Edge Detectors Based on Pauta Criterion with Application to Hybrid Compact-WENO Finite Difference Scheme (Advances in Applied Mathematics and Mechanics, 2023)
In the last two decades, many edge detection methods have been developedand widely used in image processing for edge detection and the hybrid compact-WENO finite difference (hybrid) schemes for solving the system of hyperbolic conservation laws with solutions containing both discontinuous and complex fine-scalestructures. However, many edge detection methods include the problem-dependentparameters such as the high order multi-resolution (MR) analysis (Harten, JCP, 49(1983)). Therefore, we combined the Tukey’s boxplot method with MR analysis (Gao etal., JSC, 73 (2017)) to overcome this problem in a sense. But the Tukey’s boxplot methodneeds to sort the data at the beginning of Runge-Kutta time integration method, whichis relatively time-consuming and inefficient. In this study, we employ the Pauta criterion and remove the problem-dependent parameters in the MR analysis. Furthermore, two new edge detection approaches, which are based on second-order centraldifference scheme and Ren’s idea (Ren et al., JCP, 192 (2003)), are also proposed. Theaccuracy, efficiency and robustness of the hybrid scheme with the new edge detectorsare verified by numerous classical one- and two-dimensional examples in the imageprocessing and compressible Euler equations with discontinuous solutions.