A Posteriori determination of PSF (continued)

Since image of an edge parallel to x axis is independent of x , we will write instead of ,.

Taking partial derivatives of both sides with respect to and interchanging the order of and derivative operators on RHS we obtain

or,

i.e image of a line is the derivative of image of an edge parallel to the line or LSF is the derivative of ESF . Therefore, if a picture contains edges on various orientations, then the methods preciously discussed can be used to determine PSF from derivatives of the images of these edges.Major difficulty faced in determining PSF in this way from a photograph is film grain noise which affects the derivative value.

There is another method for estimating the transfer function from the degraded picture itself.

Let the degraded picture be divided into n regions all identical in size. Let the gray level in each region be given by .Let be the gray level in the corresponding region in the undergraded picture. Let us assume that the portion of the plane in which the PSF of the degrading has values significantly different from zero is small compared to the size of the regions. Then ignoring edge effects

Taking Fourier Transformation of both sides

Taking the product over i

The logarithm of denominator on RHS is - which is the average of logarithm of Fourier transformations of .

If we assume that an average of a large number of tends to be a constant, then can be determined up to a multiple .