| Image edge detection and image fusion are two important links in digital image processing,which have great application value in practical engineering.Fractional differential have of the late years been widely used in information analysis and processing.Differentiation is a powerful tool to describe Euclidean space,and it has important applications in signal detection and extraction.It has advantages in calculating spatial gradient operator and frequency operator,which can be used in image edge detection and image fusion.As a newly proposed linear time-fractional frequency domain transform,fractional wavelet transform provides a new method for image processing in transform domain,and fractional wavelet transform has a very wide application prospect in image fusion field.This article project carried out main contents as follows:(1)Image edge detectionWhen the traditional Canny edge detection algorithm is used to detect and recognize images,it often has some problems,such as incomplete fuzzy edge detection and sensitivity to noise.Therefore,a new method of Canny edge detection based on fractional differential theory is proposed in this paper.Firstly,a new fractional step degree operator called fractional Sobel operator is constructed,by combining Grunwald-Letnikov fractional differentiation with isotropic Sobel operator,which replaces the gradient operator in the traditional Canny algorithm.Secondly,the new proposed mothed presents an improved non-maximum suppression method,which is used to refine the edges.Finally,the double thresholds are determined by Otsu method.The experimental results expresses that the image edges detected by the proposed algorithm are clear and comprehensive,insensitive to noise,and no redundant edges are generated.(2)Multi-focus image fusionThere exist some problems in multi-focus image fusion,such as easy loss of detail and artifact of image edge.To address the above problems,a new multi-focus image fusion method based on discrete fractional wavelet transform and fractional spatial frequency is proposed.Firstly,the source images are decomposed by discrete fractional wavelet transform respectively to obtain the low frequency part and high frequency part.Then,for the sake of integrating the image informations effectively,the most appropriate fractional order is selected according to the energy distribution characteristics of different order wavelet modal coefficients.For the low frequency part,the laplace energy sum is applied to get the initial decision,and then the decision graph is modified by guided filtering to get the fusion rule.Fractional spatial frequency fusion rules are adopted for the high frequency part.Finally,the inverse discrete fractional wavelet is processed to obtain the composite image.The simulation results of visual quality and quantitative evaluation show that the Gibbs effect and edge artifact effect are effectively weakened by the proposed method,and the effectiveness and superiority of the proposed method are verified. |
