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Numerical Analysis of the Explicit Group Iterative Method for Solving Poisson Image Blending Problem

Eng Jeng Hong, Azali Saudi, Jumat Sulaiman

Abstract



This paper proposes a block iterative method, namely Four Point-Explicit Group Gauss-Seidel (4-EG) to solve the Poisson image blending problem. Generally, Poisson image blending problem is illustrated as a minimization problem by Perez et al. (2003). The solution of this minimization problem is equivalent to the unique solution of Poisson equation with Dirichlet boundary condition. Thus, the purpose of this study is to solve the linear system generated from the discretization process of Poisson equation efficiently by using 4-EG iterative method. For comparison, two point iterative methods are selected, Jacobi and Gauss-Seidel (GS) iterative methods. To evaluate the efficiency and superiority of 4-EG iterative method, the number of iterations and computational time taken are used to verify its performance on solving Poisson image blending problem. Due to the characteristic of 4-EG iterative method that computes a group of four node points simultaneously in one loop of iteration, it had greatly reduced the number of iterations involved and improved the computational time taken compared to the considered iterative methods. Meanwhile, the new generated images by the three proposed block and point iterative methods have no significant difference which all are look natural and realistic.

Keywords


Poisson equation, Poisson image blending, Explicit Group iteration

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