{"type":"ScholarlyArticle","title":"Inferring Iterated Function Systems Approximately from Fractal Images","authors":[{"name":"Haotian Liu","slug":"haotian-liu","given":"Haotian","family":"Liu","affiliation":"Gaoling School of Artificial Intelligence , Renmin University of China , Beijing; School of Computer Science and Technology , Beijing Institute of Technology , Beijing"},{"name":"Dixin Luo","slug":"dixin-luo","given":"Dixin","family":"Luo","affiliation":"School of Computer Science and Technology , Beijing Institute of Technology , Beijing; Key Laboratory of Artificial Intelligence , Ministry of Education , Shanghai"},{"name":"Hongteng Xu","slug":"hongteng-xu","given":"Hongteng","family":"Xu","affiliation":"Gaoling School of Artificial Intelligence , Renmin University of China , Beijing; Beijing Key Laboratory of Big Data Management and Analysis Methods , Beijing"}],"abstract":"As an important mathematical concept, fractals commonly appear in nature and inspire the design of many artistic works.\r\nAlthough we can generate various fractal images easily based on different iterated function systems (IFSs), inferring an IFS from a given fractal image is still a challenging inverse problem for both scientific research and artistic design. \r\nIn this study, we explore the potential of deep learning techniques for this problem, learning a multi-head auto-encoding model to infer typical IFSs (including Julia set and L-system) from fractal images. \r\nIn principle, the proposed model encodes fractal images in a latent space and decodes their corresponding IFSs based on the latent representations.\r\nFor the fractal images generated by heterogeneous IFSs, we let them share the same encoder and apply two decoders to infer the sequential and non-sequential parameters of their IFSs, respectively.  \r\nBy introducing one more decoder to reconstruct fractal images, we can leverage large-scale unlabeled fractal images to learn the model in a semi-supervised way, which suppresses the risk of over-fitting.\r\nComprehensive experiments demonstrate that our method provides a promising solution to infer IFSs approximately from fractal images.\r\nCode and supplementary file are available at \\url{https://github.com/HaotianLiu123/Inferring-IFSs-From-Fractal-Images}.","doi":"10.24963/ijcai.2024/852","url":"https://ijcai.org/proceedings/2024/852","pdf":"https://ijcai.org/proceedings/2024/0852.pdf","markdown":"https://ijcai.org/proceedings/2024/852.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/852","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"AI, Arts & Creativity","track":"AI, Arts & Creativity","number":852,"pages":{"first":7699,"last":7707},"keywords":["Application domains: Science, math and programming","Methods and resources: Techniques for modeling and simulation of creativity","Application domains: Images, movies and visual arts","Application domains: Problem Solving"],"videos":[],"references":[{"position":1,"raw":"[Angeline, 1994] Peter J. 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