We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete by casting shape completion as a generative task conditioned on the incomplete shape. Our key designs are two-fold. First, we devise a hierarchical feature aggregation mechanism to inject conditional features in a spatially-consistent manner. So, we can capture both local details and broader contexts of the conditional inputs fusion strate to control gy in the our shape model completion.

The core element of EPN is the SPConv block, which consists of one SE(3) point convolution layer to learn features from spatial domain S, and one SE(3) group convolution operator to learn features within rotational groupG. For the SE(3)-equivariant 6D pose estimation branch,MLPπ is realized by another 2-layer MLP with batch normalization and a leaky ReLU activation.MLPP is just a one-layer MLP. Forallthetraining, weuseanAdamoptimizer with an initial learning rate of 0.0005, and the learning rate decay is 0.9995 per step. For all experiments oncomplete shapes, wetrain for500epochs overthewhole dataset; forexperiments on ModelNet40 partial data, we train the model for around 500k steps until convergence. Both EPN and KPConv are SOTA methods for 3D point cloud processing.

Modern data processing workflows frequently encounter ragged data: collections with variable-length elements that arise naturally in domains like natural language processing, scientific measurements, and autonomous AI agents. Existing workflow engines lack native support for tracking the shapes and dependencies inherent to ragged data, forcing users to manage complex indexing and dependency bookkeeping manually. We present Operon, a Rust-based workflow engine that addresses these challenges through a novel formalism of named dimensions with explicit dependency relations. Operon provides a domain-specific language where users declare pipelines with dimension annotations that are statically verified for correctness, while the runtime system dynamically schedules tasks as data shapes are incrementally discovered during execution. We formalize the mathematical foundation for reasoning about partial shapes and prove that Operon's incremental construction algorithm guarantees deterministic and confluent execution in parallel settings. The system's explicit modeling of partially-known states enables robust persistence and recovery mechanisms, while its per-task multi-queue architecture achieves efficient parallelism across heterogeneous task types. Empirical evaluation demonstrates that Operon outperforms an existing workflow engine with 14.94x baseline overhead reduction while maintaining near-linear end-to-end output rates as workloads scale, making it particularly suitable for large-scale data generation pipelines in machine learning applications.

Extremely low or high values yield worse results.Threshold τ l

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no correspondence annotation during training. Our key insight is to incorporate neural features learned by deep learning-based shape matching networks into an iterative, geometric shape registration pipeline. The advantage of our approach is two-fold -- On one hand, neural features provide more accurate and semantically meaningful correspondence estimation than spatial features (e.g., coordinates), which is critical in the presence of large non-rigid deformations; On the other hand, the correspondences are dynamically updated according to the intermediate registrations and filtered by consistency prior, which prominently robustify the overall pipeline. Empirical results show that, with as few as dozens of training shapes of limited variability, our pipeline achieves state-of-the-art results on several benchmarks of non-rigid point cloud matching and partial shape matching across varying settings, but also delivers high-quality correspondences between unseen challenging shape pairs that undergo both significant extrinsic and intrinsic deformations, in which case neither traditional registration methods nor intrinsic methods work.

In this paper, we propose a general unified tracking-servoing approach for controlling the shape of elastic deformable objects using robotic arms. Our approach works by forming a lattice around the object, binding the object to the lattice, and tracking and servoing the lattice instead of the object. This makes our approach have full 3D control over deformable objects of any general form (linear, thin-shell, volumetric). Furthermore, it decouples the runtime complexity of the approach from the objects' geometric complexity. Our approach is based on the As-Rigid-As-Possible (ARAP) deformation model. It requires no mechanical parameter of the object to be known and can drive the object toward desired shapes through large deformations. The inputs to our approach are the point cloud of the object's surface in its rest shape and the point cloud captured by a 3D camera in each frame. Overall, our approach is more broadly applicable than existing approaches. We validate the efficiency of our approach through numerous experiments with deformable objects of various shapes and materials (paper, rubber, plastic, foam). Experiment videos are available on the project website: https://sites.google.com/view/tracking-servoing-approach.

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.