3. Stereoscopic vision 2 hours

Transcription

1 Lctur //003 Concpt Hll/Pfiffr Fruary Stroscopic vision hours Aim: Undrstanding and application of stroscopic vision not only for photogrammtry Thory: gnral mthods of stroscopic vision masurmnt 3.1. Principls of inocular vision Th main proprty of inocular vision is th aility of dpth prcption. Nvrthlss thr is a proprty of monocular vision that allows stimating th distanc to th ojcts. It is asd on th focusing accommodation of th individual y. Monocular vision has two important for th masurmnts proprtis. Ths ar angls of distinct sight. Thr ar of two typs. First of it is th aility to distinguish two luminous points. It is at aout 45. Scond typ aility for distinct sight is for possiility to distinguish two paralll lins. It is stimatd to aout 0. Binocular vision is vry important for accptanc of spac distriution of ojcts undr osrvation. In strovision vryon put his ys in such mannr that cntral rays of sights intrsct ovr th ojct of intrst. Th point of intrsction is calld fixing point of inocular vision. Th imags of fixing point li in th cntral axilla of th ys. Th distanc twn th front nods of th ys is trmd y as (or y spacing). Th lngth of this as is twn 58 up to 7 mm and normally is aout 65mm. Th angl twn rays to th sam point is trmd parallax angl γ. Th angl twn rays for fixing point is calld convrgnt angl. Th valus of ths angls ar small. γ = (3.1) For th distanc of ttr viwing (5cm) this angl is aout 15. Th aility of human vision to accpt th imags in oth ys as on is vry important. It is possil only for points that li nar to cntral point of th y. Th points in th ys li that ar at th sam distanc from th cntral point ar symmtrical. Th imags of ojcts ovr th symmtrical points ar assumd at th sam distanc as th distanc for th fixing point. If th distancs (angl distancs) ar diffrnt th points ar accptd as nar or far from th distanc to th fixing point. FH-KA - Mastr cours Photogrammtry 003

2 Lctur //003 A F B γ O 1 O a 1 f 1 1 a f Figur 3.1. Parallax angls FH-KA - Mastr cours Photogrammtry 003

3 Lctur //003 Whn th diffrnc in angl distanc for two points is largr thy ar accptd as diffrnt and th osrvd imag is forkd. This is masurd only for points which parallax angl diffrs lss thn 70 (positiv or ngativ) thn parallax angl for fixing point. γ γ F 70' (3.) For th accuracy of dpth masurmnt and stimation it is important h minimal valu of diffrnc of parallax angl for two points at diffrnt distancs for which th distanc is accptd as not th sam. This angl is stimatd to aout γ1 = 30". Th distanc for th parallax angl qual to th γ1 is trmd th radius (distanc) of unarmd inocular vision. It is stimatd to aout 450m. (s Appndix 3.1). This distanc can nlargd y magnification of viwing systm or y th nlargmnt of th as of ntranc ojctivs. 3.. Mthods of stroscopic osrvation Stro ffct is possil to otain not only viwing th ojcts at th diffrnt distancs ut osrving projctiv imags of ojcts. In this cas th distanc twn imags (photos) must th sam as th y spacing. By this rason th siz of th photos could not too larg (approximatly 60 mm). In th procss of osrvation twn two ys must put sparating plat. This nsurs osrvation th corrsponding imag with ach of th ys. FH-KA - Mastr cours Photogrammtry 003

4 Lctur //003 A F B a f f a O 1 O a 1 f 1 1 a f Figur 3.. Stroscopic osrvation without quipmnt To otain good stro ffct it is ncssary to satisfy svral conditions. FH-KA - Mastr cours Photogrammtry 003

