Multi-Focus Image Fusion by Hessian Matrix Based Decomposition

Abstract

In this paper, a Hessian matrix based multi-focus image fusion method is proposed. First, the integral map is introduced for fast compute the Hessian matrix of source images at different scales, and the multi-scale Hessian matrix of source image is obtained. Second, the multi-scale Hessian matrix is used to decompose each source image into two kinds of regions: the feature and background regions. In order to improve the fusion performance, two new focus measures based on the multi-scale Hessian matrix and two different fusion strategies for both feature and background regions are utilized to obtain the initial decision maps, respectively. Finally, the final decision map for image fusion is achieved by post-processing on the results of the previous step. The proposed method is a primary attempt to introduce image feature and background regions decomposition strategies in the field of multi-focus image fusion. The experimental results also show that our method outperforms the existing image fusion methods in both visual perception and objective evaluations.