Abstract: Nonsubsampled Contourlet Transform（NSCT） is a new multi-resolution transform，which can give an asymptotic representation of edges and contours in image by virtue of its characteristics of multi-direction，flexible multi-scale and shift-invariant simultaneity.Non-negative Matrix Factorization（NMF） is a kind of matrix decomposition method with the constraint that each element of matrix is nonnegative.It is shown that the local feature can be obtained by choosing suitable dimension of the feature subspace in non-negative matrix factorization.An image fusion algorithm is proposed based on NSCT and NMF.Firstly，two registered original images are decomposed using NSCT separately thus the low frequency subband coefficients and varieties of directional bandpass subband coefficients are obtained.Secondly NMF is performed from original dates，which are obtained from the low frequency subband coefficients.The dimension of the feature subspace is set to 1 when using NMF and the resultant feature base is just the fusion result of low frequency subband coefficients.The selection principle of the band-pass directional subband coefficients is absolute maximum.Finally，the fused image is obtained by performing the inverse NSCT on the combined coefficients.The experimental results show that the proposed algorithm outperforms Laplacian-based，wavelet-based and NMF-based fusion algorithms.

摘要： 非采样Contourlet变换（Nonsubsampled Contourlet transform，NSCT）是一种新的多尺度变换，它同时具有方向性、各向异性和平移不变性，能有效地表示图像的边沿与轮廓。非负矩阵分解（Non-negative Matrix Factorization，NMF）是在矩阵中所有元素均为非负数的条件下的一种矩阵分解方法。在非负矩阵分解过程中，适当地选取特征空间的维数能够获得原始数据的局部特征。提出了一种基于NSCT和NMF的图像融合方法。首先用NSCT对已配准的源图像进行分解，得到低通子带系数和各带通子带系数；其次将低通子带系数作为原始数据，选取特征空间的维数为1，利用非负矩阵分解得到包含特征基的低通子带系数；对各带通子带系数采取绝对值最大的原则进行系数选择，得到融合图像的各带通子带系数；最后经过NSCT逆变换得到融合图像。实验结果表明，融合结果优于Laplacian方法、小波方法和NMF方法。