Transcription of 第 章フォトグラメトリーによる計測 Plotting 2.1 フォトグラ …
1 2 Plotting Use of coordinate systems (1) comparator coordinates . x . CRT . + + .. 2 . Hugershoff Pulfrich . (2) fiducial mark coordinates 4 . Leica RC30 4 1 , , 2( , ), 3( , ), 4( , ) .. (3) photographic coordinates . DLT .. (4) camera coordinates xy(-f) . f . (5) model coordinates 2 . X .. (6) object coordinates .. CAD UTM . NE EN .. CRT .. camera correction for geographic optic lens distortion . ( ) 2 .. radial linear distortion . 2 ( ) . D. C. Brown, 1966, 1971, 1972 John G. Fryer . and D. C. Brown, 1986 PE & RS, ASPRS . r = K1 r3 + K 2 r5 + K 3 r7 + .. r =.
2 X 2 + . y 2 (x , y ) .. x x . y . y x = r = (K1 r3 + K 2 r5 + K 3 r 7 + ) , y = r = (K1 r3 + K 2 r5 + K 3 r7 + ) .. r r r r ( ) tangential non-linear distortion Conrady 1919, Monthly Notices of the Royal Astronomical Society . (x , y ) . r = 3P(r)sin ( o ). } . t = P(r)cos ( o ).. o P(r . P(r) = J1 r2 + J2 r 4 + .. P(r) = (P12 + P22 )1/2r2 + (P12 + P22 )1/2 P3 r4 + .( ). J1 , J2 (x , y ) ( x, y) .. x = [P1 (r2 + 2x 2 ) + 2P2 x y ][1 + P3 r2 + ]. } . y = [P2 (r2 + 2y 2 ) + 2P1 x y ][1 + P3 r2 + ]. P1 , P2 , P3 J1 , J2 , o . P1 = J1 sin o P2 = J1 cos o }. P3 = J2 J1.)
3 J1 = (P12 + P22 )1/2. J2 = J1 P3 } . tan o = P1 P2 . P3 P1 , P2 .. t(x,y)=P(r)cos( - o). P(r). x . - y o o .. Brown . corrected photo coordinates .. x = x + x + x = x + x (K1 r2 + K 2 r4 + K 3 r6 + ) + [P1 (r2 + 2x 2 ) + 2P2 x y ][1 + P3 r2 + ]. } . y = y + y + y = y + y (K1 r2 + K 2 r4 + K 3 r6 + ) + [P2 (r2 + 2y 2 ) + 2P1 x y ][1 + P3 r2 + ]. , x = x xo , y = y yo , r = [(x xo )2 + (y yo )2 ]1/2. K1 , K2 , K 3 P1 , P2 , P3 . transformation of photo coordinates CRT .. 4 . x y 6 . ( ) 8 .. Geo-TIFF TFW 4 .. ( ) .. Helmert transformation . 2 (a,b,c,d).. yk u 2-F y.
4 X 3-F. i y xo x yo 1-F. v xk 4-F. (xk , yk ) CRT u,v (xf , yf ). xk = xf cos + yf sin + xo . } ..( ). yk = xf sin + yf cos + yo . xk = a xf + b yf + c . } .. yk = b xf + a yf + d S . S = a2 + b 2 , tan = a b . affine transformation . ( ) . 3 6 .. x k = x xf cos + y yf sin + xo . } ..( ). yk = x xf sin + y yf cos + yo . a1 = x cos , a2 = y sin , a3 = xo , b1 = x sin , b2 = y cos , b3 = yo . a1. a2. xk xf yf 1 0 0 0 a3. (y ) = ( ) b ..( ). k 0 0 0 xf yf 1 1. b2. (b3 ). 2 . (a1 , a2 , a3 , b1 , b2 , b3 ) . (x, y) . xf a1 a2 1 xk a3. (y ) = (b b2 ) (yk b3 ) ..( ).
5 F 1.. 2x = a21 + b12. 2y = a22 + b22. b tan = a 1 = b2. a ..( ). 1 2. xo = a3 . yo = b3 }. 8 . xk = a1 xf + a2 yf + a3 xf yf + a4. } . yk = b1 xf + b2 yf + b3 xf yf + b4.
