通过单向波动方程探索图像中的不变性
Exploring Invariance in Images through One-way Wave Equations
AI总结：
本文揭示图像共享一组单向波动方程的不变性，通过编码器-解码器框架将图像编码为初始条件并解码重建，为图像理解提供新视角。
摘要：
在本文中，我们经验性地揭示了图像上的一种不变性——图像共享一组具有潜在速度的单向波动方程。每张图像唯一地与这些波动方程的一个解相关联，从而允许从初始条件高保真地重建图像。我们使用一个直观的编码器-解码器框架来证明这一点，其中每张图像被编码为其对应的初始条件（单个向量）。随后，初始条件经过一个专门的解码器，将单向波动方程转化为一阶范数+线性自回归过程。该过程沿x和y方向传播初始条件，生成高分辨率特征图（最高达图像分辨率），随后通过几个卷积层重建图像像素。所揭示的不变性根植于共享的波动方程，为理解图像提供了新视角，并为进一步探索确立了有前景的途径。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
