TORA: Topological Representation Alignment for 3D Shape Assembly

3D assembly is fundamental to modern manufacturing and digital content creation. In this paper, we present PART, a unified transformer-based framework for 3D part retrieval and assembly: given a target shape and a part library, PART automatically selects the appropriate parts and predicts their 6-DoF poses to reconstruct the target. While prior work has achieved impressive progress on assembling a pre-defined set of parts, this more practical retrieval-based setting remains largely unexplored. The task faces three key challenges: (i) a combinatorially explosive search space that grows exponentially with library size; (ii) variable-length outputs, as different targets require different numbers of parts; and (iii) continuous 6-DoF pose estimation for part assembly. To address these, we formulate retrieval and assembly as a set prediction problem and design a novel transformer-based framework that retrieves parts and regresses their poses with variable-length output. Additionally, we exploit the duality between part pose estimation and target segmentation through joint training and a novel segmentation-enhanced optimization module. Finally, We curate a large-scale dataset of 80K+ shapes, and the results show that PART generalizes to scene layouts, image targets, and real-world scans. Project Page: https://iambrc.github.io/PART-project-page/.

While data-driven 3D shape correspondence estimation has recently seen substantial progress, robust matching under partial observations and strong non-isometric deformations remains challenging. Existing learning-based approaches often rely on hand-crafted descriptors or template-based representations, whereas recent generative models over functional maps suffer from high inference cost, limited interpretability, and poor generalisation to partial shapes. In response to these limitations, this paper introduces TokenMatch, a new transformer-based unified model for estimating 3D shape correspondences. Our feed-forward approach trained exclusively on BeCoS, a challenging non-isometric partial-to-partial shape-matching dataset, can generalise to matching full shapes without retraining or fine-tuning. TokenMatch uses self- and cross-attention mechanisms to efficiently learn patch-level and point-level relations as well as dense correspondences between shape pairs. Our core insight is that meshes can be adaptively tokenised into patches using shape curvature guidance, enabling effective learning of shape-specific geometric descriptors for correspondence estimation. We evaluate TokenMatch on standard benchmarks for partial and full shape matching, including CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19. Our method achieves consistently high performance, in most cases outperforming existing methods for partial and full shape matching in the mean geodesic error and intersection-over-union metrics, while also running faster at sub-second inference speeds.

Finding dense correspondences between 3D shapes is a fundamental yet unresolved challenge, especially in real-world environments. These environments present severe challenges, including the lack of time and sufficient samples for training, the prevalence of uncurated extreme-high resolution data with topological distortions, and the need to handle diverse 3D representations. In this paper, we present ATM, a zero-shot framework that requires no correspondence-specific training and robustly addresses these issues at once through an articulate-then-match paradigm. Rather than relying on intrinsic geometric properties, we leverage powerful pretrained vision foundation models and parametric shape priors to estimate parametric shape models from multi-view renderings, and systematically ground these estimations via multi-view geometric consistency. By mapping diverse inputs into a shared canonical parametric space, we inherently establish robust coarse correspondences that bypass topological noise, which are then refined into precise dense mappings via spectral refinement. Operating purely on test-time optimized parametric reconstructions, ATM requires no correspondence training data, is naturally immune to connectivity artifacts, and seamlessly handles diverse 3D modalities, including meshes, point clouds, and 3D Gaussians. Extensive experiments demonstrate that our method achieves strong results on non-isometric benchmarks (average geodesic errors of 2.4-TOPKIDS, 3.8-SMAL), reducing errors by 73% and 37% respectively compared to the baseline URSSM. Furthermore, it exhibits unprecedented robustness on in-the-wild raw scans of up to 200k vertices per shape while maintaining near-constant computation time and consistent superior accuracy.