Seite - 58 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

a b c d Figure2. Blinddeconvolutionof the syntheticallyblurred image fromFig.1(a)usingRRRLfor imageestimation, and thenonlinearPSFestimationmethod fromSection3.withdifferentnumbersof linearisation iterations. (a) 1 iteration. – (b)2 iterations. – (c)5 iterations. – (d)8 iterations. –From[7], adapted. a b c d Figure3.Blinddeconvolutionofanimageblurredduringacquisition. (a)Clippingfromaphotograph(Paris from Eiffeltoweratdusk)blurredbycamerashake,200×200pixels. –(b)ReconstructedimageandPSF,13×13pixels (inserted), usingRRRLfor imageestimationandPSFestimationaccording to [5],mx=my=13,α=0.002, β = 260, τ = 0.1,K = 300,Ku = 20. – (c) Same as (b) but with nonlinear PSF estimation Section 3., mx=my=13,α=0.0105,β=255, τ =0.1,K=300,Ku=20,Kh=8. – (d)Non-blindRRRL deconvolution resultwith themanually tunedPSF (shownas insert) from[13],α=0.002,Ku=30. ThePSF, 14×11pixels,hasbeengenerated fromanimpulseresponse. evident that introducing robust image estimation brings about a slight gain in reconstruction of small detail, but also an amplification of artifacts is observed which may be attributable to the mismatch between thedata termsunderlying the PSF estimation (non-robust) and non-blind deconvolution (ro- bust). Using robust estimation methods for both (d) leads to a result with visible gain in sharpness and fewer artifacts. In particular, fine details of the columns between the windows are reconstructed sharper in (d) than in (b). Regarding the visible translation by approx. 2 pixels between (d) and the two other results, it should be noted that shifting the PSF and image in opposing directions is an inherent degree of freedom of the convolution model (1). Note that this also poses a difficulty for quantitative evaluation of blind deconvolution methods: quantitative error measurements cannot be done without a registration step whose influence on the error values needs additional analysis. Since this isnot feasiblewithin thepresent paper,we restrict ourselves to avisual assessmentat thispoint. As discussed in Section 3. the non-linear system of equations arising in the PSF estimation is solved iteratively by linearisation. In Fig. 2 we demonstrate the evolution of estimated PSF and image with increasing number of linearisation iterations. With a single iteration, frame (a), the result is almost identicallytothelinearPSFestimationfromFig.1(c). Additional iterationsfirst leadtosomeartifacts, frame (b), which are apparently caused by the fact that the non-linear method places the PSF in this example at a translated position. With more iterations, the reconstruction quickly stabilises at the refined result, frame(d), which is numericallyconvergedandcorresponds to Fig.1(d). 58