Exploring Invariance in Images through One-way Wave Equations
Abstract
In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with high fidelity from an initial condition. We demonstrate it using an intuitive encoder-decoder framework where each image is encoded into its corresponding initial condition (a single vector). Subsequently, the initial condition undergoes a specialized decoder, transforming the one-way wave equations into a first-order norm + linear autoregressive process. This process propagates the initial condition along the x and y directions, generating a high-resolution feature map (up to the image resolution), followed by a few convolutional layers to reconstruct image pixels. The revealed invariance, rooted in the shared wave equations, offers a fresh perspective for comprehending images, establishing a promising avenue for further exploration.
Cite
@article{arxiv.2310.12976,
title = {Exploring Invariance in Images through One-way Wave Equations},
author = {Yinpeng Chen and Dongdong Chen and Xiyang Dai and Mengchen Liu and Yinan Feng and Youzuo Lin and Lu Yuan and Zicheng Liu},
journal= {arXiv preprint arXiv:2310.12976},
year = {2024}
}
Comments
This is an improvement version, which fuses some parts from the preliminary work arXiv:2305.16319