Learning Fractals by Gradient Descent
This work addresses a novel problem in computer vision for applications in downstream tasks and scientific understanding, though it appears incremental as it builds on existing fractal-based methods.
The paper tackles the inverse problem of generating fractal images that resemble target images by learning fractal parameters via gradient descent, achieving high visual quality and compatibility with various loss functions.
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.