5 Lctur // Photos must producd from diffrnt projction cntrs;. Scal diffrncs must lss than 16% 3. Evry y must s its own sparat photos; 4. Photos must disposd in such way that rays of viw to intrsct 5. Th angls of intrsction must lss than 16 ; 6. For th usd valus of parallax angls th y accommodation must possil. Bttr rsults can rachd if stroscopic quipmnt is usd. Svral transformations in th dimnsions of th prcivd modl may happn. If th hight and as ar sam as in th thr dimnsions thy is no chang of scal and hight. But this cas is idal and practically not happns. Th osrvd hight and scal dpnds on as/hight ratio at th momnt of rgistration and th as distanc ratio at th momnt of osrvation. This is graphically shown on th following figurs. Th nxt figur shows th rgistration of th imag from normal angl and wid angl camra from diffrnt distancs (flight hights). FH-KA - Mastr cours Photogrammtry 003

6 Lctur //003 Rgistration O 1N B O N c N H N c W O 1W O W H W Z P X Figur 3.3. Photo capturing Th imags from normal angl camra osrvd with viwing systm with sam B/ ratio and with shortst. FH-KA - Mastr cours Photogrammtry 003

7 Lctur //003 O1 Osrvation O c Osrvation O 1 O c P Z X Normal angl camra s photos Normal imag distanc P Z X Normal angl camra s photos Long imag distanc Figur 3.4. Osrvation of normal angl photos FH-KA - Mastr cours Photogrammtry 003

8 Lctur //003 Th vrtical xaggration is ratio twn as/hight of stro photos and as (y spacing)/distanc ratio in th osrvation systm. Z = B : H (3.3) For wid angl camras th rsults ar analogus. (s Appndix 3.). Th tal low shows th vrtical xaggration for viwing systm with /=65:400=1:6.. Th rsults for sam narrow angl, normal and wid angl camras follows [Kraus K., 1993, Photogrammtry v.1] ar prsntd in th tal llow. Tal 3.1 Narrow angl Normal angl Wid angl Supr-wid angl C [mm] B/H 1:6.6 1:3.3 1:1.6 1:0.9 Z Th xaggration of th rlif in stro modl is important for photo-intrprtation. For photogrammtry it is not of such grat importanc ut it is maningful for xact idntification of stro points during masurmnts. For practical purposs ar applid mirror stroscops, lns stroscops and lns mirror stroscops. Mirror stroscop only changs th ffctiv displacmnt twn two photos. Lns stroscop producs nlargmnt of imags. Th scal of nlargmnt could simpl dfind y th following figur d s dp f s FH-KA - Mastr cours Photogrammtry 003

9 Lctur //003 Figur 3.5. Magnification of lns stroscop Th lns nlargs th ffctiv angl of viwing th ojcts. This allows moving th viwing ojct closr to th y and th y can still focus. Th magnification ratio dpnds on focusing distancd of th lns f s and distanc of st viwing. ds M = = (3.4) d f p s Th lns stroscop magnifis th apparnt parallax p and as thus thr is th nlargmnt of th whol modl. This dos not chang th osrvd ratio h/ and rspctivly th vrtical xaggration. Th drivation of nlargmnt ratio is shown in Appndix 3.3. It is prsntd y quation M k = (3.5) s whr s is th scal of th photograph (imag). Th simpl lns mirror stroscop is similar to lns stroscop ut with addition of two mirrors or prisms in th path from lft and right photos. This incrass th sparation twn two photos so th largr photographs could osrvd without ovrlapping at th cntr of stroscop working plan. Th sparation of stroscopic pairs is slctd mpirically y most osrvrs. It is chosn y th st stroscopic viwing of th ojcts. From th rlation (3.4) it is found th as-distanc ratio for stroscop H = z (3.6) B Th ratio distanc/as for lns stroscop is connctd with displacmnt w with rlation. fs = w (3.7) FH-KA - Mastr cours Photogrammtry 003

10 Lctur //003 Focal plan of lnss optical axs f s w 0-w w 0-w ffctiv pair position w w 0 Figur 3.6. Mirror stroscop gomtry Th rlation for th optimal displacmnt of mirror stroscop is similar fs. B w = w0. H (3.8) Z whr w 0 is th as dfind y th mirrors Mthods of stroscopic masurmnt Osrvation and masurmnt of photo imags Parallax ar masurmnts FH-KA - Mastr cours Photogrammtry 003

