One of the essential problems in computer vision is to recover the distance information of an object from captured images. Its application areas range from industrial inspection and reverse engineering to autonomous robot navigation

Fig.4Intensitypro lesofdefocusededgesaccordingtopillboxandGaussian

models.

kDf

,c =

p f

38

basedontheGaussianlinespreadfunctionmodel.Thein-tensitypro lesofdefocusededgesaccordingtothepillboxfunctionandGaussianmodelareshowninFig.4.Foredgeimages,ablurcircleisreducedtoahorizontalblurlength.ThelengthcanbeestimatedfrombluranalysisonstepedgesandusedinEq. 37 fordepthrecovery.

3FocusCalibrationandBlurExtentEstimation3.1DefocusBlurandFocusCalibration

TocalculatethedepthofanobjectusingEqs. 8 or 37 foragivensetofcameraparameters,thecorrespondingfocusingrangepandtheblurextentsc and havetobeidenti ed.AssuggestedbyEq. 1 ,thefocuspositionqcan

bederivedforanarbitrarydistancepoftheobject.Thus,adistancepcanbeassignedandusedto ndthecorrespond-inglenspositionatq,whichwillbe xedforblurextentestimationanddepthrecovery.Theproblemofdepthrecov-eryisthendividedintotwosubproblems—focuscalibra-tionforthefocusingrangepandblurestimationfortheparameterscandd.

Forthefocuscalibration,aplanarobjectwithastepedgeisplacedinfrontofthecameraata xeddistance.Asequenceofimagesiscapturedwithdifferentlensposi-tions.Thebestfocusedimageandthecorrespondinglenspositionareselectedbytheimagewiththelargestaveragegradientchangeintheedgedirection.Forthe xedlensposition,theobjectlocationisthenslightlyadjustedto ndthebestfocusingrangep.Inthisfocuscalibrationstage,theobjectisusuallyplacedclosetothecamerabecause

the