# Using reference objects to estimate the point spread function?

I have a well-defined object and a clear image matrix of it. In subsequent frames the object moves, causing motion blur. I want to use the object as a reference to "guide" the deconvolution and eliminate the motion blur.

My idea is to use a feedback loop: do object detection, find the object, then cross correlate with the original image to estimate the quality of my deconvolution. My concern is how to the evaluate the quality of the PSF so I can find the optimal estimate.

I am looking for a critique of my approach; does it make sense, and what are the pitfalls?

• if you already have the original image, then what do you gain from deconvolving to get the original image? are you trying to find an offset or calculate the blur path or something? – endolith Oct 1 '12 at 16:32
• @endolith yes. I am trying to calculate correct Psf. – Ktuncer Oct 1 '12 at 23:23
• @endolith would you consider writing an answer? – Ktuncer Oct 12 '12 at 10:08
• I don't know how to answer this, other than to point you to this answer, which is still just a link to someone else's solution: dsp.stackexchange.com/a/140/29 – endolith Oct 12 '12 at 15:38

As you probably know, there is a developed literature on deblurring. Regarding the evaluation of the PSF, you may find these useful:

• Understanding and evaluating blind deconvolution algorithms
• Modeling the Performance of Image Restoration From Motion Blur

If the known object $X_0$ is going to be shot head on in subsequent frames $Y_i$, you can find the blur kernel $K$ by maximizing some image similarity metric $I$ for basic (say, procrustes) transformations $T$ of $X_0$:

$K_i = \underset{K, T}{\arg \max} \; I \left( K \ast T X_0 ; Y_i \right)$

In a more sophisticated formulation, you could enforce temporal smoothness priors on the $K_i$'s and $T$'s. I would also suggest using the last frame's optimal estimates as initial values for the next frame.

If $X_0$ appears at an angle in $Y_i$ (since it is moving, after all) I conjecture that you will have a hard time finding a good match (that is, $X_0$ will not be of much use). Obviously, there is some information to be leveraged, even when shot at an angle, but I suspect the effort will not be worth it. This leads me to wonder what sort of a scenario you would be able to use this technique in. You know what they say: there's one way to find out.

You could use some of the blind deconvolution methods. Using blind deconvolution you don't need the PSF. For example, this method http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5226594&tag=1 simultaneously deblurs image and finds PSF. Authors also describe the way to include prior knowledge about PSF.