimation and generalizes well across diverse object types. The proposed method is evaluated on a dataset specifically created for point clouds without known 3D models, consisting of four categories of synthetic objects and one real wheel hub collected from a production line. Experimental results demonstrate that the proposed method achieves performance comparable to methods that rely on known 3D models.
We present WireframeDETR, our submission to the Structured Semantic 3D Reconstruction (S23DR) 2026 Challenge, which requires predicting a 3D building wireframe from multi-view COLMAP point clouds. Our method applies DETR-style set prediction directly to 3D point clouds, producing wireframes as sets of edge coordinate pairs without any intermediate vertex detection stage. We introduce three technical contributions: (1) contrastive denoising training that stabilises noisy Hungarian matching in early epochs; (2) a multi-scale encoder that aggregates the last encoder layer outputs via learned scalar weights; and (3) progressive auxiliary loss weighting that concentrates gradient signal on the decoder layers that most benefit from it. Our model achieves a public test HSS of 0.575 (F1~=~0.664, IoU~=~0.516) and a best validation HSS of 0.534 on the cleaned val split.
We address 4D reconstruction from partial point cloud sequences, where depth-sensor observations are incomplete, unordered, and lack explicit temporal correspondences. This geometry-only setting is challenging due to missing observations and ambiguous dynamics. While recent progress has largely relied on image-based methods, existing point-based approaches typically focus on single objects, assume relatively complete inputs, or require explicit correspondences. To address these limitations, we propose DynaTok, a point-based framework for correspondence-free 4D reconstruction from partial point cloud sequences without images. DynaTok encodes frames into compact latent tokens, aggregates incomplete observations over time with a Transformer-based spatiotemporal encoder, and decouples geometry and motion through residual tokens in a unified model. A flow-matching decoder then reconstructs complete, temporally consistent 4D point-cloud sequences conditioned on the latent tokens. Experiments on object- and scene-level benchmarks demonstrate improved reconstruction quality and temporal coherence from partial point cloud observations. Project page: https://wrchen530.github.io/dynatok/.
This research introduces a framework for incorporating Concept Bottleneck Models (CBMs) into 3D generative architectures to address the inherent 'semantic gap' in deep geometric learning. As deep models become central to 3D content creation, explainability shifts from a peripheral feature to a fundamental requirement for trust and accountability in safety-critical domains such as healthcare and manufacturing. CBMs provide an intrinsic interpretability solution by constraining latent representations to align with human-defined concepts, yet their application to unstructured 3D data remains largely unexplored. We design, implement, and validate a formal 3D-CBM architecture that maps raw geometric inputs, including point clouds and meshes, into a multi-tiered taxonomy of interpretable primitives and functional attributes. The framework further identifies strategic datasets, such as PartNet and ShapeNet, specialized for concept-based supervision. Experimental results from a 3D part-manipulation proof-of-concept experiment demonstrate the framework's efficacy, achieving a concept prediction accuracy of 88.8\% and a Chamfer Distance of 0.0115. Critically, the model enables precise test-time intervention, allowing for the interactive correction of structural errors. This work establishes a foundation for semantically-steerable 3D generation and invites further exploration into collaborative human-in-the-loop design systems.
Danqi Zhuang, Jisui Huang, Xiaoyue Xi +4cs.CV cs.AI math.PR
Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation. While this choice is analytically convenient and empirically powerful, it provides little explicit structure for data concentrated near low-dimensional manifolds, where different regions of the data distribution may correspond to distinct local geometric or semantic factors. As a result, the reverse model must recover manifold-level structure almost entirely from an unstructured terminal reference distribution. We propose PTL-Diffusion, a proof-of-concept diffusion framework whose forward noising process converges to a nonconstant periodic family of Gaussian terminal laws rather than to a single invariant law. Unlike a phase-conditioned DDPM, where phase information only enters the denoising network while the forward process remains unchanged, PTL-Diffusion embeds phase structure directly into the forward noising dynamics. The proposed construction remains close to standard denoising diffusion models: for a periodically forced Ornstein--Uhlenbeck-type forward process, we derive closed-form forward marginals, the limiting periodic Gaussian terminal family, and explicit Gaussian reverse posteriors, enabling standard noise-prediction training. We also introduce an invariant-average regularization term coupling the phase-conditioned reverse dynamics through the averaged periodic reference law. Experiments on torus and cylinder point-cloud benchmarks and the Olivetti face dataset show that PTL-Diffusion improves manifold-level distributional matching over matched DDPM baselines, reducing phase-conditioned errors, feature-space covariance errors, and nearest-neighbour manifold distances. These results suggest structured terminal reference laws as a promising direction, while motivating more expressive phase constructions and larger-scale evaluations.
