(z,594) in search window in decompressed image, 
respectively, when lossless compression, we have 
f(, 4 — 9G.) (1) 
If the origines of two windows’ coordinate system 
are the centers of two windows, then, 
To S, (2) 
yo Ya (3) 
where (z0»ÿ0) stands for coordinate of object point 
in original image, and (z,,9y,) for coordinate of 
homelegous point in decompressed image. Because 
of losy compression, there are geometric distor- 
tions and grey value differences between homolo- 
gous points in images before and after compres- 
sion, which makes (1) and (2) not correct, thus 
(1) becomes : 
E(z,,9,) — f(z,,9y,) — 9 (,,y4) (3) 
This is the observation error equation. 
propesed im thrs paper is: clrusing target window 
centered at (z,,y,) in original image and search 
window centered cat some initial position (2,92) 
in decompressed image, then getting linearized ob- 
serving error equation , like (6) of each pair pixel in 
two windows , and finally finding out the final val- 
ues of parameters involved in (6) by interately 
solving these equations. According to (5), we can 
get the matched point (z,,y,) of (z,,y,) in decom- 
pressed image. Let 
Az =z, — z, (7) 
áy my, (8) 
for given limit error 0,,0,, we can obtain the per— 
centage of pixels that satisfy following canditions : 
|4æ | < 6, (9) 
|4y| <$, (10) 
in total points in matcking process. Finally, we use 
this percentage to quantitatively measure the degree 
  
  
  
  
  
  
  
  
  
  
  
  
under In general, the difference of grey value is moded by of geometric distortions of decompressed image on 
th the following linear relationship : the whole. 
ut the f(G,,y,) — b + 529 54591) (4) 
preci- where b, ,b, are radiometric parameters. 3. EXPERIMENT RESULTS AND CONCLUSION 
But the geometric distortion is represented by fol- 3. ] Experimental results. In experiments, we use 
lowing affine transformation : two lossy compression method, called method 1 
entific 2,| — [4i a, az\(z, and method 2, to compress one aerial photograph 
intita- [74 A [y je i £8) at different compression ratio (CR). Then we use 
ecom- where a;(i=1,2,+,6) are geometric distortion pa- above assessing method to assess the degree of geo- 
objec- rameters. Under the conditions of (4), (5), ex- metric distortions of decompressed images. The ex- 
ecom- | pending equations (3) in Tayler series in first order periment results are listed in table 1 and table 2, 
point | term, we obtain: where the method 1l is the international stardard 
ecom- | E(z,,J,) 22— b0*g, * (dMa,) JPEG (Joint Photograph Expert Group) algorithm 
r high | + y% ay) — bddag) +b) +g, + (da, + 22 (Wallace, G.K., 1991), and the method 2 is- the 
digital dag + y%dag) + db, + g 20,y9)db, compression scheme proposed by authors based on 
esults | EF Gy Rg I Rn VY (6) wavelet trans form (Malled, S.G. ,1989). 
Where n7 3,72. This is the linearized obser- — 3. 92 Conelusion. Frome the results listed in table 1 
| vation equation for every pixel pair in two win- and table 2, we can see that this method can be 
dows. used for a scientific and objective criterion for as- 
sessing accuracy of pixels’ geometric distortions in 
image 2. 2 Assessing method. The assessing method decompressed images. 
ce, in 
id ra- Table 1 Experiment result 
SKI cg, Tent of, [PSNR | Percent of-jde «0-4 Percent of |Ay |<0. 1 
e that unsuc*. point 
molo- | 2 1.1% 38. 34 99% 99% 
nakes | 
‚tched | 4 1. 394 34. 03 98% 98% 
6 3. 394 31.24 90% 90% 
LAS SF 8 7.1% 29.52 77% 81% 
and g 
161 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996