Compared with conventional photography, the newly emerging technique for capturing light field image has dramatically extended potential capabilities of post processing. Among the new capabilities, refocusing has received much interest. In this paper, we first investigate a region-adaptive multi-scale focus measure (RA-MSFM) which can more robustly and accurately measure focus of light field images. It is especially superior when measuring focus in flat areas where previous methods struggle. Following we design a novel refocusing metric which employs the RA-MSFM as a core technique. Using the metric, refocusing capability of a given light field image as a whole can be represented by a single number by combining focus score maps of each refocused image in the focal stack. The focus maps are generated using the proposed RA-MSFM. Quite unique from existing metrics for light field image that assess mostly image quality, our metric targets for assessing the refocusing capability. Our experiments have shown that the proposed refocusing metric not only achieves high correlation with subjective evaluations given in the form of mean opinion scores, but also produces all-in-focus images having 0.7~4.6dB higher PSNRs compared to previous state-of-the-art methods. The proposed refocusing metric can be used to measure refocusing loss in practical application such as compression, tone mapping, denoising, and smoothing, etc.INDEX TERMS Refocusing measure, light field images, multi-scale focus measure, all-in-focus, subjective experiment, refocusing capability