CEE598 - Visual Sensing for Civil Infrastructure Eng. & Mgmt.
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1 CEE598 - Viul Sening for Civil Infrrucure Eng. & Mgm. Seion 2 Review of Liner Algebr nd Geomeric Trnformion Mni Golprvr-Frd Deprmen of Civil nd Environmenl Engineering 329D, Newmrk Civil Engineering Lb e-mil: mgolpr@illinoi.edu Deprmen of Civil nd Environmenl Engineering, Univeri of Illinoi Urbn-Chmpign
![Ueful Reding An book on liner lgebr! [HZ] chper 2, 4.](/docs-images/89/99593620/images/2-0.jpg "(b) Imge View 3D View () Temporr rucure, ie profile, foundion")
2 Ueful Reding An book on liner lgebr! [HZ] chper 2, 4. (b) Imge View 3D View () Temporr rucure, ie profile, foundion wll, nd lb rebr re reconruced (c) Some of he lide in hi lecure re coure o Prof. Ocvi I. Cmp, Penn Se Univeri, Prof. Silvio Svree, Univeri of Michign nd Prof. Noh Snvel, Cornell Univeri. 2 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
3 Applicion of Trffic Engineering 3 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
4 Google Ar Projec 4 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
5 CAPTCHA & Re-CAPTCHA 5 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
6 Ouline Imge Formion Review of Liner Algerb nd Geomeric Trnformion Bic definiion nd properie Geomericl rnformion Applicion: removing perpecive diorion he DLT lgorihm Ne Cl 6 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
7 Wh i n imge? hp://medi.phoobucke.com/imge/be%2conrucion%2imge/joejordionfn6/burj%252dubi%2522/5oi.jpg 7 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
8 Wh i n imge? 8 Digil Cmer We ll focu on hee in hi cl Source: A. Efro (More on hi proce ler) The Ee CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 8
9 Imge Dicree repreenion of coninuou funcion Ech imge i wo dimenionl rr of piel Piel: Elemen of picure cell of conn color in digil imge (i.e., numeric vlue repreening uniform porion of n imge) Grcle All piel repreen he ineni of ligh in n imge, be i red, green, blue, or noher color Similr o holding piece of rnpren colored plic over our ee Ineni of ligh in piel i ored number, generll..255 incluive 9 Coure of Howie Choe e l. CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
10 Imge (Con d) Color Three grcle imge lered on op of ech oher wih ech ler indicing he ineni of pecific color ligh, generll red, green, nd blue (RGB) Third dimenion in digil imge Reoluion Number of piel cro in horizonl Number of piel in he vericl Number of ler ued for color Ofen meured in bi per piel (bpp) where ech color ue 8 bi of d E: bpp Coure of Howie Choe e l. CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
11 Imge (Con d) A grid (mri) of ineni vlue = (common o ue one be per vlue: = blck, 255 = whie) Source: Noh Snvel CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
12 Color Imge R G B Coure of Derek Hoiem CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 2
13 Imge in Mlb Imge repreened mri Suppoe we hve NM RGB imge clled im im(,,) = op-lef piel vlue in R-chnnel im(,, b) = piel down, piel o righ in he b h chnnel im(n, M, 3) = boom-righ piel in 3-chnnel imred(filenme) reurn uin8 imge (vlue o 255) Conver o double form (vlue o ) wih im2double Coure of Derek Hoiem row column G CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 R B 3
14 Wh i liner lgebr ueful in compuer viion? Repreenion 3D poin in he cene 2D poin in he imge Coordine will be ued o Perform geomericl rnformion Aocie 3D wih 2D poin Imge re mrice of number Find properie of hee number 4 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
15 Liner Algebr
16 Vecor (i.e., 2D or 3D vecor) P = [,,z] p = [,] 3D world Imge 6 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
17 Vecor (i.e., 2D vecor) v (, 2 ) 2 v P Mgniude: 2 2 v 2 If v, v I UNIT vecor Orienion: v v 2, v v n 2 I uni vecor 7 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
18 Vecor Addiion v w (, 2) (, 2) (, 2 2) v+w v w 8 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
19 Vecor Subrcion v w (, 2) (, 2) (, 2 2) v v-w w 9 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
20 Sclr Produc v (, 2) (, 2) v v 2 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
21 Inner (do) Produc v w v w (,2) (, 2) 22 The inner produc i SCALAR! vw (,2) (, 2) v w co if v w, v w? 2 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
22 Orhonorml Bi 2 j i v P i j (,) (,) i j i j v (, 2 ) v i 2j vi? v j ( i 2j) i 2 i 2j) j ( 22 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
23 Vecor (cro) Produc u w u vw v The cro produc i VECTOR! Mgniude: u v w v w in Orienion: u u v u v ( v w) v w u w ( v w) w if v // w? u 23 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
24 Vecor Produc Compuion i (,, ) i j (,, ) j i j i k j k k (,, ) k u vw (, 2, 3) (, 2, 3) ( ) i 2 ( 3 3 ) j ( 2 2 ) k 24 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
25 Mrice nm n n m m m m n A m n m n m n B A C Sum: ij ij ij b c Emple: A nd B mu hve he me dimenion! Piel ineni vlue CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 25
26 nm n n m m m m n A p m m n p n B A C Produc: m k kj ik j i ij b c b n n n n n n n n A B B A A nd B mu hve compible dimenion! i nm n n m m m m n b b b b b b b b b b b b B b j CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, Mrice
27 Mrice m n T n m A C Trnpoe: ij ji c T T T A AB B ) ( T T T B A B A ) ( If A A T A i mmeric Emple: T T Smmeric? Smmeric? No! Ye! CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 27
28 Mrice Deerminn: de de A mu be qure Emple: 2 de CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
29 Mrice I A A A A n n n n n n n n Invere: A mu be qure Emple:? CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 29
30 2D Geomericl Trnformion
31 2D Trnlion P P 3 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
