Lossy compression of tree architectures

Introduction Plants usually show intricate structures whose representation and management are an important source of complexity of models. Yet plant structures are also repetitive: although not identical, the organs, axes, and branches at different positions are often highly similar. From a formal perspective, this repetitive character of plant structures was first exploited in fractal-based plant models (Barnsley, 2000; Ferraro et al., 2005; Prusinkiewicz and Hanan, 1989; Smith, 1984). In particular, L-systems have extensively been used in the last two decades to amplify parsimonious rule-based models into complex branching structures by specifying how fundamental units are repeatedly duplicated and modified in space and over time (Prusinkiewicz et al., 2001). However, the inverse problem of finding a compact representation of a branching structure has remained largely opened, and is now becoming a key issue in modeling applications as it needs to be solved to both get insight into the complex organization of plants and to decrease time and space complexity of simulation algorithms. The idea is that a compressed version of a plant structure might be much more efficient to manipulate than the original extensive branching structure. For instance, Soler et al. (2003) have shown that the complexity of radiation simulation can be drastically reduced if self-similar representations of plants are used. Unfortunately, strict self-similarity has a limited range of applications, because neither real plants nor more sophisticated plant models are exactly self-similar. Consequently, we propose in this paper an algorithm that exploits approximate selfsimilarity to compress plant structures to various degrees, representing a tradeoff between compression rate and accuracy. This new compression method aims at making possible to efficiently model, simulate and analyze plants using compressed representations.