Research On Topology-preserving Image Segmentation Model And Algorith

Image segmentation plays a key role in computer vision and image processing tasks,which has been widely applied in medical imaging,remote sensing images,and intelligent transportation,etc.Despite existing methods aim to divide the image into different regions based on the image features,it is difficult to deal with the situation of object adhesion,mutual occlusion,and the fine structure of partial feature defect.Segmentation models that consider geometric and even topological constraints provide the way to comprehensively deal with above problems.Nevertheless,these benefits have been largely constrained by the computational difficulties.The Self-repelling Snake(SRS)variational model based on topology constraints is an effective model to achieve topology-preserving segmentation of objects in images,and has been successfully applied in many fields.However,traditionally,the Additive Operator Splitting(AOS)method based on the gradient descent equation is used for calculation,which has low computational efficiency and takes up a lot of memory.To this end,this thesis proposes two types of fast calculation methods.The main work and contributions are:1.For the classical SRS model,by introducing auxiliary variables,Lagrange multipliers,penalty parameters,etc.,and the corresponding Alternating Direction Method of Multipliers(ADMM)calculation method is proposed.The complex energy functional extremum problem is decomposed into two simple sub-optimization problems,which are solved by Fast Fourier Transform(FFT)and approximate generalized soft threshold formula respectively.Therefore,our method achieves much better performance on the overall computational efficiency.2.By introducing dual variables,the simple minima problem of the original SRS model is transformed into two simple sub-optimization problems of minima and maxima,and a fast-dual method is designed.The corresponding sub-problems are solved using the upwind difference scheme and the projection method,respectively.In addition,in view of the problem that the original SRS model has insufficient force in the narrow area of the image,this thesis adds a Gradient Vector Flow(GVF)directed force field on the basis of the original model to speed up the evolution of the contour line in the narrow area of the image,which effectively prevent the contour line out of bounds in the evolution process.3.The above two algorithms can avoid the problem that an increase in the image size will result in the rapid increase in the memory usage brought by the classical AOS algorithm,which lays the groundwork for topology-preserving segmentation of larger images.Numerical experiments on multiple artificial and natural images show that the two fast algorithms proposed in this thesis can ensure that the topology of the original SRS model maintains the segmentation characteristics.It also performs superiorly on simple implementation and low memory footprint.Moreover,the improved scheme of adding GVF force to the original SRS model can effectively improve the robustness of segmentation.It is expected to be applied in fields with topology preservation requirements such as medical image segmentation.