为描述油菜缺素叶片图像的特征，该文提出了一种基于多重分形去趋势波动分析方法，即局部多重分形去趋势波动分析。该方法确定的hij(q)指数能有效刻画叶片图像每个像素点的多重分形特征，并以所有像素点hij(q)的平均值Lhq表征每幅图像的多重分形特征。选取4种油菜缺素叶片图像进行试验，结果表明所提取局部多重分形去趋势波动平均指数Lhq能很好地区分叶片，并通过方差分析指出当q={-10,-9,-8,-7,-6}时的Lhq区分效果最好。最后基于每个像素点的hij(q)指数利用模糊C均值聚类对缺镁油菜叶片图像进行模糊分割，并与传统的灰度值分割及经典的基于容量测度的Hölder指数分割进行了对比试验，结果表明以上述hij(q)为特征具有最佳的分割效果。%Fertilization levels play a critical role in crops’ growth. As a vital organ of rapeseed, leaves can well reflect the nutritional level, and their images are always processed and analyzed by a computer vision system. The texture feature of the leaves’ images is very important to become a key indicator to describe the nutritional status for the rapeseeds. In recent years, multifractal methods were used to extract its features for describing a texture image. The traditional type of multifractal analysis (MFA) was calculated based on the standard partition function multifractal formalism, which describes stationary measurements. For a crop image collected in field crops, the surface itself is hardly stationary and whose gray scale volatility is likely to be more bizarre. By this token, this is not always a valid choice to analysis them based on MFA. A novel method: local multifractal detrended fluctuation (LMF-DFA) analysis was proposed in this paper to extract texture feature of every pixel for a self-similar surface based on the method of 2-D multifractal detrended fluctuation analysis (MF-DFA), which can well portray multifractal features for a non-stationary surface. A set of new multifractal descriptors, namely the local multifractal fluctuation exponents hij(q) were defined to portray every pixels’ feature effectively, the LMF-DFA exponents were calculated by a slipping window of sizes w×w. In our study, we took w=11. The components of the LMF-DFA spectrum which are used to distinguish between different textures can be considered statistically significant. As an important application, we applied the method to disclose a rapeseed leaf’s image of nutrient deficiency. Four kinds of nutrient deficiency of rapeseed leaf’s images, namely, Nitrogen deficiency, Phosphorus deficiency, Potassium deficiency, and Magnesium deficiency, were chosen for our two experiments. In order to extract real and accurate information by the proposed method, in every image the background was are removed, and circumscribed by a minimum bounding rectangle, which is the so-called standardization process. In our first experiment, initially, for each image, we calculated a set of hij(q) for the value of q=-10 to 10. And then we used Lhq which is an average of the hij(q) over all pixels, to represent the multifractal feature for each image. The result illustrated that the calculated Lhq exponents can differentiate them well. Meanwhile, it points out that the discriminant effect of Lhq exponents are best when the value q={-10,-9,-8,-7,-6}by an analysis of variance. In our second experiment, fuzzy C-means clustering was used to process fuzzy segmentation for the Magnesium deficiency of a rapeseed leaf’s image, which contains some representative regions of nutrient deficiency. Both the proposed hij(q) exponents and other two characteristics which are the traditional gray value and the classic Hölder exponent calculated by standard multifractal analysis were applied to the segmentation experiment. The comparison results demonstrated that the LMF-DFA estimation can provide most robust segmentations. The meaningful work provides a theoretical and practical method for the identification and diagnosis of a crop leaf’s nutrient deficiency. Moreover, it provides a precise positioning method for key areas of crop leaves’ nutrient deficiency.
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