Authors: Dymitr Ruta, Corrado Mio, Ernesto Damiani
Abstract: Trees continue to fascinate with their natural beauty and as engineering
masterpieces optimal with respect to several independent criteria. Pythagorean
tree is a well-known fractal design that realistically mimics the natural tree
branching structures. We study various types of Pythagorean-like fractal trees
with different shapes of the base, branching angles and relaxed scales in an
attempt to identify and explain which variants are the closest match to the
branching structures commonly observed in the natural world. Pursuing
simultaneously the realism and minimalism of the fractal tree model, we have
developed a flexibly parameterised and fast algorithm to grow and visually
examine deep Pythagorean-inspired fractal trees with the capability to orderly
over- or underestimate the Leonardo da Vinci’s tree branching rule as well as
control various imbalances and branching angles. We tested the realism of the
generated fractal tree images by means of the classification accuracy of
detecting natural tree with the transfer-trained deep Convolutional Neural
Networks (CNNs). Having empirically established the parameters of the fractal
trees that maximize the CNN’s natural tree class classification accuracy we
have translated them back to the scales and angles of branches and came to the
interesting conclusions that support the da Vinci branching rule and golden
ratio based scaling for both the shape of the branch and imbalance between the
child branches, and claim the flexibly parameterized fractal trees can be used
to generate artificial examples to train robust detectors of different species
of trees.
Source: http://arxiv.org/abs/2411.08024v1
