Photogrammetry for Large Structures

M. Kesteven

CASS, CSIRO

From Antikythera to the SKA

Kerastari Workshop, June 12-15 2012

Photogrammetry

From several photographs of a targeted 3-D object

To a table of the (x,y,z)coordinates of every target

The procedure

- Place retro-reflecting targets on the object- Photograph the object from different positions- Scan each photograph for the targets- Process the target data to recover:

- the camera locations - the target locations

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Photogrammetry essentials - 1

A camera is a multi-target theodolite: each pixel in the image corresponds to a ray oriented relative to the camera body.

Basic surveying would suggest that from pictures from 2 different (known) locations we could reconstruct the shape of a target object, if we knew accurately the camera locations and orientations.

Photogrammetry Essentials - 2

However, we can determine the camera locations from the data itself if we have > 3 photos.

With Nt targets; Np photos,

We can solve for the camera locations provided :

2 * Nt* Np > (3 * Nt + 6 * Np )

(# datums) (# unknowns)

The problem is easily over-determined; we can solve for the targets, the camera locations, and obtain an error estimate for each target.

Processing details

A special reference object is placed near the centre of the field. Its size and shape is known, so we can determine the camera location for each image from this alone, to an accuracy of about 1 cm.

This is enough to ensure that we can then iterate to a precision solution.

The critical issue is a matter of registration - the ability to identify each target in the various images.

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3D reconstruction from the images

ACCURACY ISSUES

There is an automatic estimate of the accuracy that comesfrom the metric used in the iterative algorithm : for eachtarget we have the rms perpendicular distance to therays in its bundle. We typically find ~ 0.03 mm for each axis. (for the 12m askap antennas).

The camera calibration is one contributor to this error.This is the mapping from pixel to an angle relative to the camera body. This calibration is refined as part of the iterative solution.

Accuracy issues (2)

The distribution of rays at the target can be an issue – ideally the rays should be isotropic about each target. Some care is needed in taking the photos.

Our experience is that the system is remarkably simple and robust.

Notes

The process gives us the location of each target. Whether or not the target is a representative of its immediate surroundings is a different matter. In effect, we require the scale size of panel defects to be larger than the target spacing.

Can the technique be extended to areas with no targets?

We could examine the un-targetted areas provided we could solve the registration problem – a correlation scheme, for example, might enable us to relate the point at (x,y) in photo A to the same point, at (x1,y1), in photo B.

A featureless, gently curved surface would not be suitable.

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