Learning Fractals by Gradient Descent

Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training. In this paper, we study the inverse problem --- given a target image (not necessarily a fractal), we aim to generate a fractal image that looks like it. We propose a novel approach that learns the parameters underlying a fractal image via gradient descent. We show that our approach can find fractal parameters of high visual quality and be compatible with different loss functions, opening up several potentials, e.g., learning fractals for downstream tasks, scientific understanding, etc.

Authors

• Cheng-Hao Tu The Ohio State University
• Hong-You Chen The Ohio State University
• David Carlyn The Ohio State University
• Wei-Lun Chao The Ohio State University

Keywords

• CV: Applications
• CV: Learning & Optimization for CV
• CV: Other Foundations of Computer Vision
• ML: Deep Neural Architectures