CMSC 828D: Fundamentals of Computer Vision Homework 10

Transcription

1 CMSC 88D Fundamental f Cmuter Viin CMSC 88D: Fundamental f Cmuter Viin Hmewrk 0 Intrutr: Larry Davi Ramani Duraiwami Daniel DeMenthn and Yianni Alimn Slutin baed n hmewrk ubmitted by Haiying Liu. A here f Lambertian material f radiu R lie n the grund. a. Write the funtin z f ( x that rereent the half f the here that i viible frm the amera. Slutin: The gemetry f the here and amera i hwn in the [Figure ]. amera x un light y z D R x y z Figure : Gemetry f the here and the amera. In the rdinate riginated at the enter f the here the rdinate ( x y z ) f a int in the urfae atified z i.e. x y z R. Fr the uer half art f viible urfae we have negative f ( x y ) R x y. The relatinhi between thi rdinate the amera z rdinate i a tranlatin ( 00 D ). Thu the funtin z f ( x D R x y b. Write the 3 rdinate f a unit nrmal t the here urfae fr a int t the here een at a ixel ( x. Slutin: Uing the reult frm (a) we have

2 CMSC 88D Fundamental f Cmuter Viin The nrmal i ( ) f x f y and the unit nrmal i n ( x R R x x y x y y ( ) ( x y R x y ) R. Write a Matlab funtin that give the gray level due t Slutin: Nte the nrmal f light ure i ( in 45 in 45 ) ( ) n. The brightet int i lated at ( x y ) ( R R 45 in 45 ) ( R R) where R 8 ixel. Arding t the relatinhi between ixel brightne and ene brightne we have: I( x0 y0 ) k θ 55(white) θ 0 55 k 55 0 Then every ther int an be alulated by the knwn k : ( ) I x y n k n The Matlab funtin i lited in aix. ( x n ( x ( x n ( x if 0 therwie n( x n ( x 0. d. Write a Matlab funtin that generate the image f the here and a blak bakgrund. Slutin: The Matlab funtin i lited in aix. The image i hwn belw.

3 CMSC 88D Fundamental f Cmuter Viin 3 Figure : The image f the here with Lambertian urfae.. Nw a fae made f later with Lambertian refleting rertie a. Tranfrm the image int a gray level image. Slutin: The fae image i nverted int gray level image and realed t [0 ]. Nte that the fae i flied t nfrm the ame rientatin in Prblem that the euatin derived in la an be ued diretly. The enter f the r i the ti f the ne. b. Aume that the fae i ymmetrial with Slutin: Sine the fae i ymmetrial the hrizntal mnent f the nrmal n the urve C i zer i.e. 0. Arding t the relatinhi between nrmal and ixel brightne (refletane ma) we have: ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) k I k I k k I k I ± i.e. fr eah gray level alng urve C there are generally tw ible unit nrmal ( ) 0 and ( ) 0. The Matlab funtin i lited in aix.. Find a latin alng urve C where the urfae ath fae the amera and

4 CMSC 88D Fundamental f Cmuter Viin 4 Slutin: In la we have derived that dz dx dy. In ur ae ine 0 alng the urve C dz dy. Fr a referene int at the ti f ne we an alulate the relative itin (dz ) f ther int alng the urve C. The Matlab funtin i lited in aix. The rfile f the fae i rearranged a reuired and hwn abve.

5 CMSC 88D Fundamental f Cmuter Viin 5 Aix hw0_.m funtin hw0_ Syntax: hw0_ Deritin: CMSC88D HW0_ Authr: Haiying Liu Date: Nv dbt if errr mg narghk(0 0 nargin); if (~iemty(mg)) errr(trat('error:' mg)); lear mg; I CmuteBrightne; figure; imhw(i []); xlabel('x'); ylabel('y'); rint -djeg hw0_; funtin I CmuteBrightne Syntax: I CmuteBrightne Deritin: Cmute the brightne f a lambertian here urfae. Authr: Haiying Liu Date: Nv dbt if errr mg narghk(0 0 nargin); if (~iemty(mg)) errr(trat('error:' mg)); lear mg;

6 CMSC 88D Fundamental f Cmuter Viin 6 Initializatin imsz 56; white 55; glbal R; R imsz / ; theta 45 * i / 80; n [(theta) * (theta) (theta) * in(theta) -in(theta)]; Cmute k x0 R * (theta) * (theta); y0 R * (theta) * in(theta); n_xy CmuteNrm(x0 y0); k white / (n_xy * n'); I ne(imsz) * (white ); Cmute brightne fr rw :imsz fr l :imsz y rw - R; x l - R; if x * x y * y < R * R n_xy CmuteNrm(x ; I(rw l) k * (n_xy * n'); if I(rw l) < 0 I(rw l) 0; Reale the brightne t mini~55; dark min(i(:)) I (I white ).* dark (I < white ).* I; funtin n_xy CmuteNrm(x Syntax: n_xy CmuteNrm(x Deritin: Cmute the nrm f the int n the here urfae. Authr: Haiying Liu Date: Nv dbt if errr mg narghk( nargin);