11 Lctur //003 Stroscopic masurmnt may ralizd y parallax ar that has th masuring marks. Initially w rad th micromtr scrw at principal point of on of th photos. For this point w know th ral valu of parallax p ξ. Th imag as 0 can masurd y th distanc twn th imags of th ojcts at th principls points of th photos of th stro pair. For this point th actual valu of hight must known. If it not possil th usag of any othr point is possil. Th rduction of masurd micromtr valus is mad rspctivly to this point. Th figur for hight diffrncs is shown low. O 1 O c pp 1 pp h h h P 1 P z z P 1 P Figur 3.7. Parallax ar masuring paramtrs p = p = n n = ( n n ) + ( n n ) = p + p ξ, i ξ, i P i P i A A P ξ, ia ξ, AP p = p ( p + ) ξ, ia ξ, i ξ, AP P (3.9) For hight diffrnc twn points A and i can writtn th following xprssion z i = p hp + p ξ, ip p (3.10) ξ, ip FH-KA - Mastr cours Photogrammtry 003

12 Lctur //003 Th drivation of th rlation is shown in Appndix 1.5 Floating mark principl Anothr mthod of stroscopic masurmnt is known as floating dot principl. Two lightning point or dots ar introducd in th plan of stroscopic pair of photos. Thy can alignd with any two corrsponding points on th pair. Th parallax p ξ producs a disparity angl α, which is prcivd y th osrvr as th hight h. Th masuring is mad y virtual mark hat is ralizd y two dot or light marks xposd at th cntr of th viwing fild (placd on th path of cntral rays) for th two photos of stro coupl. By moving th position of imag rspctivly to th position of flying point mark th prcption of moving up and down of mark is otaind. m1 m P1 P a 1 a a A A Figur 3.8. Floating mark principl Ral mark and anaglyph vision FH-KA - Mastr cours Photogrammtry 003

13 Lctur //003 Anothr principl that is usd in analogu apparatus is th principl of ral mark. Th modl is cratd in modl spac and is osrvd y th oprator with anaglyph glasss. Two imags ar producd y color filtrrs and ar osrvd trough th glasss with th corrsponding color. Th imag is visualizd ovr th flat scrn. On it thr is a lightning point that is th ral mark. Whn th position in plan and hight coincids with point in th modl th prcption of coincidnc twn modl and masuring point is rachd. Th anaglyph principl is usd to osrv th printd stro mags. Th diffrnc in this cas is that for printd imags th visil imag is in th opposit color. For xampl y with th grn glass will s th rd imag and th y with th rd glass will s grn imag. Th rason for this is that th whit ackground is visil as grn through grn glass and th grn imag is not sn on it. Th rd glass passs rd light from th whit ackground and th rd imag is not sn on it (through rd glass). FH-KA - Mastr cours Photogrammtry 003

14 Lctur //003 a1 a P 1 P rd filtr O 1 O grn filtr M A Figur 3.9. Ral mark osrvation Stro masurmnts of digital imags In digital photogrammtric systms ar usd som of mthods that ar applid in analogu and analytical photogrammtry. But th sourc of imag in all cass is scrn of th monitor. Thr ar usd four typs of systm for stro osrvation and masurmnt. 1. Stroscopic viwr with split scrn. Th scrn of th monitor is sparatd into two parts vrtically and in ach part is visualizd on of th stro imags. Th mirror stroscop is situatd in front of th scrn. Th systm dos not rquir th xpnsiv parts. Th paramtrs of stroscop ar adoptd for scrn siz of th monitor. This is th main limitation in this systm. Thr is a possiility for monoscopic and stroscopic osrvation of th stro pair. FH-KA - Mastr cours Photogrammtry 003

