Efficient Image Processing Problem Based On Gradient Domain

A large part of the information in the image is contained in the image gradient,such as the texture of the image,noise and so on.Many image optimization problems are related to image gradient.For example,image segmentation of M-S model is carried out along the direction of image gradient as far as possible.In order to smooth the image with a small gradient,the image uses L0,and L1 norm to denoise.Another example is Poisson image editing,which makes the image gradient in the region as consistent as possible with the foreground image.These image problems involve the energy function of the optimization problem involve both the pixel domain and the gradient domain.In many digital image processing problems,the objective function is a constraint on the image gradient and the objective energy includes the regularization term and fidelity term.In this class of problems,the constraint relationship between the gradient domain and the pixel domain is often limiting,even resulting in the hyper-linearity of the algo-rithm itself.Aiming at this kind of optimization problem,this paper proposes to trans-form the fidelity term in the pixel domain to the gradient domain,so as to transform the problem into a problem in the gradient domain.And then it's solved by the alternating direction multiplier method.Then we design an Alternating Direction Method of Mul-tipliers(ADMM)based method to solve these problems.The time complexity of the proposed algorithm in each iteration is proportional to the image resolution.After get the solution of gradient field,we chose to transform a similar Total Variation model or use breadth-first Search to traversal every pixel in area ? to reconstruct in pixel domain solution.The innovation of this paper lies in according to the nature of the loop-integration in gradient filed is 0,we construct a new constrain to express the variable in gradient filed.Because of divisibility of constrain,we divide the whole optimization into cell of image.Advantage of this formulation is that we can transform each sub-problem in each iteration into problem with two unknowns in each cell of image.So we can avoid to solve large-scale equation.Besides,the algorithm can be further parallelized based on segmenting the image.We apply the proposed algorithm to two classic image processing problems:L0 norm based image smoothing and Poisson image editing.Compared with the iterative algorithm in the original text,our algorithm in the L0 optimization problem can achieve the similar effect of the original algorithm,and at the same time,it can achieve faster convergence than the original method without using parallelization.In the Poisson im-age editing problem,we rewrote the original problem into the form of the sum of the regularization and fidelity terms,and then achieved a similar effect by using paralleliza-tion with a smaller memory in the large-scale problem,and at the same time could output the tween image in the image fusion process on the result.The surface-from-gradient problem is similarly rewritten and discussed in this paper,too.