ShapeY: A Principled Framework for Measuring Shape Recognition Capacity via Nearest-Neighbor Matching

Monocular 3D shape recovery is fundamental to geometric understanding, yet achieving robust generalization across arbitrary viewpoints and unseen object categories remains a significant challenge. In this paper, we present a generalizable deformation learning framework that reconstructs 3D objects by explicitly deforming a category-level shape template to match the target observation. To address complex shape variations between the template and the target, we introduce a geometry-guided feature modeling mechanism. This process first enriches foundation features with template topology to yield a geometry-aware representation, which is then explicitly correlated with the target observation to guide precise deformation. Furthermore, to bridge the disparity between the fixed template and arbitrary target views, we propose a view-adaptive feature aggregation module. This module leverages multi-view template features and their corresponding camera poses to enrich the canonical template representation, ensuring robust feature alignment regardless of the target's perspective. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods in handling large shape variations and diverse viewpoints, exhibiting strong generalization to novel categories and effectively supporting downstream real-world dexterous robotic manipulation tasks. Project homepage: https://GODeform.github.io/

We introduce ShapeCodeBench, a synthetic benchmark for perception-to-program reconstruction: given a rendered raster image, a model must emit an executable drawing program that a deterministic evaluator re-renders and compares with the target. The v1 DSL has four primitives on a 512 x 512 black-on-white canvas, but every instance is generated from a seeded RNG, so fresh held-out sets can be created to reduce exact-instance contamination. We release a frozen eval_v1 split with 150 samples across easy, medium, and hard tiers, scored by exact match, pixel accuracy, foreground IoU, parse success, and execution success. We evaluate an empty-program floor, a classical computer-vision heuristic, Claude Opus 4.7 at high and max effort, and GPT-5.5 at medium and extra_high reasoning effort. The heuristic is competitive on easy scenes but collapses when overlaps fuse components; the strongest multimodal configuration preserves much of the foreground structure but still misses exact match because of small parameter errors. Best overall exact match remains low, so ShapeCodeBench is far from saturated. The benchmark code, frozen dataset, run artifacts, and paper sources are released to support independent replication and extension.

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.