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a square-based
equilateral-triangle sided pyramid, with the object to be
measured in the top and the cameras at the other vertices. This
arrangement ensures low and evenly distributed errors. We
decided to use a slightly modified version of this arrangement.
(Figure 1. Mason, 1995)
Figure 1. Multi station convergent network (Mason, 1995)
2.2 Visibility constraint
One of the most important constraint of the network design is
the visibility constrain. The problem in an image-based
framework, in which we use a limited number of images of an
object taken from unknown viewpoints to determine which
subsets of features can be simultaneously visible in other views.
This constraint highly affects the positions and the directions of
the cameras.
The nature of the face measurement inflicts that occlusions
caused by external objects are not need to be dealt with,
however some parts of the face mask another parts itself. The
most significant obstructions are caused by the chin and the
nose. The four cameras will ensure that all parts of the face will
appear in at least two images, but in order to increase the
accuracy a setting should choose where the greater proportion
of the points are displayed in three (or possibly four) images. A
visibility modelling was performed to determine the ideal
spatial arrangement of the cameras.
Visibility modelling
The visibility modelling requires a 3D model or models of
faces. Obviously, the parameters of the 3D model affect the
result of the modelling. Ideally every face should be captured in
a photogrammetric network optimized for that particular person,
but it is not feasible, one arrangement should be chosen which
works for the most faces acceptably.
V. Blanz and T. Vetter (Blanz, 1999) designed a morphable
face model based on the statistics of 3D laser scans of 200
people.This model can be changed not only by mathematical
parameters (size, angle, etc) but by more "humane" parameters,
like age, sex or mood. The Singular Inversions FaceGen
Modeller software uses this morphable irregular polygon model,
and we generated an “average” face with this software for the
visibility modelling. (Figure 2.) The generated model was
adjusted further for our purpose by a 3D modelling software
(Blender), in consideration of a former study of the optimal
point density and arrangement described in (Varga, 2008).
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
Figure 2. Morphable face model
This modelling software was used to simulate the camera
parameters (viewing angle, focal length, subject distance etc.)
The face model consist of approx. 6000 vertices, the aim of the
modelling was to calculate the visible subset of these points
from different angles. The method was simple: the face model
was rotated in front of the camera and the rendered camera
images were inspected. (Figure 3.)
Figure 3. Visibility modelling in Blender
The centre of the rotation was the intersection of the Coronal,
Traverse and Sagittal planes. The rotation angles were 100? in
20 steps in both horizontally and vertically. The modelling
process resulted a visibility isoline map, showing the number of
visible vertices from a particular camera position. (Figure 4.)
The contour lines show the number of visible vertices, the axes
show the camera direction from the frontal position in degrees.
30
Figure 4. Visibility map.
