Abstract
Aiming at the conventional image edge detection algorithm, the first-order differential edge detection method is easy to lose the image details and the second-order differential edge detection method is more sensitive to noise. To deal with the problem, the Tikhonov regularization method is adopted to reconstruct the input coal-rock infrared images, so as to reduce the noise interference, and then, the reconstructed image is transformed by gray level. Finally, we consider the frequency characteristics and long memory properties of fractional differential, the classical first-order Sobel and second-order Laplacian edge detection algorithms are extended to fractional order pattern, and a new pattern of fractional order differential image edge detection is constructed to realize the coal-rock fracture edge features identification. The results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller. From the point of view of location criteria and location accuracy, the fractional order differential algorithm is better than the integer order. In addition, the proposed method is compared with Canny algorithm, B-spline wavelet transform, and multidirection fuzzy morphological edge detection method, can detect more coal-rock fracture infrared image edge details, and is more robust to noise.
Highlights
Integer Order Edge Detection OperatorIf Δx and Δy are computed according to the number of pixels between two pixels, let Δx Δy 2, and the differential form of the gradient component is represented as follows:
Aiming at the conventional image edge detection algorithm, the first-order differential edge detection method is easy to lose the image details and the second-order differential edge detection method is more sensitive to noise
We consider the frequency characteristics and long memory properties of fractional differential, the classical first-order Sobel and second-order Laplacian edge detection algorithms are extended to fractional order pattern, and a new pattern of fractional order differential image edge detection is constructed to realize the coal-rock fracture edge features identification. e results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller
Summary
If Δx and Δy are computed according to the number of pixels between two pixels, let Δx Δy 2, and the differential form of the gradient component is represented as follows:. If Δx and Δy are computed according to the number of pixels between two pixels, let Δx Δy 1, and the differential form of the second-order derivative is represented as follows: G2(u(x, y)). By introducing differential order from first order to fractional order, a fractional Sobel operator is proposed, whose differential form is along the X-axis and the Y-axis [30,31,32]: Gαx. E differential order is extended from the second order to the fractional order, a fractional Laplacian operator is proposed, whose differential form can be defined as follows [33, 34]: Gα(u(x, y)). M × N represents the image size, and pixels can be labeled as edge points when ∇αu > T
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