CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt.
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1 CEE598 - Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Sesson 4 Cer Clbrton Mn Golprr-Frd Deprtent of Cl nd Enronentl Engneerng 9D, Newrk Cl Engneerng Lb e-l: golpr@llnos.ed Deprtent of Cl nd Enronentl Engneerng, Unersty of Illnos t Urbn-Chpgn
2 Otlne Cer Clbrton Reew Cer reters Cer Clbrton roble Exple Redng: [F] Chpter [HZ] Chpter 7 [S] Chpter 6 Soe sldes n ths lectre re cortesy to rofs. S. Srese, J. once & F-F L CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
3 rojecte cer nhole perspecte projecton f O c f = focl length CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
4 rojecte cer nhole perspecte projecton f O c y y c x c f = focl length o, o = offset C=[ o, o ] x CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 4
5 rojecte cer f O c Unts: k,l [pxel/], f [] Non-sqre pxels [pxel] f = focl length o, o = offset, non-sqre pxels CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 5
6 rojecte cer f O c y y c C=[ o, o ] x c x f = focl length o, o = offset, non-sqre pxels = skewness 6 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
7 rojecte cer f c O c cot sn o o K hs 5 degrees of freedo! x y z f = focl length o, o = offset, non-sqre pxels = skewness 7 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
8 rojecte cer f R,T j w c k w O w O c w c R T w f = focl length o, o = offset, non-sqre pxels = skewness R,T = rotton, trnslton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 8
9 rojecte cer f R,T j w k w O w O c w M w KR T w Internl preters Externl preters f = focl length o, o = offset, non-sqre pxels = skewness R,T = rotton, trnslton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 9
10 Gol of clbrton Estte ntrnsc nd extrnsc preters fro or ltple ges KR T w M w Internl preters Externl preters CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
11 M w w T K R Note: To splfy notton let = w cot K o o sn T T T R r r r z y x t t t T Gol of clbrton Estte ntrnsc nd extrnsc preters fro or ltple ges CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
12 Clbrton roble Clbrton rg j C n wth known postons n [O w, w,j w,k w ] p, p n known postons n the ge Gol: copte ntrnsc nd extrnsc preters CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
13 Clbrton roble Clbrton rg j C How ny correspondences do we need? hs nknown We need eqtons 6 correspondences wold do t CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
14 Clbrton roble Clbrton rg ge j C In prctce: ser y need to look t the ge nd select the n>=6 correspondences 4 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
15 j C M p M n pxels Clbrton roble CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 5
16 ) ( ) ( Clbrton roble CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 6
17 n n n Clbrton roble CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 7
18 Reew on Block Mtrx Mltplcton A A A A A B B B B B Wht s AB? AB A A B B A A B B A A B B A A B B 8 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
19 n x x x4 T T T def 4x n n n Hoogenos lner syste known nknown Clbrton roble CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 9
20 Hoogeneos M x N Lner Systes M=nber of eqtons N=nber of nknown Sqre syste (M=N): A x = M x N Rectnglr syste (M>N) s lwys solton Rnk(A) = N A x = nosy esreents Mnze Ax nder the constrnt x = CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
21 Clbrton roble How do we sole ths hoogenos lner syste? CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
22 DLT lgorth (Drect Lner Trnsforton) H x H x x x nknown A h x H x Fncton of esreents CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
23 Generl Clbrton roble U D V T n Lst coln of V ges M p CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
24 A T T T A T K R b b b b Estted les ) ( o ) ( o cos Intrnsc b cot K o o sn Extrctng cer preters CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 4
25 Theore (Fgers, 99) 5 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
26 A T T T A T K R b b b b Estted les Intrnsc sn sn b f Extrctng cer preters CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 6
27 A T T T A b T K R b b b b Estted les Extrnsc r r r r r b K T Extrctng cer preters CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 7
28 Degenerte cses s cnnot le on the se plne! onts cnnot le on the ntersecton cre of two qdrc srfces CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 8
29 Tkng lens dstortons nto ccont Chrotc Aberrton Sphercl Aberrton Rdl Dstorton 9 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
30 Rdl Dstorton Csed by perfect lenses Detons re ost notceble for rys tht pss throgh the edge of the lens No dstorton n cshon Brrel CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
31 Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
32 p M d c b d p p κ p d λ olynol fncton Dstorton coeffcent To odel rdl behor Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
33 Esttng nd p How to do tht? d Hnt: slope Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
34 Esttng nd p ) ( ) ( ) ( ) ( ) ( ) ( n n n n Q n n Ts technqe [87] ) ( ) ( ) ( ) ( Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 4
35 Once tht nd re estted p s non lner fncton of There re soe degenerte confgrtons for whch nd cnnot be copted Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 5
36 p Q q q q q q q q p M Q q q q q Non-lner syste of eqtons Rdl Dstorton CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd, 6
37 Rdl Dstorton Conerson fro dstorted coordntes to ndstorted coordntes p' = f * r(p) * p (conerson to pxel coordntes) r(p) s fncton tht coptes sclng fctor to ndo the rdl dstorton: r(p) =. + k * p ^ + k * p ^4. 7 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
38 Generl Clbrton roble X f () f( ) s nonlner esreent preter -Newton Method -Leenberg-Mrqrdt Algorth Iterte, strts fro ntl solton My be slow f ntl solton fr fro rel solton Estted solton y be fncton of the ntl solton Newton reqres the coptton of J, H Leenberg-Mrqrdt doesn t reqre the coptton of H 8 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
39 Generl Clbrton roble X f () f( ) s nonlner esreent preter A possble lgorth. Sole lner prt of the syste to fnd pproxted solton. Use ths solton s ntl condton for the fll syste. Sole fll syste sng Newton or L.M. 9 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
40 Generl Clbrton roble X f () f( ) s nonlner esreent preter Typcl ssptons: - zero-skew, sqre pxel - o, o = known center of the ge - no dstorton Jst estte f nd R, T 4 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
41 Clbrton rocedre Cer Clbrton Toolbox for Mtlb J. Boget [998-] 4 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
42 Clbrton rocedre 4 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
43 Clbrton rocedre 4 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
44 Clbrton rocedre 44 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
45 Clbrton rocedre 45 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
46 Clbrton rocedre 46 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
47 Clbrton rocedre 47 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
48 Clbrton rocedre 48 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
49 Next lectre Sngle ew reconstrcton Assgnent wll be onlne Next Tesdy 49 CEE598 Vsl Sensng for Cl Infrstrctre Eng. & Mgt. Mn Golprr-Frd,
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