## Inverse Procedural Modeling by Automatic Generation of L-systems

Citations: | 10 - 0 self |

### BibTeX

@MISC{Beneš_inverseprocedural,

author = {B. Beneš and R. Měch and D. G. Aliaga and P. Krištof},

title = {Inverse Procedural Modeling by Automatic Generation of L-systems},

year = {}

}

### OpenURL

### Abstract

We present an important step towards the solution of the problem of inverse procedural modeling by generating parametric context-free L-systems that represent an input 2D model. The L-system rules efficiently code the regular structures and the parameters represent the properties of the structure transformations. The algorithm takes as input a 2D vector image that is composed of atomic elements, such as curves and poly-lines. Similar elements are recognized and assigned terminal symbols of an L-system alphabet. The terminal symbols ’ position and orientation are pair-wise compared and the transformations are stored as points in multiple 4D transformation spaces. By careful analysis of the clusters in the transformation spaces, we detect sequences of elements and code them as L-system rules. The coded elements are then removed from the clusters, the clusters are updated, and then the analysis attempts to code groups of elements in (hierarchies) the same way. The analysis ends with a single group of elements that is coded as an L-system axiom. We recognize and code branching sequences of linearly translated, scaled, and rotated elements and their hierarchies. The L-system not only represents the input image, but it can also be used for various editing operations. By changing the L-system parameters, the image can be randomized, symmetrized, and groups of elements and regular structures can be edited. By changing the terminal and non-terminal symbols, elements or groups of elements can be replaced.

### Citations

602 |
The Algorithmic Beauty of Plants
- Prusinkiewicz, Lindenmayer
- 1996
(Show Context)
Citation Context ...odel, texture, or behavior. One of the most significant classes of procedural techniques are grammar-based methods, out of which the most common are methods based on Lindenmayer’s systems (L-systems) =-=[PL90]-=-. L-systems use compact rules for model description yet they can generate a wide class of models. The key challenge of procedural techniques is the definition of the rules. This task is not intuitive,... |

423 |
Mathematical models for cellular interactions in development. i. filaments with onesided inputs
- Lindenmayer
- 1968
(Show Context)
Citation Context ...els. 2. Previous Work There are three main categories of related work: L-systems, attempts to generate procedural rules interactively, and symmetry detection. L-systems were introduced by Lindenmayer =-=[Lin68]-=- as a mechanism for simulation of linear cellular subdivision. Prusinkiewicz [Pru86] extended the concept of L-systems by the graphical interpretation using a turtle. L-systems present the most advanc... |

167 | Procedural modeling of cities
- Parish, Müller
- 2001
(Show Context)
Citation Context ...ibe subdivision curves [PSSK03]. Recently, grammar-based procedural modeling has been applied to urban space modeling. Parish et al. used Open L-systems to generate street layout in virtual cities in =-=[PM01]-=-. Aliaga et al. introduced inverse procedural system to generate floors in virtual buildings in [ARB07]. Müller et al. introduced CGA shape for interactive building generation [MWH ∗ 06], and [MZWG07]... |

145 | Procedural Modeling of Buildings - Müller, Wonka, et al. - 2006 |

119 | Partial and approximate symmetry detection for 3D geometry
- MITRA, GUIBAS, et al.
- 2006
(Show Context)
Citation Context ... between our approach and previous work is that we express the output using automatically determined rules for an L-system. Our work is inspired by the recent work on symmetry detection. Mitra et al. =-=[MGP06]-=- introduced algorithms for detecting symmetries in unstructured 3D models by selecting dominant transformations in a transformation space. Similar concepts have since been used by others [LE06,PSG ∗ 0... |

90 | Imagebased procedural modeling of facades
- Müller, Zeng, et al.
- 2007
(Show Context)
Citation Context ...n [PM01]. Aliaga et al. introduced inverse procedural system to generate floors in virtual buildings in [ARB07]. Müller et al. introduced CGA shape for interactive building generation [MWH ∗ 06], and =-=[MZWG07]-=- used simple recursive grammar for façade generation. Most of the previous grammar-based approaches assume the rules are provided by the user. Automatic finding of the rules for a given model (the foc... |

82 | Discovering structural regularity in 3D geometry - Pauly, Mitra, et al. |

76 | A planarreflective symmetry transform for 3d shapes - Podolak, Shilane, et al. |

57 | Graphical applications of L-systems
- Prusinkiewicz
- 1986
(Show Context)
Citation Context ...tempts to generate procedural rules interactively, and symmetry detection. L-systems were introduced by Lindenmayer [Lin68] as a mechanism for simulation of linear cellular subdivision. Prusinkiewicz =-=[Pru86]-=- extended the concept of L-systems by the graphical interpretation using a turtle. L-systems present the most advanced formal mechanism for simulation of growing structures [PL90]. They were also appl... |

33 | Przemyslaw Prusinkiewicz. Realistic modeling and rendering of plant ecosystems - Deussen, Hanrahan, et al. - 1998 |

