Hilbert Flattening: a Locality-Preserving Matrix Unfolding Method for Visual Discrimination

Flattening is essential in computer vision by converting multi-dimensional feature maps or images into one-dimensional vectors. However, existing flattening approaches neglect the preservation of local smoothness, which can impact the representational learning capacity of vision models. In this paper, we propose Hilbert curve flattening as an innovative method to preserve locality in flattened matrices. We compare it with the commonly used Zigzag operation and demonstrate that Hilbert curve flattening can better retain the spatial relationships and local smoothness of the original grid structure, while maintaining robustness against the input scale variance. And, we introduce the Localformer, a vision transformer architecture that incorporates Hilbert token sampling with a token aggregator to enhance its locality bias. Extensive experiments on image classification and semantic segmentation tasks demonstrate that the Localformer outperforms baseline models consistently. We also show it brings consistent performance boosts for other popular architectures (e.g. MLP-Mixer).