Optimal focus measure for passive autofocusing and depth-from-focus

The optimally accurate focus measure for a noisy camera in passive search based autofocusing and depth-from-focus applications depends not only on the camera characteristics but also the image of the object being focused or ranged. In this paper a new metric named autofocusing uncertainty measure (AUM) is defined which is useful in selecting the most accurate focus measure from a given set of focus measures. AUM is a metric for comparing the noise sensitivity of different focus measures. It is similar to the traditional root-mean-square (RMS) error, but, while RMS error cannot be computed in practical applications, AUM can be computed easily. AUM is based on a theoretical noise sensitivity analysis of focus measures. In comparison, all known work on comparing the noise sensitivity of focus measures have been a combination of subjective judgement and experimental observations. For a given camera, the optimally accurate focus measure may change from one object to the other depending on their focused images. Therefore selecting the optimal focus measure from a given set involves computing all focus measures in the set. However, if computation needs to be minimized, then it is argued that energy of the Laplacian of the image is a good focus measure and is recommended for use in practical applications.