15 Lctur //003. Anaglyph osrvation of stro imags. In this cas th monochromatic imags ar colord in two colors and ovrlappd ovr th scrn. Th main disadvantag is that such approach is suital only for monochromatic imags. Th ovrlapping color vctor graphic if xist is not sn wll. This mad systm vry poor applical for plotting of complx aras and colour codd oundaris. Th third and fourth systms ar asd on usag of polarizd light. Th systm that ar usd ar of two typs: a) with passiv scrn and activ spctacls; ) activ scrn and passiv spctacls. Th main principl of opration is asd on th passing of th polarizd light through th spctacls with polarizd glasss. This switching of th imags coms mor than 50 tims pr scond and du to th faturs of human ys to mmoriz imags for th short tim th visil imag is stal. Th plan of polarization is changd so th corrsponding glass locks or passs light. Th main disadvantag of this systm is thir high pric. 3. Polarisd light osrving systm with activ scrn. Activ scrn is mountd in front of th monitor scrn. Its plan of polarization is changd y lctrical fild. Th passiv spctacls, that ar usd, hav glasss with prpndicular plans of polarization. Whn th plan of th polarization of scrn and glass ar th sam th imag is visil. So at sam tim th scrn is visil only through on of th glasss. Th chang of th lft and right imag is mad synchronously with th chang of polarization. Th principl diagram of this mthod is shown on th figur low. FH-KA - Mastr cours Photogrammtry 003

16 Lctur //003 Monitor Activ scrn Polarisd spctacls Figur Osrving stro systm with activ scrn 4. Polarisd light osrving systm with activ spctacls. This systm dos not uss activ scrn. Th commutation of imags is in th spctacls. Evry on of thir glass consists of two parts fixd polarisd glass and activ glass lctrically controlld. Th synchronization twn monitor and spctacls is nsurd y infrard or ultra-sonic mittr situatd ovr or nar to monitor and rcivr in th spctacls. Main disadvantag of this systm is that thir glasss ar too havy and xpnsiv. Th dvlopmnt of tchnology maks this disadvantag mor and mor unimportant. This systm has mor advantags and is widly usd. Th principl diagram of this mthod is shown in following figur. FH-KA - Mastr cours Photogrammtry 003

17 Lctur //003 Synchronisr Monitor Activ polarisd spctacls Figur Polarisd light mthod with activ spctacls Th comparison of th main proprtis of th four mthods is shown in th following tal. Tal 3. Proprty Stroscopic Anaglyph Activ Activ viwr mthod polarizd polarizd scrn spctacls Imags Color Monochromatic Color Color Numr of osrvrs Monitor Standard Standard High frquncy High frquncy Cost Low Mdium High High Main On osrvr Monochromatic Low imag Havy disadvantag imags intnsity spctacls In th rcnt ars th most prspctiv mthod for stro masurmnt in digital photogrammtry is usag of systms with activ spctacls. Appndixs Appndix 3.1 Th accuracy of dpth stimation for unarmd vision w may otain from th quation for parallax angl at optimal distanc. FH-KA - Mastr cours Photogrammtry 003

18 Lctur //003 = (3.3) γ iffrntiating this w otain =. =. γ = γ (3.4) γ γ ( / ) Analogu it is dfind th distinct aility to distinguish two vrtical lins. Empirically it is stimatd to aout γ = 10". Th distanc for th parallax angl that is qual to th γ1 is trmd th radius (distanc) of unarmd inocular vision. It is stimatd to aout R ρ " = = = 450m (3.5) γ 30" whr ρ " = π Practically this distanc is littl it mor. This distanc could nlargd artificially if w us inoculars or stro trnch-priscop (stro viwing tu). B S FH-KA - Mastr cours Photogrammtry 003

