Part B5. Istanbul 2004 
) — 4010 in the case 
  
010 3260 3510 3760 401 
pixel) 
y0) obtained when the 
ed 
S, we observe the extent 
cal length influenced by 
> principal point and the 
)? — 70? in the case 
50 55 60 65 70 
egree) 
y0) obtained when the 
influences little on the 
influences much on the 
an see when A = 45° 
owever, in practice it is 
angle, thus the precision 
gle-view calibration is 
this method of camera 
method based on multi 
WITH VANISHING 
hing points, the exterior 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
orientation parameters of camera are not obvious in the model of 
calibration, therefore they are irrelevant with interior orientation 
parameters. Accordingly, the view of angle has a great impact on 
the accuracy of interior orientation parameters. According to 
error analysis above, we propose the idea that formulate interior 
and exterior orientation parameters into the adjustment model, 
and then calibrate by multi views rotating around the object. This 
method can restrain the error existing in single-view calibration. 
Orientation parameters are the function of vanishing points, on 
the other hand, vanishing points are also the function of 
orientation parameters. Fig. 7 is illustrated as plane scenograph 
of Fig. 1. 
Yo 
Zo G Xoc 
Figure 7. Plane scenograph 
Linking with Fig. 1, we can obtain the functional relationship 
between exterior angle orientation parameters and vanishing 
points: 
Xx 2:02 GA COSK -o0Gsinx 
— f cotosecocosx — f tano sinx 
Py 7-—GXosnxr-oGcosx 
— —f cotosecosinx — f tane cosx 
Xs = Oyosinx = f cotæœsinx (6) 
Yi. = OYocosx = f cotæcosx 
“an meGAocoSK -oGsinx 
= — f tan psecæw cos x — f tan œ sin x 
Va, c mGZesina-oGcosx 
— ftangsecosinx — f tano cosx 
The computation of vanishing points is not the aim of calibration, 
it just links straight lines of image to calibrating parameters. 
Therefore, vanishing point shouldn't be viewed as unknown in 
adjustment model. Linearizing formula (6), 
dee 1 0 m. um. ced 
ay y.. ay 0 1 ay as ay | dx 
dv. _ | Q3ı | 0 de tesa le a (n 
dv, aO. da 0:0, bald dp 
d, U sua san iss Asa AO) 
0 dk 
  
  
  
  
  
  
a, = cot@ sec œ cos K — tan wsink 
2 
a, = —f csc’ psecacosk 
a; = f cotpgtano seco cosx — f sec osink 
d 7 —/f cot gsecasinx — f tan wcosk 
a,, = —cot psecœ sin K — tan @ CosK 
2 . 
d4,- f csc psecosin K 
d, — — f cot ptan o seco sin x — f sec” w cosx 
a, =—f cotpsecæcosx + f tanœsin K 
= 1 = 2 . 
d4, — coto sink d,s = fest esinx 
Ad, = f cotwcosk a, = cot@cosk 
a,, =—fcsc’ wcosk a, = fcotwsink 
as, = —tan @secwcosk — tan sin « 
5 
ds, = —f sec’ psecw cosy 
2 . 
d, — —f tangtano seco cosx — f sec osink 
a, = f tanpsecæsin x — f tano cosx« 
a, = tan psecœsin K — tan @ cos x 
2 . 
Acı = | SEC’ PSECMHSINK 
. 2 
a, = ftanptan wsecwsink — f sec” wCcosk 
a, = f tan@psecwcosk + f tan wsin x 
Put formula (7) into formula (3), thus, an adjustment model, 
where straight lines are directly relevant to calibrating parameters. 
Take X00 as example, get formula (8)(functions of Yoo, Zoo 
are the same with function of X00 ): 
(vy —y 3 +(x = 3 J 
+ (X: —v wv, id (x, > X;)Vy 
+ (Ay Ya + An xy) t (asy +ayx;)dx, 
t(asyj tax; )dy, + (a4 yj t dX; )do 
+ (ds La Tant, da + (ay à Ta, )dx 
T5àg-0 
Fico, TES Xy Xu 2X 
Ij J 
Li=x, (yy —y,) + y,(x —X,) 
{