FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization
This addresses the problem of estimating dense optical flow without labeled data for computer vision applications, representing an incremental improvement with a novel architecture.
The authors tackled unsupervised optical flow estimation by introducing FractalPINN-Flow, a deep learning framework that learns from consecutive grayscale frames without ground truth, resulting in accurate, smooth, and edge-preserving flow fields effective for high-resolution data and limited-annotation scenarios.
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.