International Archives of the Photogrammetry, Remote Sensing
Similar to laser range scanners, the uncertainty is not a pure
scalar function of distance to the target. A more complete
camera model and exhaustive error representation can show that
the error distribution is also skewed and oriented with the line
of sight like laser scanners (see Figure 2). Nevertheless, to get
lower uncertainty one needs geometric configurations (large
baseline, shorter distance camera-target), a long focal length
(not always possible), a low disparity measurement uncertainty
and multiple images (in a multi-station convergent geometry).
Camera model is covered by Atkinson, 1996. This reference
gives the details of the collinearity equations for the three-
dimensional case where both internal (focal length, scaling,
distortions) and external (pose matrix containing both rotation
and translation information of a camera) parameters of a multi-
camera arrangement are considered. The complete system of
equations can be solved by the bundle adjustment method. If
the interior parameters are not available prior to this step
(through an adequate camera calibration), a self-calibrating
bundle adjustment is used. Actual lenses have optical
aberrations. Of these aberrations (spherical, coma, etc.), only
optical distortions are modelled in photogrammetry. Calibration
of the internal parameters of a camera is critical for accurate
measurements. Self-calibration is necessary if camera settings
are unknown and vary between images. But to achieve accurate
self-calibration, certain geometric configurations of images are
needed. Since this is not guaranteed at the project site, and
makes imaging more restrictive, it is sensible to decide on high-
quality camera and take the images at fixed known settings.
Many modern digital cameras can save à number of settings.
We then calibrate in the lab at those settings using surveyed
points. Figure 3 shows an example of an array of targets
arranged on two walls that provide a 3D grid for camera
calibration.
ak
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: 305 y
3 330
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Figure 3 Calibration targets placed on walls.
Fraser, 1987; Forstner, 1994: El-Hakim et al., 2003 discuss the
need for accuracy evaluation tools for 3D image-based
modelling and identify the key factors and critical
configurations affecting this accuracy. Since internal evaluation
using the covariance matrix may give too optimistic results
(particularly for weak geometry, low redundancy, and presence
of systematic errors), El-Hakim et al., 2003 propose a novel
technique that creates simulated data based on the actual project
data. The simulation was very useful in uncovering behaviour
that the covariance matrix alone did not reveal. As a result,
guidelines for some phases of 3D modelling from images are
given. They focus on modelling relatively large structures like
monuments and architectures for accurate documentation where
and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
knowledge of uncertainty is important. Here are the most
significant conclusions:
* [n practice, it is difficult to achieve optimum network design.
Therefore, the goal should be to avoid weak geometric
configurations, low redundancy, and incorrect calibration.
- To avoid low redundancy, points should be tracked over 4 or
more images, at least two of which have baseline to depth ratio
of 0.4 or larger, and over at least 6 images for closely spaced
sequences. This is the most effective way to increase accuracy
even for poor configurations.
* Weak geometric configurations are directly function of the
baseline to depth ratio, and the effect is more pronounced when
this ratio is small (D/Z is less than 0.3).
« Since conditions for accurate self-calibration may not be
achievable in practice, separate camera calibration at the focal
settings used in the actual project is recommended.
« On natural features, the accuracy of the input data improves
significantly as camera resolution increases, while the
improvement is less significant on well-defined large resolved
targets.
* [n practical projects, using natural features and less than
optimum configuration, but high redundancy and correct pre-
calibration, we can expect about 1: 4000 to 1: 10000 accuracy.
This should be reduced if practical conditions reduce the
redundancy or the pointing precision.
It is interesting to note that a 2D camera can address problems
in a wide range of volumes. This is not the case for laser
scanners as demonstrated in Section 2.1!
3. CHARACTERIZATION OF 3D SYSTEMS
3.1 Signal detection chain
Beyond the 3D sensing technique used (see Section 2), the
measurement of shape, appearance and motion parameters of an
object using optical techniques depend on the characteristics of
the different elements found in the measuring chain:
e Sensor detection modes: incoherent versus coherent,
current gain mechanism with Avalanche Photodiodes
(APD) or Micro-channel Plates (MCP)
e Light source spatial considerations: extended, point,
line, grid, random patterns, coded pattern projection,
scanned or not
e Operating wavelength: single/broad spectrum, visible
e Temporal considerations: AM or FM modulated,
pulsed
e Power versus dwell time (data rate) on target object
Furthermore, we should add the following system level aspects:
e Object modification: retro-targets, paint, abrasion
e Object type: topology, material, size
e Level of development: prototype, commercial
e System location: laboratory, shop floor, remote site
e User levels: novice, skilled, expert
Combination of the above listed elements and aspects will
determine the final system characteristics:
e Dimensionality: field-of-view (FOV), depth-of-field
(DOF), standoff, maximum range
e Spatial discrimination: resolution, uncertainty and
accuracy
e Costs to: purchase, use, repair and calibrate
We now cover some of these characteristics in the following
sections.
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