中文摘要：

图像的多尺度分解技术和融合规则是决定多聚焦图像融合效果的关键因素。k次W系是一类以k次多项式和k次分段多项式为基函数的新的混合正交函数系统,对应的W变换是一种具有正交性和精确重构性的有效多分辨分析工具。结合W变换的多尺度特点和非子采样方向滤波器组变换的多方向性,提出了一种新的基于W变换和非子采样方向滤波器组（NSDFB）的多尺度多方向变换。该变换利用W变换对图像进行多尺度分解,利用二维NSDFB对W分解的高频子带系数进行方向分解,得到不同尺度不同方向的子带图像。在此基础上,提出了一种新的多聚焦图像融合算法。该算法针对多聚焦图像高频系数的特点,改进了常用简化脉冲耦合神经网络算法,并将其用于高频系数的融合规则中。实验结果表明,提出的融合方法能够有效地选择源图像中的聚焦良好区域,抑制伪影信息,产生视觉效果更好的融合图像,且在标准差、信息熵、平均梯度和空间频率等客观评价指标上都优于传统的基于Contourlet变换、非下采样Contourlet变换、离散小波变换的融合方法。

英文摘要：

Multi-scale decomposition method and fusion rule are two key factors for multi-focus image fusion method.The W-system of degree k is an orthogonal hybrid function system consisting of polynomials of degree k and piecewise polynomials of degree k.The corresponding W-transform is an effective multi-resolution analysis tool with orthogonality and reproducibility.By combining the multiscale characteristics of W-transform and multidirection property of the non-subsampled directional filter bank （NSDFB） transform, a new multi-scale and multi-directional transform is proposed in this paper, in which multi-scale decomposition is performed by the W-transform and the multi-directional decomposition is obtained from NSDFB.On this basis, a new multi-focus image fusion algorithm is proposed.According to the characteristics of the high frequency coefficients, the often used simplified PCNN is modified, and applied on the fusion rules of the high frequency coefficients.The experimental results show that the proposed fusion method can select pixels from focus areas of the source images and effectively avoid generation of artifacts.The fused image has better visual effect.The objective evaluation index including standard deviation, entropy, average gradient, and spatial frequency of the fused image demonstrate that the proposed method outperforms the fusion methods based on Contourlet transform, NSCT transform and discrete wavelet.