In this study, the leaf area was estimated by different regression models and new methods of image processing by using artificial intelligence (AI) in bread (Triticum aestivum L.) and durum wheat (Triticum durum L.) and triticale (×Tritosecale Wittm. ex A. Camus) at seedling, booting, and milk development stages. Data on leaf traits in 1,000 plants of breed wheat, triticale, and durum wheat were studied. Among regression models using general data, $\mathrm{LA}=a+b\sqrt{LW}$, $\mathrm{LA}=a+b(W)$, and $\mathrm{LA}=a+b(W/L)$ models had a R² > 90% for all three cultivars (L and W represented length and width of leaves). For wheat bread, models $W+(LW)$ and $\sqrt{L}\times (LW)$ exhibited a good estimate of the leaf area at all stages of growth, whereas in triticale, the linear models that used the product of $\sqrt{W}\times L$ and $\sqrt{LW}$ were more suitable to estimate leaf areas in booting and milk development. The multilayer perceptron (MLP) neural network modeling indicated that the ‘trainlm,’ ‘trainlm,’ and ‘traincgb’ algorithms with an optimal structure of 2‐10‐1, 2‐3‐1, and 2‐10‐1 had the least amount of the mean square error for bread wheat, triticale, and durum wheat, respectively, for each of the growth stages. Furthermore, based on the adaptive neuro‐fuzzy inference system (ANFIS) method, a very accurate estimate of the leaf area was obtained for each of the growth stages. The comparison of different models in the leaf area estimation showed that unlike estimating leaf area by regression, AI‐based methods did not depend on plant growth stages. In this study, we suggested the utilization of image processing and artificial intelligence in leaf area estimation. It will accelerate leaf area measurement in the field, by extending these methods and transferring it into smartphone applications.

中文翻译：

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谷物中叶面积的图像处理和预测：人工神经网络，自适应神经模糊推理系统和回归方法的比较

在这项研究中，通过使用人工智能（AI）对面包（Triticum aestivum L.）和硬粒小麦（Triticum durum L.）和小黑麦（× Tritosecale Wittm）中的不同回归模型和图像处理新方法进行估计，从而得出叶面积。 ex A. Camus）处于苗期，孕穗期和乳汁发育阶段。研究了1000种小麦，黑小麦和硬质小麦的叶片性状数据。在使用一般数据的回归模型中，$\mathrm{洛杉矶}=\mathrm{一个}+b\sqrt{\mathrm{大号}\mathrm{w\; ^}}$， $\mathrm{洛杉矶}=\mathrm{一个}+b（\mathrm{w\; ^}）$， 和 $\mathrm{洛杉矶}=\mathrm{一个}+b（\mathrm{w\; ^}/\mathrm{大号}）$所有三个品种的模型R ² > 90％（L和W代表叶片的长度和宽度）。对于小麦面包，型号$\mathrm{w\; ^}+（\mathrm{大号}\mathrm{w\; ^}）$ 和 $\sqrt{\mathrm{大号}}\times （\mathrm{大号}\mathrm{w\; ^}）$ 对生长的所有阶段都显示出对叶面积的良好估计，而在黑小麦中，使用 $\sqrt{\mathrm{w\; ^}}\times \mathrm{大号}$ 和 $\sqrt{\mathrm{大号}\mathrm{w\; ^}}$更适合估计靴子和牛奶发育中的叶面积。多层感知器（MLP）神经网络建模表明，最佳结构为2-10-1、2-3-1和2-10-1的``trainlm''，``trainlm''和``traincgb''算法具有以下特征：在每个生育阶段，面包小麦，黑小麦和硬质小麦的均方误差最小。此外，基于自适应神经模糊推理系统（ANFIS）方法，可以对每个生长阶段的叶面积进行非常准确的估算。叶面积估计中不同模型的比较表明，与通过回归估计叶面积不同，基于AI的方法不依赖于植物生长阶段。在这项研究中，我们建议在叶面积估计中利用图像处理和人工智能。