Maa-57.260 Fotogrammetrian erikoissovellutukset

Luento-ohjelma 1 2 3 4 5 6 7 8 9 10 11 12 13

(Henrik Haggrén, 19.1.2001)

Luento 11: Järjestelmien kalibrointi




In case of film cameras, the fiducials can be reproduced by image corners. A proper way to observe image corners is to locate them by measuring image edges and fitting lines to those. Interior orientation is performed individually for each digitizing or session of comparator measurement. Image adopted from (Cruz, 2000).

First approximation for principal point x0, y0 in case of digital cameras would be the center of image coordinates. The image coordinate axes follow columns and lines of pixels. Note that the coordinate system of a digital image usually is a left-hand system.

Calibration function. (Fryer, 2000)

Calibration plate. A simple calibration plate consists of straight lines on the edges, a scale bar with at least one known reference distance, and 30 to 70 targets. These targets do not have to be known by their coordinates. Assuming that an image is taken by aiming the camera perpendicularly to the plate center, camera constant can be determined by scaling. For this purpose we will measure the distance between the camera and the calibration plate, and the length of the reference distance on the image. The straight lines on the edges will be then used for defining the radial and decentering optical distortions. (Fryer, 2000)

After a good approximation for radial and decentering distortions, the values for the rest of the calibration unknowns will be estimated based on collinearity equations. For this purpose we take four pairs of convergent images from the plate. Within each pair the camera should be rotated 90°. The parameters of decentering distortion will be kept fixed during the bundle adjustment. The procedure is iterative and should be repeated until the principal point is determided with sufficient accuracy. (Fryer, 2000)

1. Plumbline image  assuming x0, y0 in the image center
- get good approximations for K1, P1, P2
2. Calculate approximative c
3. Bundle adjustment images  holding P1, P2 fixed
- get good estimations for K1 and  c
- get x0, y0, mx, my,
- get improved K1, K2, K3
4. Repeat step 1 with x0, y0
- get excellent K1, P1, P2
5. Repeat bundle adjustment holding P1, P2 fixed
- get excellent estimations for dx0, dy0, mx, myxy, c, K1, K2, K3

Calibration procedure according to Fryer (2000). A typical number of targeted calibration points would be 50.




Typical radial lens distortion curves for 25, 16, 8,5 and 6,5 mm C-mount lenses fitted to a Pulnix TM6CN camera. (Figure 2.7 from: Atkinson, 1996)

Gaussian radial distrotion at various image scales for a 25 mm Fujinon lens fitted to a Pulnix CCD camera. (Figure 6.3 from: Atkinson, 1996)

Balanced radial distortion graphs at various image scales for a 25 mm Fujinon lens fitted to a Pulnix CCD camera. (Figure 6.4 from: Atkinson, 1996)

Variation in Gaussian radial distortion for a range of nominal proncipal distances for a 35 - 70 mm Canon FD zoom lens fitted to a Canon AE-1 Program camera. (Figure 6.11 from: Atkinson, 1996)

Decentering distortion for Fujinon 25 mm lens fitted to a Pulnix CCD camera. (Figure 6.6 from: Atkinson, 1996)

Linssin syvyysterävyysalue. Kuvassa pA on fokusointietäisyys, pN  ja pF tätä vastaavat terävänä kuvautumisen etu- ja takarajat. Kuvan terävyyttä arvioidaan suureella c, joka on kuvalle kuvautuvan pisteen halkaisija. D on kameran aukkoluku ja f linssin polttoväli. pH on hyperfokaalietäisyys, jolle etäisyydelle fokusoitaessa kuva on terävä välillä  pNDepth_of_field.xls

Calibration and relative orientation artifact. (Clarke, 2000)

Calibration bench at Cern, 2 m x 3 m. Tämä kalibrointikehikko on koottu mittaussuunnittelun ja -simuloinnin varmistamiseksi. Kehikko koostuu 60 koodatusta tähyksestä ja 7 mittakaavajanasta (vertausetäisyydestä). (Nummiaro, 1999)

Kuvamittausaseman kalibrointi

Scale bar used for calibration reference.

 External check for 3-D measuring accuracy.

Image observations for calibration.

Retro targets used as external stability control.

Stereokameran kalibrointi

Videoprofilometrin kalibrointi

Projektiiviset muunnokset

DLT Direct Linear Transformation


Literature and software

Maa-57.260 Fotogrammetrian erikoissovellutukset
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