用分形结构网络无监督估计光流，更准更平滑。
FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization
- 分形递归结构捕捉细节与远距离运动
- 结合TV正则化，生成平滑且保边的光流
- 适合高分辨率数据和标注少的场景
我们提出FractalPINN-Flow，一种无需真实光流标签的无监督深度学习框架，直接从连续灰度帧中学习稠密光流。核心是分形变形网络（FDN），一种受分形几何和自相似性启发的递归编码器-解码器结构。与传统CNN逐层下采样不同，FDN通过重复嵌套编码器-解码器并使用跳跃连接，同时捕捉细粒度细节与长程运动模式。训练目标基于经典变分公式，采用总变差（TV）正则化：最小化包含$L^1$和$L^2$数据保真项（保持亮度恒定）与TV项（促进空间平滑性和流场一致性）的能量泛函。在合成数据和基准数据集上的实验表明，该模型能生成准确、平滑且边缘保持良好的光流场，尤其适用于高分辨率数据及标注有限的场景。
原文摘要 · Abstract (English)
We present FractalPINN-Flow, an unsupervised deep learning framework for dense optical flow estimation that learns directly from consecutive grayscale frames without requiring ground truth. The architecture centers on the Fractal Deformation Network (FDN) - a recursive encoder-decoder inspired by fractal geometry and self-similarity. Unlike traditional CNNs with sequential downsampling, FDN uses repeated encoder-decoder nesting with skip connections to capture both fine-grained details and long-range motion patterns. The training objective is based on a classical variational formulation using total variation (TV) regularization. Specifically, we minimize an energy functional that combines $L^1$ and $L^2$ data fidelity terms to enforce brightness constancy, along with a TV term that promotes spatial smoothness and coherent flow fields. Experiments on synthetic and benchmark datasets show that FractalPINN-Flow produces accurate, smooth, and edge-preserving optical flow fields. The model is especially effective for high-resolution data and scenarios with limited annotations.
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