Fractional Differential In The Image Of Rock Fractures

For the fractional differential has a weaker high-frequency-enhanced ability than the integer order ones, it will be very helpful if the fractional differential is introduced into the image processing while we needing to enhance the high-frequency image signals. This is also the main reason for introducing the fractional differential into the project of the rocks.At first, it gives a great deal of analysis and research about the fractional differential operator within Tiansi template, and a better template form basing on the Tiansi template is given. The orders of new fractional template and the ones of integer-order template have a very good compatibility, and also the new template has a very good continuous differential effect. It proves that the new template is more suitable in playing a fractional operator role.Secondly, it gives a new algorithm that applied to the application of fractional differential through the characteristic of the rock fracture image and the mathematical meaning of the fractional differential template. The new mature algorithm integrates the fractional differential characteristics very well, and it plays out the advantages of the convolution by fractional differential operator. The experiments show that this method has a better ability to extract high-frequency details of the images.Finally, the iterative deconvolution algorithm is extended to the application of the general images. It shows that the new algorithm will pay more attention to the image texture that in lower gray value differences, while the classical differential operator pay more attention to the higher gray value difference.This study is very meaningful for expanding the application areas of fractional differential and carrying out a significant exploration.