Image formation with PSF

The aim of this graphical interface application is to show the effect of PSF as a factor in an image degradation model. This distortion operator, called point spread function (PSF), in the spatial domain, describes the degree to which an optical system blurs (spreads) a point of light. The PSF is the inverse Fourier transform of the optical transfer function (OTF). In the frequency domain, the OTF is the Fourier transform of the point spread function (PSF). The distortion operator, when convolved with the image, creates the distortion. Typically the effect of having PSF results in a blurry image. No lens is perfect, in fact the lens itself adds its own distortion which results in an optical transfer function H(r,c), that when convolved with the original image it produces a distorted image. The complete image degradation model can be expressed with the following equation:

In order to demonstrate de effect of image degradation due to PSF and added noise the following application was designed:

Initially, the default image that appears on the window is the undegraded image (I). Right below it, the user will find two different sliders, one to specify the length of the blur he wants the image to have, and another one to specify the angle of the blur. These two parameters are needed for the matLab function "fspecial" which simulates the effect of having real PSF on images. Here is an example on how this works:

Using the first slider to modify the PSF blur length:

Using the second slider to modify the PSF blur angle:

Function used in Matlab in order to implement the PSF effect on the image:

Once the PSF is created, it is necessary to use the "imfilter" function to convolve the PSF with the original image, I, to generate the blurred image.

Finally, to complete the degradation model, some noise is added to the image. Similarly to the PSF slider, the user is able to increase or decrease the amount of noise he wants to add to the already partially degraded image, by moving the "Noise Level" slider. Like the example shown below:

Function used in Matlab in order to incorporate noise to the second image (which now has the previously applied PSF):