32 2D Trnlion Equion P P ), ( ' P P ), ( ), ( P CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 32
33 2D Trnlion uing Mrice P P ), ( ), ( P ' P CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, Homogeneou Coordine
34 Homogeneou Coordine Mulipl he coordine b non-zero clr nd dd n er coordine equl o h clr. For emple, ),,, ( ),, ( ),, ( ), ( w w w z w w z z z z z CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 34
35 Bck o Crein Coordine Divide b he l coordine nd elimine i. For emple, NOTE: in our emple he clr w CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, ) /, /, / ( ),,, ( ) /, / ( ),, ( w z w w w w z z z z z
36 2D Trnlion uing Homogeneou Coordine P P ' P,), ( ), (,), ( ), ( P P P T P I CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 36
37 Scling P P 37 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
38 Scling Equion P P ' P,), ( ), ( ',), ( ), ( P P S P S P S ' ), ( ' ), ( P P CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 38
39 Scling & Trnling P P P =S P P =T P P =T P =T (S P)=(T S) P = A P 39 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
40 Scling & Trnling S '' P S T P A CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 4
41 Trnling & Scling = Scling & Trnling? ''' P T S P '' ' P S T P CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 4
42 Roion P P 42 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
43 Roion Equion Couner-clockwie roion b n ngle P ' ' coθ coθ in θ in θ P ' ' co in in co P' R P CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 43
44 Degree of Freedom ' ' co in in co R i 22 4 elemen Noe: R belong o he cegor of norml mrice nd ifie mn inereing properie: R R T R T R I de( R) 44 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
45 Roion+ Scling +Trnlion P = (T R S) P coθ inθ in θ coθ R ' P S T P coθ inθ in θ coθ S R S R If =, hi i imilri rnformion! CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 45
46 Trnformion in 2D Iomerie Similriie Affini Projecive 46 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
47 Trnformion in 2D Iomerie: H R ' ' e - Preerve dince (re) - 3 DOF - Regule moion of rigid objec [Eucliden] CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 47
48 Trnformion in 2D Similriie: H R ' ' - Preerve - rio of lengh - ngle - 4 DOF CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 48
49 Trnformion in 2D Affiniie: H A ' ' A ) R( D ) R( ) ( R D CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 49
50 Trnformion in 2D Affiniie: H A ' ' A ) R( D ) R( ) ( R D -Preerve: - Prllel line - Rio of re - Rio of lengh on colliner line - oher - 6 DOF CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 5
51 Trnformion in 2D Projecive: H b v A ' ' p -Preerve: - cro rio of 4 colliner poin - collineri - nd few oher - 8 DOF CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 5
52 Trnformion in 2D 52 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
53 Removing Perpecive Diorion (recificion) H p 53 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
54 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 54
55 Compuing H p - 8 DOF - how mn poin do I need o eime H p? A le 4 poin! (8 equion) - There re everl lgorihm 55 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
56 DLT lgorihm (Direc Liner Trnformion) H i i H i i 56 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
57 DLT lgorihm (Direc Liner Trnformion) Unknown [9] i H i A h i (h ) T Funcion of meuremen [39] 9 h h h h equion (onl wo re independen) CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 57
58 DLT lgorihm (Direc Liner Trnformion) H A 29 h 9 A i h A A 2 A N h h h i i A h N9 9 2 Over deermined Homogenou em 58 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
59 DLT lgorihm (Direc Liner Trnformion) A h N9 9 2 How o olve? Singulr Vlue Decompoiion (SVD)! 59 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
60 Eigenvlue nd Eigenvecor 6 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
61 Eigenvlue nd Eigenvecor The eigenvlue of A re he roo of he chrceriic equion S AS p( ) de( I A) S v v N N 2. N digonl form of mri Eigenvecor of A re column of S 6 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
62 Singulr Vlue Decompoiion h A U V U AV 2. N 62 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
63 DLT lgorihm (direc Liner Trnformion) A h N9 9 2 How o olve? Singulr Vlue Decompoiion (SVD)! U D V 2n9 99 T 99 L column of V give h! H! 63 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
64 DLT lgorihm (direc Liner Trnformion) A h N9 9 2 How o olve? [U, D, V] = SVD(A); X= V(:,end); 64 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
65 Mrili Mchion Producer & Direcor UCSD ICAM undergrdue Vincen Rbud Technicl Advior UCSD CSE uden Serge Belongie Projec Advior UCSD CSE Deprmen A: wch Illinoi Comp2g Sie> Coure Conen> Supplemenr Documen> 3DViion.vi A: review SVD decompoiion 65 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
66 Ne lecure Cmer model 66 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
67 Appendi Properie of SVD 67 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
68 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 68
69 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 69
70 Appendi: DLT lgorihm (Direc Liner Trnformion) From: Muliple View Geomer in Compuer Viion, b R. Hrle nd A. Ziermn, Acdemic Pre, 22 7 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23
71 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 7
72 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 72
73 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 73
74 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 74
75 CEE598 Viul Sening for Civil Infrrucure Eng. & Mgm. Mni Golprvr-Frd, 23 75
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