Abstract
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.
Abstract (translated)
我们提出了一种无监督深度学习框架FractalPINN-Flow，用于从连续的灰度帧中直接估计稠密光流，而无需依赖真实标签。该架构的核心是分形变形网络（FDN），这是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。与传统的使用顺序下采样的CNN不同，FDN通过重复的编码器-解码器嵌套以及跳跃连接来捕捉细粒度细节和长距离运动模式。 训练目标基于经典的变分方法，该方法采用了总变化（TV）正则化。具体而言，我们最小化一个能量泛函，该函数结合了$L^1$和$L^2$数据保真项以强制执行亮度恒常性，并且加入了一个TV项来促进空间平滑度和一致的流场。 在合成数据集和基准数据集上的实验表明，FractalPINN-Flow能够生成准确、平滑并保持边缘特性的光流场。该模型对于高分辨率数据和标注有限的情景特别有效。
URL
https://arxiv.org/abs/2509.08670
