DVI: A Derivative-based Vision Network for INR

Recent advancements in computer vision have seen Implicit Neural Representations (INR) becoming a dominant representation form for data due to their compactness and expressive power. To solve various vision tasks with INR data, vision networks can either be purely INR-based, but are thereby limited by simplistic operations and performance constraints, or include raster-based methods, which then tend to lose crucial structural features and important information of the INR during the conversion process. To address these issues, we propose DVI, a novel Derivative-based Vision network for INR, capable of handling a variety of vision tasks across various data modalities, while achieving the best performance among the existing methods by incorporating state of the art raster-based methods into a INR based architecture. DVI excels by leveraging the valuable features captured in the high order derivative map of the INR, then seamlessly fusing them into a pre-existing raster-based vision network, enhancing its performance with additional, task-relevant structural information. Extensive experiments on five vision tasks across three data modalities demonstrate DVI's superiority over existing methods. Additionally, our study encompasses comprehensive ablation studies to affirm the efficacy of each element of DVI, the influence of different derivative computation techniques and the impact of derivative orders. Reproducible codes are provided in the supplementary materials.