Detection of Black Spot of Rose Based on Hyperspectral Imaging and Convolutional Neural Network

Black spot is one of the seriously damaging plant diseases in China, especially in rose production. Hyperspectral technology reflects both external features and internal structure information of measured samples, which can be used to identify the disease. In this research, both the spectral and image features of two infected roses with black spot were used to train a convolutional neural network (CNN) model. Multiple scattering correction (MSC) and standard normal variable (SNV) methods were applied to preprocess the spectral data. Cropping, median filtering and binarization were pretreatments used on the hyperspectral images. Three CNN models based on Alexnet, VGG16 and neural discriminative dimensionality reduction (NDDR) were evaluated by analyzing the classification accuracy and loss function. The results show that the CNN model based on the fusion of features has higher accuracy. The highest accuracies of detection of blackspot in different roses are 12–26 (100%) and 13–54 (99.95%), applying the NDDR-CNN model. Therefore, this research indicates that the spectral analysis based on CNN can detect black spot of roses, which provides a reference for the detection of other plant diseases, and has favorable research significance as well as prospect for development.

Rates of convergence for U-Statistics with varying kernels

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).

On the duality between the behaviour of sums of independent random variables and the sums of their squares

Let Xnj, 1 ≤ j ≤ kn, be independent, asymptotically negligible random variables for each n ≥ 1. In certain cases there exists a duality between the behaviour of ΣjXnj and . We extend one of the known forms of this duality, and show that, under mild conditions on the truncated moments of the Xnj, the convergence of to 1 in the mean of order p (p ≥ 1) is equivalent to the convergence of ΣjXnj to the standard normal law, together with the convergence of its 2pth absolute moment to that of a standard normal variable. A similar result holds in the case of convergence to a Poisson law.