Inverse Procedural Modeling of Branching Structures by Inferring L-Systems

Jianwei Guo, Haiyong Jiang, Bedrich Benes, Oliver Deussen, Xiaopeng Zhang, Dani Lischinski, Hui Huang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We introduce an inverse procedural modeling approach that learns L-system representations of pixel images with branching structures. Our fully automatic model generates a compact set of textual rewriting rules that describe the input. We use deep learning to discover atomic structures such as line segments or branchings. Orientation and scaling of these structures are determined and the detected structures are combined into a tree. The initial representation is analyzed, and repeating parts are encoded into a small grammar by using greedy optimization while the user can control the size of the detected rules. The output is an L-system that represents the input image as a simple text and a set of terminal symbols. We apply our approach to a variety of examples, demonstrate its robustness against noise and blur, and we show that it can detect user sketches and complex input structures.

Original languageAmerican English
Article number3394105
JournalACM Transactions on Graphics
Issue number5
StatePublished - Sep 2020

Bibliographical note

Funding Information:
This work was supported in parts by National Key R&D Program (2018YFB2100602), NSFC (61861130365, 61761146002, 61802406, 61802362), GD Higher Education Key Program (2018KZDXM058), LHTD (20170003), GD Leading Talent Program (00201509), DFG (422037984), NSF (10001387), FAR (602757), and GD Laboratory of Artificial Intelligence and Digital Economy (SZ). Authors’ addresses: J. Guo and X. Zhang, NLPR, Institute of Automation, CAS, Beijing, China; emails:,; H. Jiang, UCAS, Beijing, NTU Singapore; email:; B. Benes, Pur-due University; email:; O. Deussen, SIAT Shenzhen and University Konstanz; email:; D. Lischinski, The Hebrew University of Jerusalem; email:; H. Huang (corresponding author), College of Computer Science & Soft-ware Engineering, Shenzhen University; email: Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from © 2020 Association for Computing Machinery. 0730-0301/2020/06-ART155 $15.00

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  • L-systems
  • grammar induction
  • procedural generation


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