The detection of edges in images is a pressing issue in the field of image processing. This technique has found widespread application in image pattern recognition, machine vision, and a variety of other areas. The feasibility and effectiveness of grey theory in image engineering applications have prompted researchers to continuously explore it. The grey model (GM (1,1)) with the first-order differentiation of one variable is the grey prediction model that is most frequently used. It is a typical trend analysis model and can be used for image edge detection. The traditional integer-order differential image edge detection operator has problems such as blurred and discontinuous edges, incomplete image details, and high influence by noise. We present a novel grey model for detecting image edges based on a fractional-order discrete operator in this paper. To improve the features of the original image, our model first preprocesses it before calculating the prediction of the original image using our fractional-order cumulative greyscale model. We obtain the edge information of the image by first subtracting a preprocessed image from the predicted image and then eliminating isolated noise points using the median filtering method. Based on the discrete wavelet transform, image edges are finally extracted. The comparison experiments with a traditional edge detection operator show that our algorithm can accurately locate the image edges, the image edges are clear and complete, and this model has better anti-noise performance.

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To address the problems in the traditional classroom of linear algebra, we make full use of self-built MOOC resources and propose a hybrid teaching model that combines online and offline learning suitable for applied undergraduate institutions. This mode of teaching meets students' needs for "fragmented" learning, not only stimulates students' enthusiasm for learning, but also increases students' motivation and initiative. Practice shows that this teaching mode emphasizes the "main" position of students and the "leading" role of teachers, which solves the problem of "difficult interaction" between teachers and students and improves the teaching effect of linear algebra courses.