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£ he xetherlnds yrgniztion for ienti eserh is grtefully knowledged for nnil supportF I P R. Duits, M. Felsberg, G.H. Granlund , B.M. ter Haar Romeny Abstract snspired y the erly visul system of mny mmmlins we onsider the onstrution ofE nd reonstrution fromE n orienttion sore U f X R P ¢ S I 3 C s lol orienttion representtion of n imgeD f X R P 3 RF he mpping f U 3 U f is wvelet trnsform orresponding to reduile representtion of the iuliden motion group onto L P @R P A nd oriented wvelet P L P @R P AF his wvelet trnsform is speil se of reently developed generliztion of the stndrd wvelet theory nd hs the prtil dvntge over the usul wvelet pprohes in imge nlysis @onstruted y irreduile representtions of the similitude groupA tht it llows stle reonstrution from one @single sleA orienttion soreF ine our wvelet trnsform is unitry mpping with stle inverseD we diretly relte opertions on orienttion sores to opertions on imges in roust mnnerF purthermoreD y geometril exmintion of the iuliden motion group G a R P o TD whih is the domin of our orienttion soresD we dedue tht n opertor¨on orienE ttion sores must e left invrint to ensure tht the orresponding opertor I ¨ on imges is iuliden invrintF es n exmple we onsider ll liner seond order left invrint evolutions on orienttion sores orresponding to stohsti proesses on GF es n pplition we detet elongted strutures in @medilA imges nd utomtilly lose the gps etween themF pinllyD we onsider roust orienttion estimtes y mens of hnnel representtionsD where we omine roust orienttion estimtion nd lerning of wvelets resulting in n utoEssoitive proessing of orienttion feturesF rere liner verging of the hnnel repE resenttion is equivlent to roust orienttion estimtion nd n dpttion of the wvelet to the sttistis of the onsidered imge lss leds to n utoEssoitive ehvior of the systemF

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