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arXiv · 2509.08670

FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization

Sara Behnamian·Rasoul Khaksarinezhad·Andreas Langer
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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.

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Sara Behnamian, Rasoul Khaksarinezhad, Andreas Langer. 2025-09-10. FractalPINN-Flow: A Fractal-Inspired Network for Unsupervised Optical Flow Estimation with Total Variation Regularization. https://doi.org/10.11588/heidok.00037608

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