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Multi-focus image fusion (MFIF) tries to combine images with different in-focus regions and get a composite image that is in focus everywhere. Although many new MFIF algorithms based on various new representation models have been proposed in recent years, the performance evaluation of MFIF is still a challenging issue. In this study, a novel MFIF objective evaluation metric based on jointly sparse representation and atom focus measure is proposed. It not only provides a more reliable alternative for MFIF quality measurement but also supplies a unique MFIF performance analysis method at the same time. In the measurement, the sources and their fusion results are decomposed jointly sparse with an over-complete learning dictionary to extract the atom remnants of the source images. Meanwhile, in order to emphasise the fusion effect of in-focus atoms, the sum-modified-Laplacian model is used to measure the atom focus degree. Then, the atom remnants weighted by their focus measures are used to measure MFIF quality. In the experiments, nine recently proposed fusion algorithms were tested to contrast the proposed metrics with other four widely used objective metrics. The experimental results demonstrated the rationality and accuracy of our method. Moreover, it was also proved quantificationally that the fusion degree of atoms is directly related to their in-focus degree, the high in-focus degree atoms usually have poor fusion effect. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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