Guehring, Jens 
  
3.3.5 Improvement of Accuracy, Reliability and Flexibility by use of multiple Cameras 
Accuracy and reliability can be significantly improved if image data from multiple cameras is available, all sharing the 
same projector. 
Because line shift processing directly links projector lines to camera coordinates, corresponding pairs of image points 
between different cameras, as well as pairings of image points between the cameras and the projector can easily be 
found. Each pair contributes four observations to solve for the three unknown object point coordinates. It is obvious, 
that a large number of observations, corresponding to a high redundancy, yields more accurate results. 
The data, obtained by multiple cameras, can also be used to enforce explicit consistency tests. Specular reflections, as 
they are likely to occur on the surface of machined metal parts, cause spurious 3-D point measurements. The 
consistency tests are based on the observation, that specular reflections are viewpoint dependent. If the cameras view 
the object from different angles we can compute the deviation between object points, computed from different pairings 
of image points. This allows us to either discard one single observation or completely discard all the observations for 
the corresponding surface point. 
If multiple cameras are available, we can also omit the projector’s contribution to the observations and use it just as an 
aid to establish point correspondences between multiple cameras. This variant makes it possible to use projection 
devices, that have not been specifically designed for measurement purposes, the same way as our projector is used in an 
uncalibrated setup. A particularly attractive solution combines a standard video beamer with a stereo camera pair to 
collect surface information of large-scale objects for virtual reality applications. 
It has to be noted that in a setup where only the cameras deliver image point observations, errors due to reflectance 
discontinuities on the object surface are inherently accounted for. 
3.4 Computation of Object Point Coordinates 
3-D point determination is carried out using a forward intersection based on the extrinsic and intrinsic parameters 
obtained from the bundle. Forward intersection uses a minimum of four observed image coordinates to estimate three 
world coordinates. Using more than one camera and a calibrated projector, redundancy and hereby accuracy and 
reliability can be significantly improved. The same holds true for a combination of more than two cameras and an 
uncalibrated projector 
In every case, object point coordinates are obtained by inverting a 3x3 matrix which afterwards contains the 
covariance information. 
4 SYSTEM CALIBRATION 
4.1 Direct Calibration vs. Model Based Calibration 
There are two basic approaches for the calibration of an optical 3-D system. 
Direct calibration uses an arbitrary calibration function (usually a polynomial) to describe the mapping from 
observations to three-dimensional coordinates. The parameters of this function are obtained by measuring a large 
number of well-known points throughout the measuring volume. An immediate advantage is, that no care has to be 
taken to model any phenomena, since every source of error is implicitly handled by the computed coefficients. 
However, direct calibration requires a highly accurate calibration normal. Especially for sensors with a large 
measurement volume, this requirement complicates the calibration procedure or makes it even impossible. Since the 
calibration function acts as a black box, there is no information about the quality of measurements. 
In model based calibration, parameters of a geometric model of the sensor, so called intrinsic and extrinsic parameters, 
are determined. The model describes how points in 3-D space are projected onto the image plane, considering imperfect 
cameras and lenses. There exist techniques in photogrammetry to simultaneously estimate these parameters during 
measurement tasks, however, most commonly a specially designed test object is used to effectively compute the desired 
quantities from a few calibration measurements. Since any short-term geometrically stable object can be used for 
calibration, there is no need for an accurate calibration normal. Nonetheless, if absolute measurements are required, at 
least one accurate distance (e.g. from a scale bar) is needed to fix the scale. 
On the down side, highly accurate measurements require complicated sensor models and some effects in the image 
formation process might remain uncorrected. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 335