为达芬奇正名：用于自然分支结构最小重建的毕达哥拉斯树
Leonardo vindicated: Pythagorean trees for minimal reconstruction of the natural branching structures
AI总结：
研究提出灵活参数化的毕达哥拉斯分形树算法，通过CNN分类准确率验证，发现其支持达芬奇分支规则与黄金比例缩放，可用于生成人工样本训练树种检测器。
摘要：
树木以其自然之美和作为在多个独立标准下达到最优的工程杰作持续令人着迷。毕达哥拉斯树是一种著名的分形设计，能逼真地模拟自然树木的分支结构。我们研究了多种类毕达哥拉斯分形树，它们具有不同形状的底座、分支角度和宽松的尺度，试图识别并解释哪些变体与自然界中常见的分支结构最匹配。为了同时追求分形树模型的真实性与极简性，我们开发了一种灵活参数化且快速的算法，用于生长并视觉检查深层的受毕达哥拉斯启发的分形树，该算法能够有序地高估或低估达芬奇树木分支规则，并控制各种不平衡和分支角度。我们通过迁移训练的深度卷积神经网络检测自然树的分类准确率，测试了生成的分形树图像的真实性。在经验性地确定了使CNN自然树类别分类准确率最大化的分形树参数后，我们将它们转换回分支的尺度和角度，得出了支持达芬奇分支规则和基于黄金比例的缩放的有趣结论，这适用于分支形状和子分支之间的不平衡，并声称灵活参数化的分形树可用于生成人工样本来训练不同树种的鲁棒检测器。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