7 CMSC 88D Fundamental f Cmuter Viin 7 if (~iemty(mg)) errr(trat('error:' mg)); lear mg; glbal R; tem rt(r * R - x * x - y * ; x / tem; y / tem; n_xy [ -]; n_xy n_xy./ nrm(n_x; hw0_.m funtin hw0_ Syntax: hw0_ Deritin: CMSC88D HW0_ Authr: Haiying Liu Date: Nv dbt if errr mg narghk(0 0 nargin); if (~iemty(mg)) errr(trat('error:' mg)); lear mg; Part a. Read the image. fae imread('face.jeg'); fae rgbgray(fae); fae duble(fae); Smth the image by the wiener filter t redue the nie intrdued by JPEG mrein. fae wiener(fae [5 5]); Reale it t dark~white; white ; dark 0; maxi max(fae(:)); mini min(fae(:)); fae (fae - mini) * (white - dark) / (maxi - mini) dark;

8 CMSC 88D Fundamental f Cmuter Viin 8 Fli the fae that it ha the ame rientatin a Prblem that the euatin an be diretly alied. fae flilr(fae); fae fliud(fae); nrw ize(fae ); ncl ize(fae ); Shw the fae. figure; imhw(fae []); Part b. See funtin Cmute_n belw. Cmute_n(0.6) e.g. Part. Find the ne ti fae the amera. urvec_x ncl - 68 ; lane P netirw 0; Initializatin neti_n [0 0 0]; Initializatin idealneti_n [0 0 -]; netirwrange [67 77]; mindiff Inf; fr rw netirwrange():netirwrange() intenity fae(rw urvec_x); Cmute_(intenit; fr index : n [0 (index) -]; diff nrm(n / nrm(n) - idealneti_n); if diff < mindiff mindiff diff; netirw rw; neti_n n; Mark ut the ne ti. hld n; lt([0 ncl] [netirw netirw] 'w'); lt([urvec_x urvec_x] [0 nrw] 'w'); rint -djeg hw0_a; Cmute rfile. faerwrange [ 7]; z zer(nrw ); lat_n neti_n;

9 CMSC 88D Fundamental f Cmuter Viin 9 Frm ne ti t frehead. (nte the fae i uide dwn) fr rw netirw :faerwrange() intenity fae(rw urvec_x); Cmute_(intenit; n [0 () -]; n [0 () -]; unit_lat_n lat_n / nrm(lat_n); if nrm(n / nrm(n) - unit_lat_n) <... nrm(n / nrm(n) - unit_lat_n) dz (); lat_n n; ele dz (); lat_n n; z(rw) z(rw - ) dz; Frm ne ti t hin. (nte the fae i uide dwn) fr rw netirw - :-:faerwrange() intenity fae(rw urvec_x); Cmute_(intenit; n [0 () -]; n [0 () -]; unit_lat_n lat_n / nrm(lat_n); if nrm(n / nrm(n) - unit_lat_n) <... nrm(n / nrm(n) - unit_lat_n) dz -(); lat_n n; ele dz -(); lat_n n; z(rw) z(rw ) dz; Rearrange the rfile that the frehead i at rigin f (y z) rrdinate ytem. rfile z(faerwrange():-:faerwrange()); rfile rfile - rfile(); take frehead a rigin f (y z) figure; npint ize(rfile ); lt([:npint] rfile); axi ij; axi eual; xlabel('y'); ylabel('z');

10 CMSC 88D Fundamental f Cmuter Viin 0 rint -djeg hw0_b; funtin Cmute_(I) Syntax: Cmute_(I) Deritin: Cmute the tw ' ardint t the intenity. Authr: Haiying Liu Date: Nv dbt if errr mg narghk( nargin); if (~iemty(mg)) errr(trat('error:' mg)); lear mg; glbal white; Cmute unit nrmal fr light ure n [ r]. theta 45 * i / 80; (theta) * (theta); (theta) * in(theta); r -in(theta); Cmute. The tw nrm will be in the frm f [0 -]. () * - I * I; () - * * r; (3) r * r - I * I; rt(); funtin n_unit Cmute_n(I) Syntax: n_unit Cmute_n(I) Deritin: Cmute the unit nrmal frm the intenity. Authr: Haiying Liu Date: Nv dbt if errr

11 CMSC 88D Fundamental f Cmuter Viin mg narghk( nargin); if (~iemty(mg)) errr(trat('error:' mg)); lear mg; glbal white; Cmute unit nrmal fr light ure n [ r]. Cmute_(I); nrw ize( ); n [zer(nrw ) -ne(nrw )]; fr index :nrw n_unit(index :) n(index :) / nrm(n(index :));