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

LinandChang:Depthfrommotionanddefocusblur

Table1Depthrecoveryfromdefocusblur withthefocusingrangep=265mm .

Aperture15mm

Distance

mm 50060070080090010001100

Fig.8Blurextentsfordifferentobjectdistances focusat265mm ;solidanddottedlinescorrespondtoaperturediametersof7.2and15mm,

respectively.

12001300

Blur668699107113115126127129130133

Depth44655967877085990311791201127712881438

Error10.76.73.03.74.49.67.10.11.77.94.1

Aperture7.2mmBlur3439454854535659636464

Depth4615266126718528059291027126813761376

Error7.712.212.416.05.219.415.514.32.41.68.2

ferentobjectdistancesfortheaperturediametersof7.2mm solidlines and15mm dottedlines ,respectively.Theplotindicatesthatthemaximumblurextentsapproach24and50pixelsforthesetwocameraparametersettings.Di-rectioncomputationsgiveblurextentsof39.5and82.4pixels,whichyieldthecameraconstantkof0.61forbothcases.

Fordepthfromdefocusblur,thecameraiscalibratedsuchthatthefocusingrangeis265mmfromthecamera,asdescribedinSec.3.1.Atestpatternwithanidealstepedgeisusedtoobtaintheblurextentsfordifferentdistances.Theobjectisplacedatdistancesof500to1500mmfromthecameraforevery100mmapart.Twoexperimentsarecar-riedoutwiththeaperturediametersof7.2and15mm.ThedepthsarecomputedusingEq. 37 withthefocusingrangep=265mm,andthemaximumblurextentsc =79and163

14001500

pixelsfromfocuscalibration.Table1showstheblurex-tents inpixel ,recovereddepths inmillimeters ,andrela-tiveerrors inpercent intheexperiments.TheresultsarealsoillustratedinFig.10,whichindicatesthatthereisalinearrelationbetweentheactualandestimateddepthsinthedistanceof500to1500mm.

4.2MotionBlur

Fordepthfrommotionanddefocusblur,thecameraisinstalledsothatthemotiondirectionisperpendicularto

the

Fig.9Blurextentsfordifferentobjectdistances focusatFig.10Objectdistanceversusthecomputeddepth;solidanddot-