To solve the issues with conventional level set segmentation algorithms, which are sensitive to the initial contours and less noise-resistant, a segmentation model based on the coupling of texture information and structural information is developed. In this model, a rotation invariant mask produced by fractional-order differentiation is used to first describe the image's global information. Then, the power function of the energy generalization function is solved by applying factorization theory, and for each pixel of the image, not only its information but also its surrounding pixel information is taken into account and integrated into the energy generalization function via weight scaling. At the same time, the L2 norm of the fractional-order image and the difference from the fitted image are used to generate the energy generalization function of the model. The final results of this study demonstrate that the proposed model achieved a better segmentation performance than the current active contour models in terms of robustness to Gaussian noise and pretzel noise, as well as the segmentation accuracy and algorithm running time. These results were obtained in synthetic images, real images, and natural images.

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Parameter inversion of solute BOD-DO water quality model was generally solved through a nonlinear operator equation. The original problem is finally transformed into an optimization problem by creating fit function. We used the genetic algorithm, which can search the best solution from many initial points and obtain the total optimum solution of water quality model three parameters at the same time, and solve the problem by means of crossover and mutation operator. The results of numerical simulation show that the method has higher accuracy, quicker convergent speed and better stabilization than existing methods and is easy to program and calculate.

By means of Newton’s difference quotient and Thiele type continued fraction combined with the generalized inverse matrix, we present a kind of bivariate matrix-valued blending difference quotient. On this basis, we construct the bivariate Newton-Thiele type rational interpolants and give its iterative algorithm.