Extending the Universal Quality Index to assess N-image fusion in light microscopy

The depth of focus is a constraint of all the light microscopes, being not possible to acquire a single, completely in-focus, image of 3D objects characterized by a wide depth dimension. Since the Seventies, many methods have been proposed to extend the microscope’s depth of focus. However, it is difficult to define which method yields the best result because there is not a tested metric and a validated approach to compare them using a set of images lacking of a reference ground truth. Typically, the Universal Quality Index (UQI) is used to evaluate output's quality in image processing, but it requires a reference ground truth. Some UQI extensions were proposed to evaluate the output of fusion methods without a ground truth, but no exhaustive analysis was proposed to prove their equivalence, in terms of evaluation performance, to the standard UQI. In this work, first we prove that the output of the proposed UQI extensions is different from the UQI’s one, then we provide and validate a new approach to evaluate extended depth of focus methods, such as the UQI would do, but without requiring a reference ground truth.