Image Processing Based On Euler's Elastic Energy

Image processing refers to the technique of obtaining the data that people want through a series of operations on the image by the computer,Variational method plays an important role in the field of image processing because of its strong theoretical basis and experimental basis.But traditional low-order variational models often produce various deficiencies in image processing,and the use of higher-order models can effectively solve Various problems in low-order modalities,so the related research of high-order models has become a hot topic in the near future.This paper mainly focuses on the variational image denoising model,segmentation model and repair model with Euler elastic energy.The use of the curvature term minimization function helps to capture the geometry of the recovered shape,but it is caused by its non-convexity and higher order derivatives The complexity makes the model extremely difficult to solve,and the model has both the first and second derivatives at the same time,and the numerical algorithm design is complicated.So first of all,this article will review two previous fast algorithms,which are augmented Lagrang method(ALM)and the dual method,these two algorithms are for effectively calculating the minimum problem based on the curvature term,and on the basis of these algorithms,a faster and simpler fast dual projection algorithm is proposed.The core of this paper is a fast dual projection algorithm combining dual algorithm and augmented Lagrangian method,and applying this algorithm to the three fields of image denoising,image segmentation,and image restoration.The algorithm can transform the complex variational energy repair problem with Euler's elastic energy function into a simple iterative optimization weighted total variation problem solution,and the corresponding fast dual method is designed by introducing a dual variable and a constraint condition,and Constraints can be calculated by projection,thus transforming the original problem into a simple projection calculation,which greatly saves the time required for model calculation,and through specific demonstrations and experiments can prove that the algorithm can be simpler and faster to solve Euler elastic energy Variational image repair model.