Abstract: To overcome the limitation of the wavelet domain hidden Markov tree (HMT) in computational speed and sparse direction, a novel image fusion algorithm using the contourlet HMT model is presented. After the Contourlet transform on the images, the low-frequency subbands are compared to preserve the coefficients whose module are minimum, and local inner-product are performed on the new high-frequency directional subbands which are acquired from the product by the high-frequency directional coefficients and the edge probability density function which is acquired from the contourlet HMT model training on the images. Then the fusion image can be obtained by taking an inverse Contourlet transform. Because the dependence tree in the contourlet HMT can span several adjacent directions in the finer scales and inter-direction dependencies are modeled in a similar way as inter-location dependencies, this method can improve modeling precision and reduce computational complexity (reduce the number of parameters). Experimental results show that when compared with the Contourlet and wavelet HMT, our proposed method can get more accurate and smooth fusion images, and a remarkable improvement over wavelet HMT about standard deviation, average gradient and average cross entropy. Moreover, the training speed of the Contourlet HMT is reduced to1／15 that of the wavelet HMT, and more important, some images such as the “medicine” and “office” images which are difficult to process using the wavelet domain HMT can be fused quickly using the contourlet domain HMT.

Key words: Contourlet, hidden Markov tree model, edge probability density function, image fusion