发表机构
Faculty of Information Engineering, Fukuoka Institute of Technology（福冈工业大学信息工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出摊销集预测方法，通过学习估计器从密度图直接预测仿射映射集，解决逆IFS重建问题，在合成与真实图像上均实现更快且更优的重建效果。
AI 中文摘要
迭代函数系统（IFS）通过若干个收缩仿射映射生成自相似分形，从参数到图像的正向映射计算成本低且已被充分研究，而从图像估计映射的逆问题难度较大，通常通过逐图像优化处理。本文用学习到的估计器的单次前向传播替代该循环，该估计器直接从访问频率密度图预测仿射映射集，从而摊销逆问题。设计遵循两个约束：第一，密度图无法唯一标识IFS参数，因此评估基于重建而非参数恢复，无序映射集通过匈牙利匹配处理，真实参数提供稳定的训练代理；第二，完全已知的正向模型允许生成精确的合成训练对，还支持仅图像的测试时优化。在分布内测试中，摊销初始化加少量优化步骤的质量-速度权衡优于相同预算的随机初始化逐图像优化，30步优化（每个样本约0.56秒）仍优于预算加倍的基线；将优化扩展到1000步表明，优势不仅在于速度：摊销初始化比随机启动更频繁地达到高质量重建。在真实图像（MNIST和Fashion-MNIST）上，它平均提升了已发表逐图像优化器的密度指标，同时速度快约12至2600倍。
英文摘要
Iterated Function Systems (IFS) generate self-similar fractals from a few contractive affine maps. The forward map from parameters to images is computationally inexpensive and well understood, whereas the inverse problem of estimating maps from an image is difficult and is typically handled by per-image optimization. We replace this loop with a single forward pass of a learned estimator that predicts the affine-map set directly from a visit-frequency density map, thereby amortizing the inverse problem. The design follows two constraints. First, density maps do not uniquely identify IFS parameters, so evaluation is based on reconstruction rather than parameter recovery; unordered map sets are handled by Hungarian matching, and ground-truth parameters provide a stable training surrogate. Second, the fully known forward model lets us generate exact synthetic training pairs and also supports image-only test-time refinement. On in-distribution tests, amortized initialization plus a few refinement steps lies on a better quality--speed frontier than equal-budget random-initialized per-image optimization, and a 30-step refinement (about $0.56$ s per sample) remains better than a doubled-budget baseline. Extending optimization to 1000 steps shows that the benefit is not only speed: amortized initialization reaches high-quality reconstructions more frequently than random starts. On real images (MNIST and Fashion-MNIST), it improves density metrics on average over a published per-image optimizer while being roughly 12 to 2600 times faster.
Comments24 pages, 12 figures
