Blurred Noisy Convolution ( Brightness normalized ) Integrate Measure

The optimal focus measure for a noisy camera in passive search based autofocusing (AF) and depth-from-focus (DFF) applications depends not only the camera characteristics but also the image of the object being focused or ranged. In the early stage of this research, a new metric named Autofocusing Uncertainty Measure (AUM) was deened 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 diierent focus measures. In the later stage of this research, an improved metric named Autofocusing Root-Mean-Square Error (ARMS error) was deened. Explicit expressions have been derived for both AUM and ARMS error, and the two metrics are shown to be related by a monotonic expression. AUM and ARMS error metrics are based on a theoretical noise sensitivity analysis of focus measures. In comparison, all known prior 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. Important properties of the Laplacian focus measure are investigated.