statistical shape modeling

This work addresses the challenges of modeling complex dependencies and mitigating redundancy in high-dimensional parameter spaces for discrete data generation. It introduces, for the first time, a Riemannian geometric structure with isometric properties into the exponential parameter space of product manifolds over categorical distributions, thereby constructing a low-dimensional latent subspace. By leveraging the Riemannian metric, geodesics within this subspace become straight lines, enabling consistent and efficient flow-matching training. The proposed approach substantially reduces the dimensionality of latent variables while preserving strong representational capacity for discrete data distributions. Experimental results demonstrate that the model achieves accurate and efficient discrete data generation using a significantly lower-dimensional latent space, effectively balancing computational efficiency with modeling performance.

Existing interpolation methods for generative models lack a universal, principle-driven definition—often relying on strong assumptions or requiring architectural modifications. Method: We propose a general interpolation framework that models interpolation paths as Riemannian geodesics constrained by the data distribution: leveraging gradient information of the probability density, it computes high-density, quasi-geodesic paths directly in the pre-trained model’s latent space, without additional training or fine-tuning. Contribution/Results: Theoretically, the path satisfies the geodesic equation locally under a Riemannian metric induced by the data density. Algorithmically, the method is agnostic to the choice of distance metric and data distribution. Empirically, it significantly improves interpolation smoothness and semantic plausibility across diverse generative models—including VAEs, GANs, and diffusion models—and on both image and text datasets, outperforming state-of-the-art baselines.

This study addresses the challenge posed by high-dimensional CAD geometric design parameters, which complicate downstream simulation and optimization tasks. While conventional principal component analysis (PCA) struggles to accurately reconstruct the original interpretable parameters from reduced representations, this work systematically examines the impact of each PCA stage on geometric fidelity. It reveals the equivalence between domain-specific PCA variants and standard PCA, and establishes theoretical bounds and conditions under which interpretable parameter reconstruction is feasible. Through geometric parametrization modeling, interpretability analysis, and numerical experiments, the study demonstrates that, under specific conditions, original design parameters can be recovered from PCA representations with high accuracy. These findings provide both theoretical grounding and practical guidance for interpretable dimensionality reduction in high-dimensional geometric design spaces.

Controllable geometric generation remains challenging in scenarios lacking large-scale 3D shape datasets. Method: This paper proposes a data-free neural implicit field generation framework that encodes user-specified design objectives—such as smoothness, genus (number of holes), and connectivity—as partial differential equation (PDE) constraints, geometric differential operator regularizers, and a multi-objective Lagrangian optimization objective, all directly embedded into neural field training. Contribution/Results: It establishes the first data-free paradigm for implicit shape generation; introduces explicit diversity constraints to mitigate mode collapse; and enables joint yet disentangled control over geometric and topological attributes. Experiments on multiple benchmarks and real-world engineering design tasks demonstrate precise, stable control over surface smoothness, connectivity, and genus, while consistently producing high-quality, diverse, and feasible shape ensembles.

High annotation cost and poor generalizability plague geometric feature labeling in engineering design images. Method: We propose a large-model-driven automated annotation framework featuring (1) GeoBiked—the first bicycle-structure-specific dataset (4,355 images); (2) Diffusion-Hyperfeatures, a novel representation technique enabling precise cross-image correspondence of geometric keypoints; (3) a dual-path GPT-4o input mechanism integrating image and category labels, enhanced by systematic prompt engineering and a structured annotation schema to ensure fidelity and consistency of technical descriptions; and (4) a multi-source image collaborative geometric localization strategy. Results: Experiments demonstrate significant improvements in keypoint detection accuracy on unseen samples, with high descriptive accuracy from GPT-4o outputs. The framework validates the feasibility and strong generalization capability of large language-vision models for engineering image understanding and fine-grained geometric annotation.

This work addresses the challenge of achieving cross-shape consistency in spherical parameterizations for genus-zero 3D shape collections. The authors propose a continuous parameterization method based on neural generative modeling, which learns a continuous mapping from the unit sphere to each target shape and leverages its inverse to obtain consistent spherical parameterizations. To mitigate discretization artifacts, an intermediate shape is introduced to bridge the sphere and target geometry, while a generative tree in latent space propagates initial correspondences across the collection. By integrating neural generative modeling, continuous deformation representations, and latent structural analysis, the method significantly reduces geometric distortion and achieves markedly superior cross-shape parameterization consistency compared to existing approaches on the ShapeNet dataset.

This work proposes DreamCAD, a multimodal generative framework that addresses the limited scalability of existing CAD generation methods, which are constrained by small annotated datasets and unable to leverage vast unlabeled 3D meshes. DreamCAD enables end-to-end editable BRep generation supervised solely by point clouds—eliminating the need for CAD-specific annotations—and supports diverse inputs including text, images, and point clouds. It represents BReps using parametric surfaces such as Bézier patches and employs differentiable tessellation to produce meshes, facilitating training on large-scale 3D data. The authors also introduce CADCap-1M, a million-scale dataset of CAD models paired with textual descriptions, to advance text-to-CAD generation research. Evaluated on ABC and Objaverse benchmarks, DreamCAD achieves state-of-the-art performance with significantly improved geometric fidelity and a user preference rate exceeding 75%.

This work addresses the lack of effective support for Kendall’s 3D shape space in existing Python libraries—such as Geomstats—which has hindered the practical application of Riemannian geometry in three-dimensional shape analysis. We present the first systematic implementation of an efficient and user-friendly Python toolkit tailored specifically to Kendall’s 3D shape space, enabling scale-, position-, and orientation-invariant shape modeling and statistical analysis. By providing a ready-to-use, open-source solution for shape statistics on manifolds, this contribution fills a critical software gap in advanced 3D shape analysis, substantially lowering the barrier to entry for researchers, improving computational efficiency, and enhancing the reproducibility of results.

This work addresses the challenge of generating industrial-scale, complex CAD models, whose parameter sequences are excessively long and fine-grained, rendering existing generative methods ineffective. To this end, we propose Mamba-CAD, the first approach to introduce the state space model Mamba into CAD generation. Our method employs a self-supervised encoder-decoder framework, where a latent representation is learned through CAD reconstruction pretraining. A generative adversarial network (GAN) is then leveraged to produce high-quality CAD latent codes, which are subsequently decoded into complete, parameterized sequences. We also release a new dataset comprising 77,078 complex CAD models. Experimental results demonstrate that Mamba-CAD significantly outperforms current methods across multiple metrics, particularly excelling in generating valid, long-sequence parametric CAD models.

This work addresses the challenge of enabling Transformer-based models to generate high-quality, editable CAD sketches while preserving design intent and parametric control. Inspired by classical compass-and-straightedge constructions, the authors propose modeling sketch generation as a sequence of geometric construction steps—such as offsetting, rotation, and intersection—and introduce, for the first time, a “chain-of-thought”-like sequence of geometric operations. The generation process is optimized via reinforcement learning and implemented using a Transformer architecture capable of handling floating-point parameters, thereby supporting fine-grained parametric editing. Experimental results demonstrate that the proposed method significantly outperforms existing baselines in terms of sketch quality, editability, and multiple evaluation metrics, with consistent improvements even on metrics not explicitly optimized during training.