24 | Interactive visual editing of grammars for procedural architecture
- Lipp, Wonka, et al.
- 2008
(Show Context)
Citation Context ... Lsystem rule that is then used for an interactive plant generation. However, more complex rules cannot be generated and the system allows only for matching one predefined rule. Similarly Lipp et al. =-=[LWW08]-=- generate shape grammars from user input. Again, in their system only a predefined set of rules can be used. Ijiri et al. [IMIM08] introduced an example-based framework for procedural element arrangem... |

23 | Style grammars for interactive visualization of architecture
- ALIAGA, ROSEN, et al.
- 2009
(Show Context)
Citation Context ... space modeling. Parish et al. used Open L-systems to generate street layout in virtual cities in [PM01]. Aliaga et al. introduced inverse procedural system to generate floors in virtual buildings in =-=[ARB07]-=-. Müller et al. introduced CGA shape for interactive building generation [MWH ∗ 06], and [MZWG07] used simple recursive grammar for façade generation. Most of the previous grammar-based approaches ass... |

23 | and Przemyslaw Prusinkiewicz. “Visual Models of Plants Interacting with Their Environment - Mech - 1996 |

21 | The sketch Lsystem: Global control of tree modeling using free-form strokes
- IJIRI, OWADA, et al.
- 2006
(Show Context)
Citation Context ...problems of procedural modeling (see an early attempt to detect linear fractals [HCF97]). Some recent related works describe attempts to actually create procedural rules from user input. Ijiri et al. =-=[IOI06]-=- c○ 2010 The Author(s) Journal compilation c○ 2010 The Eurographics Association and Blackwell Publishing Ltd.O.Št’ava et. al. / Inverse Procedural Modeling by Automatic Generation of L-systems Figure... |

21 | Y.: Partial intrinsic reflectional symmetry of 3d shapes - XU, ZHANG, et al. - 2009 |

19 | An example-based procedural system for element arrangement
- Ijiri, Mech, et al.
(Show Context)
Citation Context ...em allows only for matching one predefined rule. Similarly Lipp et al. [LWW08] generate shape grammars from user input. Again, in their system only a predefined set of rules can be used. Ijiri et al. =-=[IMIM08]-=- introduced an example-based framework for procedural element arrangement generation and recently [YM09] used transformation spaces to detect symmetries and curvilinear arrangement in vector images. T... |

19 | A fractal model of mountains with rivers
- Prusinkiewicz, Hammel
- 1993
(Show Context)
Citation Context ... mechanism for simulation of growing structures [PL90]. They were also applied to determine plant distribution in plant ecosystems in [DHL ∗ 98], to simulate river formation in artificial terrains in =-=[PH93]-=-, and to describe subdivision curves [PSSK03]. Recently, grammar-based procedural modeling has been applied to urban space modeling. Parish et al. used Open L-systems to generate street layout in virt... |

17 | H.-P.: A graph-based approach to symmetry detection - BERNER, BOKELOH, et al. - 2008 |

17 | M.: Symmetrization
- MITRA, GUIBAS, et al.
(Show Context)
Citation Context ...nto the transformation space. As clusters of points correspond to potential symmetries, the clusters are detected and the symmetries are stored in a symmetry graph. The next paper by the same authors =-=[MGP07]-=- uses the symmetries to modify objects to express more symmetries than the originals. Pauly et al. [PMW ∗ 08] presented a paper on discovering regular and repeated geometric structures. They detect sc... |

17 | L-system description of subdivision curves
- Prusinkiewicz, Samavati, et al.
(Show Context)
Citation Context ...ures [PL90]. They were also applied to determine plant distribution in plant ecosystems in [DHL ∗ 98], to simulate river formation in artificial terrains in [PH93], and to describe subdivision curves =-=[PSSK03]-=-. Recently, grammar-based procedural modeling has been applied to urban space modeling. Parish et al. used Open L-systems to generate street layout in virtual cities in [PM01]. Aliaga et al. introduce... |

16 | A.: Symmetry detection using line features - Bokeloh, Berner, et al. - 2009 |

12 | Radomír Měch. Synthetic topiary - Prusinkiewicz, James - 1994 |

6 |
R.: Detecting symmetries and curvilinear arrangements in vector art
- YEH, MECH
(Show Context)
Citation Context ...m user input. Again, in their system only a predefined set of rules can be used. Ijiri et al. [IMIM08] introduced an example-based framework for procedural element arrangement generation and recently =-=[YM09]-=- used transformation spaces to detect symmetries and curvilinear arrangement in vector images. The above two user-assisted systems use simple algorithms for procedural models generation and they can e... |

4 | P.: Similarity hashing: A computer vision solution to the inverse problem of linear fractals. Fractals 5
- HART, FLYNN
- 1997
(Show Context)
Citation Context ... user. Automatic finding of the rules for a given model (the focus of this paper) has been recognized as one of the key problems of procedural modeling (see an early attempt to detect linear fractals =-=[HCF97]-=-). Some recent related works describe attempts to actually create procedural rules from user input. Ijiri et al. [IOI06] c○ 2010 The Author(s) Journal compilation c○ 2010 The Eurographics Association ... |

2 | EKLUNDH J.-O.: Detecting symmetry and symmetric constellations of features - LOY |