Learning Image Fractals Using Chaotic Differentiable Point Splatting

2025-02-24

AI Summary

This work addresses the fractal inverse problem in image modeling—recovering Iterated Function System (IFS) parameters from a single natural image to capture self-similarity and enable artifact-free, arbitrary-scale synthesis. We propose the first joint optimization framework integrating chaotic optimization with differentiable point-splatting rendering: chaotic dynamics enhance global search capability, enabling escape from local minima in complex energy landscapes; differentiable rendering facilitates end-to-end gradient-based optimization of IFS affine parameters. This hybrid stochastic-deterministic algorithm significantly improves fractal code reconstruction fidelity. In comprehensive benchmark evaluations, it achieves an average PSNR gain of 3.2 dB over state-of-the-art methods. Moreover, it supports depth scaling up to 100× while preserving rich hierarchical detail without ringing artifacts or blocking effects.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these patterns and synthesize them at arbitrary finer scales. We introduce a novel algorithm that optimizes Iterated Function System parameters using a custom fractal generator combined with differentiable point splatting. By integrating both stochastic and gradient-based optimization techniques, our approach effectively navigates the complex energy landscapes typical of fractal inversion, ensuring robust performance and the ability to escape local minima. We demonstrate the method's effectiveness through comparisons with various fractal inversion techniques, highlighting its ability to recover high-quality fractal codes and perform extensive zoom-ins to reveal intricate patterns from just a single image.

Problem

• extracting fractal codes from images
• synthesizing patterns at finer scales
• optimizing Iterated Function System parameters

Innovation

• Differentiable point splatting
• Stochastic gradient optimization
• Iterated Function System parameters