This paper presents a new approach to estimate accurate and robust 3D semantic correspondence with the hierarchical neural semantic representation. Our work has three key contributions. First, we design the hierarchical neural semantic representation (HNSR), which consists of a global semantic feature to capture high-level structure and multi-resolution local geometric features to preserve fine details, by carefully harnessing 3D priors from pre-trained 3D generative models. Second, we design a progressive global-to-local matching strategy, which establishes coarse semantic correspondence using the global semantic feature, then iteratively refines it with local geometric features, yielding accurate and semantically-consistent mappings. Third, our framework is training-free and broadly compatible with various pre-trained 3D generative backbones, demonstrating strong generalization across diverse shape categories. Our method also supports various applications, such as shape co-segmentation, keypoint matching, and texture transfer, and generalizes well to structurally diverse shapes, with promising results even in cross-category scenarios. Both qualitative and quantitative evaluations show that our method outperforms previous state-of-the-art techniques.

This paper presents a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose acompact wavelet representationwith a pair of coarse and detail coefficient volumes to implicitly represent 3D shapes via truncated signed distance functions and multi-scale biorthogonal wavelets. Then, we design a pair of neural networks: a diffusion-basedgeneratorto produce diverse shapes in the form of the coarse coefficient volumes and adetail predictorto produce compatible detail coefficient volumes for introducing fine structures and details. Further, we may jointly train anencoder networkto learn a latent space for inverting shapes, allowing us to enable a rich variety of whole-shape and region-aware shape manipulations. Both quantitative and qualitative experimental results manifest the compelling shape generation, inversion, and manipulation capabilities of our approach over the state-of-the-art methods.

This paper presents CLIPXPlore, a new framework that leverages a vision-language model to guide the exploration of the 3D shape space. Many recent methods have been developed to encode 3D shapes into a learned latent shape space to enable generative design and modeling. Yet, existing methods lack effective exploration mechanisms, despite the rich information. To this end, we propose to leverage CLIP, a powerful pre-trained vision-language model, to aid the shape-space exploration. Our idea is threefold. First, we couple the CLIP and shape spaces by generating paired CLIP and shape codes through sketch images and training a mapper network to connect the two spaces. Second, to explore the space around a given shape, we formulate a co-optimization strategy to search for the CLIP code that better matches the geometry of the shape. Third, we design three exploration modes, binary-attribute-guided, text-guided, and sketch-guided, to locate suitable exploration trajectories in shape space and induce meaningful changes to the shape. We perform a series of experiments to quantitatively and visually compare CLIPXPlore with different baselines in each of the three exploration modes, showing that CLIPXPlore can produce many meaningful exploration results that cannot be achieved by the existing solutions.

This paper presents a new text-guided technique for generating 3D shapes. The technique leverages a hybrid 3D shape representation, namely EXIM, combining the strengths of explicit and implicit representations. Specifically, the explicit stage controls the topology of the generated 3D shapes and enables local modifications, whereas the implicit stage refines the shape and paints it with plausible colors. Also, the hybrid approach separates the shape and color and generates color conditioned on shape to ensure shape-color consistency. Unlike the existing state-of-the-art methods, we achieve high-fidelity shape generation from natural-language descriptions without the need for time-consuming per-shape optimization or reliance on human-annotated texts during training or test-time optimization. Further, we demonstrate the applicability of our approach to generate indoor scenes with consistent styles using text-induced 3D shapes. Through extensive experiments, we demonstrate the compelling quality of our results and the high coherency of our generated shapes with the input texts, surpassing the performance of existing methods by a significant margin. Codes and models are released at https://github.com/liuzhengzhe/EXIM.

This paper introduces a novel framework called DTNet for 3D mesh reconstruction and generation via Disentangled Topology. Beyond previous works, we learn a topology-aware neural template specific to each input then deform the template to reconstruct a detailed mesh while preserving the learned topology. One key insight is to decouple the complex mesh reconstruction into two sub-tasks: topology formulation and shape deformation. Thanks to the decoupling, DT-Net implicitly learns a disentangled representation for the topology and shape in the latent space. Hence, it can enable novel disentangled controls for supporting various shape generation applications, e.g., remix the topologies of 3D objects, that are not achievable by previous reconstruction works. Extensive experimental results demonstrate that our method11Code available at https://github.com/edward1997104/Neural-Template. is able to produce high-quality meshes, particularly with diverse topologies, as compared with the state-of-the-art methods.

This paper presents a new approach for 3D shape generation, enabling direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet representation with a pair of coarse and detail coefficient volumes to implicitly represent 3D shapes via truncated signed distance functions and multi-scale biorthogonal wavelets, and formulate a pair of neural networks: a generator based on the diffusion model to produce diverse shapes in the form of coarse coefficient volumes; and a detail predictor to further produce compatible detail coefficient volumes for enriching the generated shapes with fine structures and details. Both quantitative and qualitative experimental results manifest the superiority of our approach in generating diverse and high-quality shapes with complex topology and structures, clean surfaces, and fine details, exceeding the 3D generation capabilities of the state-of-the-art models.

Abstract We study structural rigidity for assemblies with mechanical joints. Existing methods identify whether an assembly is structurally rigid by assuming parts are perfectly rigid. Yet, an assembly identified as rigid may not be that “rigid” in practice, and existing methods cannot quantify how rigid an assembly is. We address this limitation by developing a new measure, worst‐case rigidity, to quantify the rigidity of an assembly as the largest possible deformation that the assembly undergoes for arbitrary external loads of fixed magnitude. Computing worst‐case rigidity is non‐trivial due to non‐rigid parts and different joint types. We thus formulate a new computational approach by encoding parts and their connections into a stiffness matrix, in which parts are modeled as deformable objects and joints as soft constraints. Based on this, we formulate worst‐case rigidity analysis as an optimization that seeks the worst‐case deformation of an assembly for arbitrary external loads, and solve the optimization problem via an eigenanalysis. Furthermore, we present methods to optimize the geometry and topology of various assemblies to enhance their rigidity, as guided by our rigidity measure. In the end, we validate our method on a variety of assembly structures with physical experiments and demonstrate its effectiveness by designing and fabricating several structurally rigid assemblies.