A classification and fuzzy-based approach for digital multi-focus image fusion

This paper presents a new wavelet-based method for fusion of spatially registered multi-focus images. We have formulated the image fusion process as a two-class classification problem: in and out-of-focus classes. First, a 12-dimensional feature vector using dual-tree discrete wavelet transform (DT-DWT) sub-bands of the source images are extracted, and then a trained two-class fisher classifier projects it to the class labels. The classifier output is used as a decision map for fusing high-frequency wavelet coefficients of multi-focus source images in different directions and decomposition levels of the DT-DWT. In addition, there is an uncertainty for selecting high-frequency wavelet coefficients in smooth regions of source images, which causes some misclassified pixels in the classification output or the decision map. In order to solve this uncertainty and integrate as much information as possible from the source images into the fused image, we propose an algorithm based on fuzzy logic, which combines outputs of two different fusion rules based on a dissimilarity measure from the source images: Selection based on the decision map and weighted averaging. An estimation of the decision map is also used for fusing low-frequency wavelet coefficients of the source images instead of simple averaging. After fusing low- and high-frequency wavelet coefficients of the source images, the final fused image is obtained using the inverse DT-DWT. This new method provides improved subjective and objectives results (more than 4.5 dB on average) as compared to previous fusion methods.