Suitability Assessment of A4 Format Desktop Publishing Scanners
Results and analysis
The resultant vector error plots of image distortion pattern at the control points for the 300 and 600 dpi images scanned in the Apple, HP Scanjet IIC, Epson and the two HP Scanjet 4c scanners are shown in Figure 1. Since the calibrated grid plate is considered error free, the distortion pattern and the magnitude of distortion of the scanned images can be considered as due to scanner error. In all the figures, the systematic nature of the distortion pattern can clearly be seen, although the distortion patterns of images scanned in different scanners differ significantly (including images scanned in two scanners of the same model). Only the distortion patterns of images scanned at 300 and 600 dpi in the Apple scanner are similar.
Figure 1. Distortion pattern of different DTP scanners.
The summary of results on the magnitude of image distortions for the Apple, HP, Epson and HP Scanjet 4c scanners is given in Table 1.
Table 1 Magnitude of distortions at the control and check points in desktop scanners
| |
R.m.s.e. at Control points (in pixel) |
R.m.s.e. at Check-points (in pixel) |
Max. Error at Control points (in pixel) |
Max. Error at Check points (in pixel) |
| Scanner |
Mx My Mv |
Mx My Mv |
Ex Ey Ev |
Ex Ey Ev |
| Apple Colour One Scanner* |
3.41 2.27 *4.01 |
3.35 2.20 4.00 |
6.03 5.98 6.03 |
5.92 5.61 5.92 |
| Apple Colour OneScanner |
1.97 1.21 2.31 |
1.80 1.34 2.24 |
3.51 2.63 3.65 |
3.35 2.33 3.59 |
| HP Scanjet lic |
0.83 0.50 0.97 |
0.79 0.45 0.91 |
2.02 1.08 2.02 |
1.96 0.93 1.96 |
| Epson GT-9000 |
0.80 0.75 1.19 |
0.71 0.71 1.00 |
2.01 1.62 2.06 |
1.49 1.67 2.19 |
| HP Scanjet 4c (Scanner 1) |
0.84 0.73 1.11 |
0.68 0.78 1.04 |
1.56 1.42 1.61 |
1.33 1.59 1.62 |
| HP Scanjet 4c (Scanner 2) |
1.89 1.82 2.62 |
1.87 1.93 2.67 |
4.21 3.28 4.41 |
3.82 3.75 3.82 |
From Table 1 it can clearly be seen that the magnitude of image distortion of he five scanners tested differ from one another. The original magnitude of image distortions in the Apple Colour OneScanner is more than twice the scanning resolution while for the HP Scanjet IIc Epson scanners the distotion is approximately the same as the scanning resolution. Compared to the HP Scanjet IIc, Epson and HP Scanjet 4c (Scanner 1) scanners, the magnitude of image distortions in the Apple Colour OneScanner is approximately twice as large. Different scanners of the same model (HP Scanjet 4c) gives different magnitude of image distortions. Although the overall magnitude of image distortion in the HP Scanjet IIc, Epson and HP Scanjet 4c (Scanner 1) scanners is not significant, the maximum resultant error at certain location within the image is still large (approximately twice the scanning resolution).
Suitable Mathematical Model to Eliminate Image Distortion
The earlier test shows the distortions of image scanned in A4 format DTP scanners are quite significant, which poses the question of how distortion of images scanned in these scanners can be minimized. This test was aimed to test the suitability of using different mathematical models to minimize image distortions. The affine and polynomial transformation were used in this test.
Two-dimensional polynomial transformation
| X = a1 |
constant term |
| + a2x +a3y |
1st order terms (affine) |
| + a4xy + a5x2 + a6+y2 |
2nd order terms |
| + a7x2y + a8xy2 + a9x3 + a10y3 |
3rd order terms |
| + a11x3y + a12xy3 + a13x4 + a14x2y2 + a15y4 |
4th order terms |
| Y = b1 |
| +b2x + b3y |
| + b4xy + b5x2 + b6y2 |
| +b7x2y + b8xy2 + b9x3 + b10y3 |
| +b11x3y + b12xy3 + b13x4 + b14x2y2 + b15y4 |
where
X, Y-calibrated grid intersection coordinates a
1, a
2...a
15 -transformation parameters
x, y -image coordinates b
1, b
2...b
15 - transformation parameters
