Year: 2026
Type: article
Abstract: Space-filling curves (SFCs) have enabled transformers to process massive 3D point clouds with linear complexity by mapping them into 1D sequences. However, standard SFCs rely on fixed, axis-aligned traversal orders, which introduce systematic axial anisotropy and frequently sever the connectivity of oblique geometric structures – a phenomenon we term “locality breaches”. While existing methods attempt to mitigate this by sequentially stacking multiple patterns, they incur a prohibitive linear increase in latency. To resolve this efficiency–accuracy dilemma, we propose GAPS (Group-wise Affine-Perturbed Serialization). Mathematically, we derive a flexible mechanism to generate diverse, bijective scanning paths via affine transformations over the Galois field 𝔽 2 . This allows for the synthesis of “sheared” and “rotated” traversals that effectively establish neighborhood connectivity along non-axial geometries. Architecturally, GAPS employs a group-wise parallel design that splits feature channels to aggregate multiple-perspective contexts simultaneously, thereby circumventing the computational penalty of serial execution. Extensive experiments on the ScanNet200 benchmark demonstrate that GAPS achieves 36.8 % mean Intersection over Union (mIoU), outperforming the strong baseline, Point Transformer V3 (PTv3), by 1.6 %. Remarkably, GAPS delivers this significant gain with zero parameter overhead and minimal latency overhead, establishing a new state-of-the-art performance among standard train-from-scratch 3D backbones.
Source: Mechanical sciences
Authors: Yubin Tang, Yangchen Liu, Zichuan Fan
Institution: Southwest University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $765
OpenAlex ID: W7135016785