Research Of Image Segmentation Based On Fractional Derivative

With the development of the digital image technology,image has become a new medium for information dissemination,so image processing gets more and more attention.Being the basis of image processing,the importance of image segmentation is increasingly prominent too.In recent decades,the image segmentation methods based on the active contour model have gradually formed a relatively complete set of architecture,and become an important branch of image segmentation.The current active contour models could be mainly divided into three types,i.e.,the edge-based,the region-based,and the edge & region-based as well.The edge stop function plays an important role in any type of the aforementioned methods,and it is usually designed by using the gradient of the image,it,however,is calculated by the integer derivative that is not robust against image noise,and cannot distinguish the true or the false edges.On the other hand,the active contour models firstly design an energy functional,then obtain the partial differential equation based on the Euler-Lagrange equation of the energy functional,and finally solves the partial differential equation to obtain the final segmentation result.In other words,the essence of the active contour model is a functional optimization problem that is usually realized by iteratively solving an evolution equation via the gradient descent method.However,the classical gradient descent methods usually update the gradient of the function to be optimized to guide the optimization direction.That often leads to a slow optimization process and the local optimum due to its local characteristics.The fractional derivative,an extension of the integer derivative,extends the order from integer to fraction.By analyzing the definition of the fractional derivative,we could find that it has the global characteristics in both time and spatial domain,and possesses the advantages that the integer derivative does not have for some physical processes with the "memory" in the time domain or the non-local dependence characteristics in the spatial domain.In other words,it could solve the local extremum problem caused by the integer derivative to some extent.When the order of the fractional derivative is between 0 and 1,the high-frequency parts and the medium-frequency parts could be enhanced,and the low-frequency parts could be retained nonlinearly as well.For image processing,preserving the texture and the spatial information of low and medium frequency could be beneficial to improve the robustness against noise.This paper takes the characters of fractional derivatives into consideration,and propose two image segmentation methods based on active contour model as follows:(1)In its amplitude-frequency characteristic curve,fractional derivative shows good retention of low-frequency information,which has a broader application prospect compared with the suppression of low-frequency information of integer derivative.On the basis of previous research,this paper fully combines the low-frequency reservation of fractional derivative to design and realize the image feature descriptor based on fractional derivative,which enhances the robustness against noise and improves the ability to judge the authenticity of target edge.(2)Due to its computational characteristics,integer derivative is usually obtained by using the information of only a few points in the neighborhood of the point to be calculated.It can bring about the convenience by using local information,but it may also cause the deviation.This paper uses the global characteristics of fractional derivative to transform the traditional optimization algorithm,and realizes a set of functional optimization methods based on fractional derivative,including the demonstration of fractional gradient descent flow,as well as the fractional Euler-Lagrange equation.Finally this method successfully improves the the local optimum problem caused by the traditional gradient descent method.In summary,under the framework of curve evolution,based on the characteristics of the fractional derivative,this paper researches the design of image edge descriptor,the design of the energy functional,the optimization method for energy functional,and propose two image segmentation methods based on the fractional derivative to enhance the discriminant ability on the pseudo edges and solve the problem of the local extremum caused by the traditional optimization algorithm to some extent.At the same time,it improves the effectiveness and efficiency of the image segmentation method based on curve evolution.