L25-26+Notes+%28Geometric+Transformations%29

L25-26+Notes+%28Geometric+Transformations%29 - Translation...

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Unformatted text preview: Translation Rotation Scaling Texture Mapping 2. Gray-Level Interpolation (8.2) Nearest Neighbor {0th order) Bilinear Interpolation 11st order] Higher Order Interpolation - visually/graphically: - visually/graphically ° visually/graphically - geometrically: - geometrically (linearly interpolate the - geometrically: Iinearinterpolation): mm Wheyf ,EijcewA we; klporlmaccl than! Al V M mu CUSQ ita mongol; FNEKQ "rm .. I. a, , “l3 3 ax 4! 9 q- » a 0 . o 9.00 ; -mfithematically/algorithmically: ' mathematicallylalgorithmically i r , Last" Azlx‘il Balm-ll ’ m "D “5*: W“ W ' Intermittent! Tubal; Vi: (i—Ma. + Na l5 0C E :0.“ “:0. 'l- (atzxtxl\3'(af3)lu‘l+l was.er (in? El” t 2 '” fi‘fifffi? cw o {:{K\’~l a ‘ o | z ' : -0. ‘ _ _ _ a“ 515%) PM i l‘ infierpolttiad V = c *- Ac +~ Ad :— MXV'SG-lilh Salim-46L L 'theutslt | « "— 0‘ Ac‘bé‘ 13m. Lame-2. | 1 I093»: mm“ a $35 ‘ '= (PB) LLl-AMJAQ l-BK“I¥)L HM - Implementation: map forward or backward? (Splitting Pixels: The very idea) ' H. , . Woasvfi- almajs MP ' Backward r, \ “0 TU»an i +o (ner load-{0&5 ' a (meal; «LL13 52"”‘4" I . i Mcuj Praia-55.9, “holes f ffidblalfl1 E:— B( 3 L J incur}wa (“WNW ~ 7A/J— Mbww? mifmlk-d, MS I Mqu er 6¢¢Lliu > in wwwmajm‘or er I +- - "I i i q A B and gene—rakea value (mink {-o u$a P, m. 1 cm'tevfoiaififi‘fl- or ' Averaging U‘CL‘W‘PI‘J?) .1: = cos(6)x7sin(3)y y’ : sin(o9)z + cos(6‘)y 3. Spatial Transformations (8.3) (simple, separable, q :55. La. i; . , = - o . - Translatlon: mt : L- + :130 Rotation: 23.3—— 25' Scaimg: I: = SI; 1U] : y + 110 33': 5697‘] “ (’5) ('53 fi’fi’ 3" = 3331' q” I 3' = 5(5) +C-Qi-‘1'D‘ “‘35 (/7 i‘p 17 a- //:a.“ f S; " 2.: i? c Kd, ll 9 [can b r x: 5 I 2.. 3 b one Simple class of transformations is the “fin-‘1 ‘mniformafitlm! 37’ = mm + by + c Affine Wansfonnations are simply linear combinations of at, y, and 1. “hi—mi m” 1! Matrix Form of Affine Transformations i y’ 5133 + cg + f Translation, rotation, and scaling are all affine transformations. '3! e f y ' 0 9 1 1 005(3) ‘5111i91 '3 :L' cos(6)x—sin(6)y SI 0 U x Sm sin(6‘) 608(9) 0 y = sin(6)m+cos(5‘)y 0 33 U y = big 1 0 $0 a: w+wo 0 0 1 1 1 . . . . Exam 1e: rotation around the int 1 , : - Warping: (control pomt or polynomial) transformations - j p 1” (“to m) “lax. war “L : V 1 0 3:0 cos-1(6) fismm) 0 1 U —.'i'20 .1: I ———%— —-—E—-—a I 0 1 yo sink?) c0509) 0 0 1 —yu 'y X. . , ‘5: xi.“ 001 a e 1 001 1 / x, (:1! rmwée {.- eflCjiu-s’c tramslmira \Zlf‘jz‘ 2'33: i I bad-3k. ‘03 C“ $3“ch l x3553 (“‘33 «a {5 “TQMAqu‘Lflj‘ G) seine st C0€¥£i¢i€fi3c$ a— f: engines”? (?re_ win-11:1 {313,} if: 9.2g. +b$ti~c For Wu K; t1”! *1: ’uuLKL "W551i? iiuci x: infle. x9 :a'x9fb33 inc SammieJ €2.12. _ ii: : (i if “WV? p use 1041.511»:er MFng) (33 Lg-lizmuxiip Infaveamie l t - -' i- “F 3‘ taxi‘b‘éi’c Gr -ievel axl- Kjla A 141‘. —M; rep ,tfixfe I”; 43 #3.: AX; +£33+1C 3} some hr Mr % --‘siMu.L+. e if C smtclfih egsxm Aeiemmflj’ ‘0 damn-rams; 4. Applications of Geometric Operations (8.4) B V O i? N IT L RE A F PS 0 Geometric Calibration (TV cameras - geometric distortion) o N AM 9 AK MoH'TA 6E ' Image Rectification: Image Intensifier Grid Rectification; Fish-eye lens 4, V m W A L 0 LV H p H; 5 0 Image Registration N A U \r 0 <3 ' Map Projection: Digital Orthoquads Bo M AM PA K . . . ‘ 1.. "‘ *Lus'i-ulwe. v Morphmg E) Hflu‘fiola TMLSC“ (£53135: (3‘53.- Easw ire 4mm: Casts-3am) ...
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This note was uploaded on 03/02/2012 for the course C S 450 taught by Professor Morse,b during the Winter '08 term at BYU.

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L25-26+Notes+%28Geometric+Transformations%29 - Translation...

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