In recent years, the fractional order derivative has been introduced for image enhancement. It was proved that the medical image enhancement method based on the fractional order derivative has better effect than the method based on the integral order calculus. However, a priori information such as texture surrounding a pixel is normally ignored by the traditional fractional differential operators with the same value in the eight directions. To address the above problem, this paper presents a new medical image enhancement method by taking the merits of fractional differential and directional derivative. The proposed method considers the surrounding information (such as the image edge, clarity and texture information) and structural features of different pixels, as well as the directional derivative of each pixel in constructing the masks. By proposing this method, it can not only improve the high frequency information, but also improve the low frequency information of the image. Ultimately, it enhances the texture information of the image. Extensive experiments on four kinds of medical image demonstrate that the proposed algorithm is in favor of preserving more texture details and superior to the existing fractional differential algorithms on medical image enhancement.

Aiming at the problem of portrait of members in shopping malls, this paper analyzes the similarities and differences of consumption behaviors between member groups and nonmember groups, and constructs the LRFMC model with [Formula: see text]-means algorithm to analyze the value of membership. Second, active states of members are divided according to the consumption time interval, and KNN algorithm model is established to predict member states and used to predict the membership status. Finally, it discusses which types of goods are more suitable for promotional activities and can bring more profits to the shopping mall.

The colorimetric method is usually used to test the concentration of substances. However, this method has a big error since different people have different sensitivities to colors. In this paper, in order to solve the identification problem of the color and the concentration of the test paper, firstly, we found out that the concentration of substance is correlated with the color reading by using the Pearson’s Chi-squared test method. And by the concentration coefficient of Pearson correlation analysis, the concentration of substance and color reading is highly correlated. Secondly, according to the RGB value of the paper image, the color moments of the image are calculated as the characteristics of the image, and the Levenberg–Marquardt (LM) neural network is established to classify the concentration of the substance. The accuracy of the training set model is 94.5%, and the accuracy of the test set model is 87.5%. The model precision is high, and the model has stronger generalization ability. Therefore, according to the RGB value of the test paper image, it is effective to establish the LM neural network model to identify the substance concentration.