本文以江中猴姑早餐米稀、乐事薯片、港荣奶香蒸蛋糕、豪士乳酸菌酸奶小口袋面包作为食品样品研究对象，并选取相对应造假样品，通过分数阶微积分方法对食品质量进行防伪检测。在市场上获取真伪样品各90个，采用分数阶微积分获取食品能量信号的分数阶微分算子及函数分数阶导数，加强食品二维码原图灰度值改变较大的高频边缘信息，同时保持其灰度直方图分布包络，保证了食品二维码图像纹理细节信息的基本完整性，以实现分析不同食品真伪二维码分数阶微积分的差异。经实验结果发现，采用分数阶微积分方法在初始分类检测时，总初始准确检测率高达95.56%；在交叉验证中，总检测准确率为88.89%，能够为食品质量防伪检测提供技术支持，为维护食品质量的市场秩序奠定理论基础。

In this work, the food samples of the functional food (Jiangzhong Hou Gu Mi Xi), Leshi potato chips, steamed cake (Gang Rong), small bread (Haushi Lactobacillus yoghurt) were studied, and the corresponding counterfeit samples were selected. The anti-counterfeiting detection of food quality was carried out by fractional calculus method. Ninety true and false samples were obtained in the market. The fractional differential operators and fractional derivatives of the functions were obtained by fractional calculus. The high frequency edge information of the original gray value of the two-dimensional food code was enhanced, while the distribution envelope of the gray histogram was maintained. The basic integrity of the texture details of the two-dimensional food code image was guaranteed so as to realize different analysis. The difference of fractional calculus between true and false two-dimensional codes of food. The results showed that the total initial detection accuracy of the fractional calculus method was as high as 95.56% in the initial classification detection and 88.89% in the cross-validation, which can provide technical support for anti-counterfeiting detection of food quality and provide a theoretical foundation for maintaining the market order of food quality.

河南省社科联项目（SKL-2016-3688）