However, constructing a high-resolution occupancy map remains infeasible for large scenes due to computational constraints.

We further introduce a multi-scale diversity penalty that operates in the feature space of our discriminators.

Existing works usually estimate the missing shape by decoding a latent feature encoded from the input points.

While 3D shape representations enable powerful reasoning in many visual and perception applications, learning 3D shape priors tends to be constrained to the specific categories trained on, leading to an inefficient learning process, particularly for general applications with unseen categories. Thus, we propose PatchComplete, which learns effective shape priors based on multi-resolution local patches, which are often more general than full shapes (e.g., chairs and tables often both share legs) and thus enable geometric reasoning about unseen class categories. To learn these shared substructures, we learn multi-resolution patch priors across all train categories, which are then associated to input partial shape observations by attention across the patch priors, and finally decoded into a complete shape reconstruction. Such patch-based priors avoid overfitting to specific train categories and enable reconstruction on entirely unseen categories at test time. We demonstrate the effectiveness of our approach on synthetic ShapeNet data as well as challenging real-scanned objects from ScanNet, which include noise and clutter, improving over state of the art in novel-category shape completion by 19.3% in chamfer distance on ShapeNet, and 9.0% for ScanNet.

Point completion refers to complete the missing geometries of objects from partial point clouds. Existing works usually estimate the missing shape by decoding a latent feature encoded from the input points. However, real-world objects are usually with diverse topologies and surface details, which a latent feature may fail to represent to recover a clean and complete surface. To this end, we propose a skeleton-bridged point completion network (SK-PCN) for shape completion. Given a partial scan, our method first predicts its 3D skeleton to obtain the global structure, and completes the surface by learning displacements from skeletal points. We decouple the shape completion into structure estimation and surface reconstruction, which eases the learning difficulty and benefits our method to obtain on-surface details. Besides, considering the missing features during encoding input points, SK-PCN adopts a local adjustment strategy that merges the input point cloud to our predictions for surface refinement. Comparing with previous methods, our skeleton-bridged manner better supports point normal estimation to obtain the full surface mesh beyond point clouds. The qualitative and quantitative experiments on both point cloud and mesh completion show that our approach outperforms the existing methods on various object categories.

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17% and Chamfer distance $\ell1$ on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion. Project page: https://sime-completion.github.io.

Ultrasound offers a radiation-free, cost-effective solution for real-time visualization of spinal landmarks, paraspinal soft tissues and neurovascular structures, making it valuable for intraoperative guidance during spinal procedures. However, ultrasound suffers from inherent limitations in visualizing complete vertebral anatomy, in particular vertebral bodies, due to acoustic shadowing effects caused by bone. In this work, we present a novel multi-modal deep learning method for completing occluded anatomical structures in 3D ultrasound by leveraging complementary information from a single X-ray image. To enable training, we generate paired training data consisting of: (1) 2D lateral vertebral views that simulate X-ray scans, and (2) 3D partial vertebrae representations that mimic the limited visibility and occlusions encountered during ultrasound spine imaging. Our method integrates morphological information from both imaging modalities and demonstrates significant improvements in vertebral reconstruction (p < 0.001) compared to state of art in 3D ultrasound vertebral completion. We perform phantom studies as an initial step to future clinical translation, and achieve a more accurate, complete volumetric lumbar spine visualization overlayed on the ultrasound scan without the need for registration with preoperative modalities such as computed tomography. This demonstrates that integrating a single X-ray projection mitigates ultrasound's key limitation while preserving its strengths as the primary imaging modality.