Unmanned Aerial Vehicle (UAV) multispectral point clouds (MPC) provide high-dimensional spatial-spectral data for sub-canopy target detection; however, their efficacy is significantly compromised by severe illumination heterogeneity caused by vegetation shadows. To address this, we propose a prior-free anomaly detection framework capable of robustly handling lighting variations. First, we formulate solar angle estimation as an inverse optimization problem. By coupling spectral indices with a ray-tracing model, this strategy achieves Prior-Free Shadow Extraction without relying on flight metadata, effectively distinguishing dark objects from true shadows. Second, to mitigate spectral distortions, we introduce an Illumination-Consistent Sparse Representation mechanism. Unlike standard reconstruction methods, we construct a background dictionary strictly from neighbors sharing the same illumination state. This constraint effectively disentangles spectral reflectance from lighting variations, ensuring that targets are represented solely by physically consistent background points. Experimental results indicate that the proposed method significantly improves the separability between anomalies and background in complex forest environments, demonstrating superior performance over state-of-the-art baselines. This framework is particularly suited for identifying camouflaged military targets, mapping fallen tree trunks, and uncovering archaeological ruins hidden beneath dense foliage.
Maciej Wielgosz, Stefano Puliti, Rasmus Astrupcs.CV cs.LG
We present SegmentAnyTreeV2, a sensor- and platform-agnostic framework for semantic and instance segmentation of forest point clouds. The model combines a serialization-based Point Transformer v3 backbone with a lightweight semantic head and a tree-focused cross-attention mask decoder. Semantic predictions restrict instance decoding to tree-class voxels, while instance-aware query initialization, one-to-many seed supervision, and asymmetric mask scoring improve separation in dense and structurally complex stands. We further introduce FOR-instance v3, an expanded benchmark comprising 427 scenes and 26,496 annotated trees across diverse biomes, forest structures, and LiDAR platforms. On the FOR-instanceV2 test split, SegmentAnyTreeV2 achieves 90.5% precision, 80.2% recall, 85.0% F1, 90.7% coverage, and 87.6% semantic mIoU, outperforming previous learning-based methods in both instance detection and mask completeness. Zero-shot evaluation on independent sites further demonstrates strong cross-domain generalization.
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.
Generating compact polygonal models from point clouds is a key problem in 3D vision and computer graphics. However, due to inherent limitations of LiDAR scanning (e.g. range constraints and occlusions), critical scene information is often missing, leading to degraded reconstruction accuracy. To address this, we propose a plane assembling strategy that effectively recovers missing details while maintaining model compactness. We classify all the planes extracted from the scene into three categories: highly visible, barely visible, and invisible. The invisible planes, which are recovered by scene structure analysis, indicate the missing details. The three types of planes correspond to the three growth priorities. Each plane grows according to the priority level, and the space is partitioned progressively, namely, the hierarchical partition. Subsequently, we generate a watertight polygonal mesh from the partition via a min-cut-based optimization. Finally, comparisons on public datasets show the effectiveness and superiority of our method against mainstream approaches. The project page is available at https://hsr-3dv.github.io/.
3D vision has rapidly evolved, driven by increasingly diverse data representations, learning paradigms, and modeling strategies. Yet the field remains fragmented across representations and benchmarks, making it difficult to develop unified perspectives on efficiency, fidelity, and scalability. This work provides a data-centric taxonomy of 3D vision that connects geometric representations, datasets, learning frameworks, and applications within a single conceptual map. We begin by analysing the principal structural representations of 3D data--point clouds, meshes, voxels, and 3D Gaussians--along with their acquisition pipelines. We then examine how dataset design, benchmark construction, and supervision regimes shape recent advances, spanning 2D-supervised 3D learning, implicit neural representations, and 4D world modeling. Through this integrative lens, we clarify the relationships among representations, learning paradigms, and downstream tasks in reconstruction, generation, and video modeling, offering a consolidated view of emerging trends toward balancing efficiency and fidelity and toward multimodal geometric grounding.