19 Lctur //003 Figur 3.1. Stro viwing tu Two factors nlarg this radius: magnification of th imags and th iggr as thn y spacing. R a Bs = vr = ω. R (3.6) whr ω = Bs v Appndix 3. Th planimtric to hight nlargmnt Thr ar discussd th osrvation of imags takn with wid-angl camra with th viwing systm for normal photos and with short distanc. Th usag of appropriat short distanc nsurs th sam planimtric scal to hight ratio as in th ojct. This is not possil for all camra typs. FH-KA - Mastr cours Photogrammtry 003

20 Lctur //003 Osrvation o 1 o Osrvation o 1 o c c Z X Wid angl camra s photos Normal imag distanc P P Z X Wid angl camra s photos Short imag distanc Figur Osrvation of wid angl photos Th stimation of vrtical xaggration z is valuatd from th figurs 3.5 and 3.6. z Z Z = : X X (3.7) Th X displacmnt is chosn as th n-th part of as distancs. B X = X n = n (3.8) Th valus of Z is stimatd from rlation twn parallax and projction cntr distanc FH-KA - Mastr cours Photogrammtry 003

21 Lctur //003 cb. cb. Z0 = HU HP = (3.9) p p ξ, U ξ, P Th horizontal parallax for plan U xists in th osrvation too. c p = c (3.10) p ξ, U, = ξ U By analogy w otain for Z th rlation p p p p p p p Z = c = = ξ, P ξ, U ξ, U ξ,,,. P ξ U ξ P ξ, U pξ, U. pξ, P pξ, U. pξ, P pξ, U. pξ, P (3.11) Sustituting th valus for Z and Z in rlation for Z w finally otain Z p ξ, U B B = =. = : (3.1) c H H Th rsult shows that vrtical xaggration is ratio twn as/hight of stro photos and as (y spacing)/distanc ratio in th osrvation systm. Appndix 3.3 Th following rlation dfins th magnification of th ojct ds k = (3.14) d t whr d s is visil siz and d t is siz at th ojct spac Th scal of photograph s is dfins as dt s = (3.15) d p For quation of lns magnification d s = d p (3.16) f s Solving th aov quations givs th ojct magnification d p M k =. = = (3.17) f d s. f s s t s FH-KA - Mastr cours Photogrammtry 003

22 Lctur //003 Appndix 3.4 Th optimal displacmnt for mirror stroscop is dpnding on th displacmnt du to th mirrors (from similar triangls) on th figur 3.6. Solving this and sustituting th valu from ratio quation w otain fs. w = fs : fs : = = B. H For mirror stroscop th rlation is slightly diffrnt (from figur 3.8) fs = w w 0 For th optimal displacmnt w otain H f. w = w f = w f = w s B. H 0 s : 0 s : Z 0 B Z Z (3.18) (3.19) (3.0) Appndix 3.5 Osrvr is using stroscop (mor oftn mirror lns) and is coincids th marks with th stro ojct. At this momnt th valu rad from th drum scal is fixd. Th masurd valus ar rlativly to som as point for which th ral parallax must known. pξ, i = pξ,0 + ( ni n0) (3.1) Th diffrnc of th two radings of th micromtric scrw, rlativly to any aritrary origin, is th parallax diffrnc. n n = p = p p ξ (3.) 1 ξ ξ, Th hights h1 and h can drivd for th normal cas h 1 pξ,1 pξ,,1 cb. cb. = h = (3.3) For hight diffrnc w otain Aftr sustitution cb. cb. pξ, pξ,1 pξ z = h1 h = = cb. = cb. (3.4) p p p. p p. p ξ, ξ,1 ξ,1 ξ, ξ,1 ξ, cb. h = p = p + ξ (3.5) 1 and ξ, ξ,1 p pξ,1 Th xprssion for hight diffrnc could prsntd in th following form FH-KA - Mastr cours Photogrammtry 003

23 Lctur //003 z = p ξ,1 h1 + p ξ p ξ (3.6) In cas whn th first point is as point w otain z i = h0 + p ξi p ξi (3.7) FH-KA - Mastr cours Photogrammtry 003