Noise Sensitivity Analysis for Shape from Focus Methods

Shape from focus (SFF) methods provide a useful technique for passive autofocusing and threedimensional (3D) shape recovery of objects. In these methods, focus measures are used to extract 3D information from a sequence of images taken with different camera parameters such as lens/object position or focal length. The accuracy of autofocusing and 3D shape measurement using the image focus analysis technique depends on the particular focus measure that is used. Experimental evaluations of different focus measures have been reported by some researchers. In the existing literature, all known work have been a combination of experimental observations and subjective judgement. Th e noise sensitivity of a focus measure depends not only on the noise characteristics but also on the image itself. The optimally accurate focus measure for a given noise characteristics may change from one object to the other depending on its image. This makes it difficult to arrive at general conclusions from experiments alone. For a given camera and object, the most accurate focus measure can be selected from a given set through experiments by many trials. The focus measure with the minimum estimate of root-mean-square (RMS) errors is taken to be the optimal. In practical applications such as consumer video cameras or digital still cameras, it is desirable to find the best focus measure from a given set by autofocusing only once. It is quite undesirable to repeat several trials. If one has a detailed and accurate information on the focused image of the object to be focused and the camera characteristics such as its OTF, noise behaviour, and camera parameters, then it would be possible to estimate the RMS error theoretically with only one trial. However such information is rarely available in practical applications. In the absence of such detailed and accurate information, I address this important problem and derive theoretical results and provide supporting experimental results. The theroy based on probability and stochastic processes is able to give the computation of RMS error with only one trial of autofocusing. It is assumed that each focus measure y at lens position si is associated with a probability density function Pi and the focused position sk is with the maximum 6 ys,), ecus measure which has the highest probability as compare