针对数字全息中不同再现距离获得的携带不同聚焦信息的再现像, 提出了一种基于数学形态学的多聚焦再现像融合方法, 以有效扩展成像景深。首先通过小波-Controulet变换获得源图像的高频和低频分量;然后, 针对数字全息中含散斑噪声的特点, 对高频分量采用基于数学形态学区域能量的方法进行融合, 对低频分量采用加权对比度法进行融合;最后, 将融合系数反变换得到融合图像。通过对算法的有效性分析和实验验证, 将本文提出的方法与不加入数学形态学的融合方法进行了对比研究。结果表明, 基于数学形态学的融合方法能充分抑制散斑噪声的影响, 保留更多细节信息, 有效扩展了成像景深范围达11.5 cm。其中, 对于表面粗糙且信息量较少的骰子, 基于数学形态学方法的空间梯度算子提高了11.8%, 熵值提高了2.7%;对于表面光滑且信息量较多的硬币, 其空间梯度算子提高了13.6%, 熵值提高了2.8%。
In digital holography, multi-focus holographic images can be reconstructed by applying values for the reconstruction distance during the reconstruction process. And then the hologram can be fused to extend the depth-of-field by images fusion method. Since the speckle noise in the digital holography images, an efficient fusion algorithm based on mathematical morphology is proposed. First, the decomposed high-frequency and low-frequency sub-band coefficients are obtained by the Wavelet-Controulet transform. Then, it fused coefficients with different rules. To suppress the speckle noise, the local energy combined with mathematical morphology is presented for high-frequency coefficients and the contrast method is used to fuse the low-frequency coefficients. Finally, the invers transform is employed to get the fused image. The effectiveness analysis of the algorithm and the experiment results show that for the digital holography images with speckle noise, the fusion method with mathematical morphology can reduce the speckle noise and keep more detail information. At last, the depth-field of the image can be extended up to 11.5 cm. As compared with the conventional method without mathematical morphology, for dices, the proposed method enhances its Tenengrad and Entropy by 11.8% and 2.7%. For coins, the proposed method enhances its Tenengrad and Entropy by 13.6% and 2.8%.