基于NSCT的多聚焦图像融合算法

摘要

发明公开了一种基于NSCT的图像融合算法，该方法的处理过程是：首先非采样的轮廓波变换(NSCT)对经过均值滤波器滤波(mean)的源图像进行分解，再分别采用平均值和绝对值最大为低频子带和高频方向子带的融合规则，以NSCT的逆运算(inverse NSCT)进行图像重构，获得初始融合图像；其次，应用均方根误差(RMSE)提取初始融合图像的融合区域(fusion region)；根据融合区域的特性设计融合规则，最后采用inverseNSCT进行图像融合。实验结果表明，本发明方法是非常有效，并且融合后的图像符合人眼视觉效果。

主权项

1.一种基于NSCT的多聚焦图像融合算法，包括如下过程：步骤1：初始融合图像的获得1)采用均值滤波器对两幅多聚焦图像A和B进行滤波处理，得到滤波后的多聚焦图像，分别记为A′和B′；2)应用NSCT变换将图像A′和图像B′进行分解，得到两图像分解后的低频系数为和高频系数为和其中l为尺度分解数，k为方向分解级数；3)采用均值法和绝对值最大法分别作为低频子带和高频方向子带的融合规则，具体见公式(1)和公式(2)；$I_F^L(i,j)=\frac{I_l^{A^{\prime }}(i,j)+I_l^{B^{\prime }}(i,j)}{2}---\left(1\right)$$I_{l,k}^F(i,j)=\left\{\begin{array}{c}{I}_{l,k}^{A^{\prime }}(i,j),\mathrm{if}\left|I_{l,k}^{A^{\prime }}(i,j)\right|\ge \left|I_{l,k}^{B^{\prime }}(i,j)\right|\\ I_{l,k}^{B^{\prime }}(i,j),\mathrm{if}\left|I_{l,k}^{A^{\prime }}(i,j)\right|<\left|I_{l,k}^{B^{\prime }}(i,j)\right|\end{array}\right.---\left(2\right)$4)根据上述融合策略，经过NSCT逆变换重构图像，即为初始融合图像F。步骤2：融合区域的提取应用公式(3)计算初始融合图像F和多聚焦图像A′、B′之间在像素点(x，y)的均方根误差，分别记为RMSE_A′(i，j)和RMSE_B′(i，j)，由此应用公式(4)确定标识矩阵Z，提取初始融合图像的融合区域。${\mathrm{RMSE}}_{A^{\prime }}(i,j)={\left(\frac{\underset{a=-M}{\overset{M}{\Sigma }}\underset{b=-N}{\overset{N}{\Sigma }}{(I_F(i+a,j+b)-I_{A^{\prime }}(i+a,j+b))}^2}{(2M+1)(2N+1)}\right)}^{1/2}$(3)${\mathrm{RMSE}}_{B^{\prime }}(i,j)={\left(\frac{\underset{a=-M}{\overset{M}{\Sigma }}\underset{b=-N}{\overset{N}{\Sigma }}{(I_F(i+a,j+b)-I_{B^{\prime }}(i+a,j+b))}^2}{(2M+1)(2N+1)}\right)}^{1/2}$$z(i,j)=\left\{\begin{array}{cc}1,& \mathrm{if}{\mathrm{RMSE}}_{A^{\prime }}(i,j)<{\mathrm{RMSE}}_{B^{\prime }}(i,j)\\ 0,& \mathrm{if}{\mathrm{RMSE}}_{A^{\prime }}(i,j)\ge {\mathrm{RMSE}}_{B^{\prime }}(i,j)\end{array}\right.---\left(4\right)$步骤3：建立融合规则本发明在窗口大小为m₁×n₁上确定低频子带和高频方向子带的融合规则。具体如下：1)低频子带的融合策略$I_L^F(i,j)=\left\{\begin{array}{cc}{I}_L^{A^{\prime }}(i,j),& \mathrm{if\; Z}(i,j)=1\mathrm{and\; e}(i,j)=m_1{n}_1;\\ I_L^{B^{\prime }}(i,j),& \mathrm{ifZ}(i,j)=1\mathrm{ande}(i,j)=m_1{n}_1;\\ I_L^{A^{\prime }}(i,j),& \mathrm{if}0<e(i,j)<m_1{n}_1\mathrm{and}{\mathrm{VI}}_l^A(i,j)\ge {\mathrm{VI}}_l^B(i,j);\\ I_L^{B^{\prime }}(i,j),& \mathrm{if}0<e(i,j)<m_1{n}_1\mathrm{and}{\mathrm{VI}}_l^A(i,j)<{\mathrm{VI}}_l^B(i,j).\end{array}\right.$其中，$e(i,j)=\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}Z(i+k_1,j+k_2);$${\mathrm{VI}}_l^{A^{\prime }}=\frac{1}{(2m_1+1)(2n_1+1)}\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}\frac{|I_l^{A^{\prime }}(i+k_1,j+k_2)-\overline{I_l^{A^{\prime }}}(i,j)|}{\overline{I_l^{A^{\prime }}}{(i,j)}^{\alpha +1}};$${\mathrm{VI}}_l^{B^{\prime }}=\frac{1}{(2m_1+1)(2n_1+1)}\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}\frac{|I_l^{B^{\prime }}(i+k_1,j+k_2)-\overline{I_l^{B^{\prime }}}(i,j)|}{\overline{I_l^{B^{\prime }}}{(i,j)}^{\alpha +1}}.$2)高频方向子带的融合策略$I_{l,k}^F(i,j)=\left\{\begin{array}{cc}{I}_{l,k}^{A^{\prime }}(i,j),& \mathrm{if\; Z}(i,j)=1\mathrm{and\; e}(i,j)=m_1{n}_1;\\ I_{l,k}^{B^{\prime }}(i,j),& \mathrm{ifZ}(i,j)=1\mathrm{ande}(i,j)=m_1{n}_1;\\ I_{l,k}^{A^{\prime }}(i,j),& \mathrm{if}0<e(i,j)<m_1{n}_1\mathrm{and}{\mathrm{SF}}_l^A(i,j)\ge {\mathrm{SF}}_l^B(i,j);\\ I_{l,k}^{B^{\prime }}(i,j),& \mathrm{if}0<e(i,j)<m_1{n}_1\mathrm{and}{\mathrm{SF}}_l^A(i,j)<{\mathrm{SF}}_l^B(i,j).\end{array}\right.$其中，$e(i,j)=\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}Z(i+k_1,j+k),$${\mathrm{SF}}_l^A(i,j)=\frac{\sqrt{\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}(I_{l,k}^{A^{\prime }}(i,j)-I_{l,k}^{A^{\prime }}(i,j-1))+\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}(I_{l,k}^{A^{\prime }}(i,j)-I_{l,k}^{A^{\prime }}(i-1,j))}}{(2M_1+1)2(N_1+1)}$${\mathrm{SF}}_l^B(i,j)=\frac{\sqrt{\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}(I_{l,k}^{B^{\prime }}(i,j)-I_{l,k}^{B^{\prime }}(i,j-1))+\underset{k_1=-(m_1-1)/2}{\overset{(m_1-1)/2}{\Sigma }}\underset{k_2=-(n_1-1)/2}{\overset{(n_1-1)/2}{\Sigma }}(I_{l,k}^{B^{\prime }}(i,j)-I_{l,k}^{B^{\prime }}(i-1,j))}}{(2M_1+1)2(N_1+1)}$步骤4：融合图像的获得根据上述融合策略，经过NSCT逆变换得到图像即为融合图像。