Inverse Procedural Modeling of Branching Structures by Inferring L-Systems

Abstract

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.

Learning to reconstruct botanical trees from single images

“…Early approaches for modeling branching structures use rule-based algorithms [Honda 1971;Prusinkiewicz and Lindenmayer 1990], repetitive patterns [Aono and Kunii 1984;Kawaguchi 1982;Oppenheimer 1986;Smith 1984], cellular automata [Greene 1989], particle systems [Reeves and Blau 1985], or the combination of approaches [Lintermann and Deussen 1999]. As plants rarely grow in isolation, many methods focus on the plant interaction with the environment through query modules [Měch and Prusinkiewicz 1996] or random-walk [Benes and Millán 2002], inverse procedural modeling [Guo et al 2020;Stava et al 2014], by modeling the competition for resources and self-organization [Palubicki et al 2009], space colonization [Runions et al 2007], or by inversely modeling the growth response [Pirk et al 2012b].…”

TreePartNet

“…Shape decomposition. To reveal the higher-level structure of a shape for its better approximation, reconstruction, and manipulation, a variety of techniques were presented to decompose shapes into simple geometric primitives [Kaiser et al 2019], polycubes [Livesu et al 2013], bounding proxies [Calderon and Boubekeur 2017], or branching elements [Guo et al 2020]. Close to our work are approaches that decompose data into generalized cylinders (GCs).…”

A Survey of Control Mechanisms for Creative Pattern Generation

“…Example‐based G uo et al [GJB*20] focus specifically on creating branching structures with an inverse modeling process for inferring a generating L‐system. The technique is robust and takes a variety of input designs such as real‐world images or hand‐drawn sketches of the branching.…”

“…Visual examples for branching structures from G uo et al [GJB*20], who recreate a user sketch (left) with a procedural L‐system (right) through inverse modeling.…”