Research On Fast Calculation Of Gradient Vector Flow For Large Image

The gradient vector flow(GVF)model or the generalized gradient vector flow(GGVF)model are widely used in image applications,such as denoising filtering,edge enhancement,edge extraction and so on,especially active contour model and image segmentation.It is also widely used in medical image processing applications.However,the application of gradient vector flow or generalized gradient vector flow in large images is limited due to its large amount of computation and low computational efficiency.In this context,this paper presents a fast calculation research scheme for large-image GVF models.At present,there are two most classical algorithms in fast computing GVF or generalized GGVF model:fast calculation method based on Multigrid model and fast calculation method based on imexact augmented Lagrange method.On the basis of these two classical methods,some new fast calculation method is proposed,which combines fast Fourier transform,discrete sine transform and discrete cosine transform.The research content of this article is divided into two parts:In the first part,based on the inexact augmented Lagrange method,the corresponding fast calculation method is proposed for the three boundary conditions of periodic,Dirichlet and Neumann.Firstly,it is shown that when the periodic boundary condition is used,the result of the GVF or the GGVF model will result in errors in the boundary area.Then use two other boundary conditions to avoid this defect.Fast Fourier transform(FFT),Discrete sine transform(DST)or discrete cosine transform(DCT)are used in the proposed fast algorithm.Finally,the time complexity of the proposed algorithms are Cnlog(n).The second part,based on the first part of the study,combines the classic multigrid based fast computing method.Under the framework of the fully multigrid method,the algorithms proposed in part 1 are expanded.Combined with the perfect multigrid algorithm,the time complexity of the new algorithms are the same as before the expansion,and its computational efficiency has been improved.Finally,we use three sets of image to test the performance of the algorithm,whose sizes are 256x256?512x512 and 1024×1024.Compared with the two classical algorithms,the efficiency of the algorithms proposed in this paper are improved.Then take the Lena image as an example,compare three different boundary conditions algorithm.In the middle region of the image,GVF or GGVF have little difference,while in the boundary region,the Dirichlet and the Neumann boundary condition algorithm can avoid the deviation of the true result of the GVF from the results of the periodic boundary condition algorithm.