A method is described for selecting the optimal focus measure with respect to gray-level noise from a given set of focus measures in passive autofocusing and depth-from-focus applications. The method is based on two new metrics that have been defined for estimating the noise-sensitivity of different focus measures. The first metric-the autofocusing uncertainty measure (AUM)-is useful in understanding the relation between gray-level noise and the resulting error in lens position for autofocusing. The second metric-autofocusing root-mean-square error (ARMS error)-is an improved metric closely related to AUM. AUM and ARMS error metrics are based on a theoretical noise sensitivity analysis of focus measures, and they are related by a monotonic expression. The theoretical results are validated by actual and simulation experiments. 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.

A new shape-from-focus method is described which is based on a new concept, named focused image surface (FIS). FIS of an object is defined as the surface formed by the set of points at which the object points are focused by a camera lens. According to paraxial-geometric optics, there is a one-to-one correspondence between the shape of an object and the shape of its FIS. Therefore, the problem of shape recovery can be posed as the problem of determining the shape of the FIS. From the shape of FIS the shape of the object is easily obtained. In this paper the shape of the FIS is determined by searching for a shape which maximizes a focus measure. In contrast to previous literature where the focus measure is computed over the planar image detector of the camera, here the focus measure is computed over the FIS. This results in more accurate shape recovery than the traditional methods. Also, using FIS, a more accurate focused image can be reconstructed from a sequence of images than is possible with traditional methods. The new method has been implemented on an actual camera system, and the results of shape recovery and focused image reconstruction are presented.>

A general formulation is described for the interpretation of image flow. In the framework of this formulation, computational methods have been derived for image flow interpretation for many important cases, including simple cases of nonrigid and nonuniform motions. It is possible to derive computational methods for other situations not considered explicitly. The formulation is general in that it is applicable to any situation provided that the scene geometry, the scene transformation, and the image flow are all 'smooth' or analytic.>

A method is proposed for recovering depth from a measure of the degree of blur of an edge. Closed-form solution is derived for an edge which is a step discontinuity of intensity in the focused image. The method is simpler and more general than two earlier methods proposed by A.P. Pentland (1987) and P. Grossman (1987). It has been verified experimentally and found to provide useful depth information.>