International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
have to be carried out to make sure that all points can be
measured with satisfying quality. Each iteration includes an
update of the visibility model of object points followed by
camera placement using the fuzzy inference system based on
the updated visibility model.
2. MODELING VISION CONSTRAINTS
Sensor placement in computer vision (Cowan and Kovesi,
1988) has to deal with satisfying some vision constraints as well
as with optimization of accuracy and cost criteria (Fraser,
1984). To prepare for fuzzy modelling of vision constraints in
our approach, vision constraints are divided into three classes
(Figure 2).
User accessibility N ae
Iser accessibility constraint
constraint
Resolution
Field-of-view — constraint
constraint
Workspace | x
constraint Y m
Visibility
trees X 2 goal
u ^
7
Nuniber and m
distribution of,”
Depth-of-field image points
constraint M
ba
Incidence ">.
angle "———T—
constraint
Targeted object
Figure 2. Vision constraints for camera placement (motivated
by the work of Mason (1995))
Range Related Constraints are a class of constraints which limit
the distance between object points and camera stations
including image resolution, image scale, field of view, and
workspace upper limits, depth of field and number and
distribution of image points for the lower limit.
Visibility Related Constraints: The visibility of an object point
from a camera station is a complex interrclated matter that
depends on radiometric and geometric constraints. Radiometric
constraints with constant “point to image quality” are easily
satisfied in presence of retro-reflective targets and special
flashing equipment. Geometric constraints include an incidence
angle constraint, workspace obstructions, camera field of view,
and position and situation of the camera station (Figure 3).
Accessibility Related Constraints depend on camera position
accessibility, the workspace constraint, and object and
obstructions inside. In addition to positional accessibility of
camera, time accessibility is might have to be taken into
account.
Camera
z \ 3 FOV
Target“
cone 71 / — Visible ray
Le Invisible rays
Figure 3. Visibility is a function of the target cone, camera
FOV, and hidden areas
As already mentioned, a given or simulated model of the object
and workspace is not assumed. Based on a high number of
images of object and workspace in the primary network taken
from different directions, target visibility is predictable by
studying the corresponding image point observations and
camera accessibility is predictable taking closeness to existing
camera stations into account.
2.1 Visibility Prediction Modelling (VPM)
VPM concept is based on two principals: 1) Visibility of each
direction toward a point is constant and does not depend on
distance. 2) Visibility of a direction is the same as the visibility
of its immediate vicinity directions for a point. The first
principal causes to simplify the modelling by defining a
visibility prediction sphere (VPS) and second principal is a
basic for predicting hidden area in unknown directions by using
known directions.
As illustrated in Figure 3, modelling of target visibility can be
done by sequentially. This implies considering the effects of the
camera field of view, target incidence angle, and hidden area
constraints on the visibility of all rays between the target and
related camera stations. In our modelling a fuzzy visibility
index v between 0 (perfectly invisible) and 1 (perfectly visible)
is assigned to each ray. A corresponding visualisation is shown
in Figure 4.
Figure 4. Three examples of visibility prediction on VPS.
The black and white stars are visible and invisible rays
correspondingly which predict visible (bright) and
invisible (dark) areas.
2.2 Accessibility Prediction Modelling (APM)
Briefly, APM concept is based on closeness to the positions of
existing camera stations. In other words, a point closer to these
positions probably has a higher accessibility. A proper way to
model this concept is using analytical function like as
Butterworth function which is a low pass frequency filter in
signal processing (Gonzalez, 1993). In Equation 1, D, is the
accessible vicinity radius around existing camera stations. 7 is
the fuzzy behaviour factor that controls the width of fuzzy
boundary between accessible and unknown transit areas.
Usually 5 is less than 4 especially when camera stations are far
from each other. D, is specified depending on object and
workspace conditions and is usually about half of the average
density of camera positions.
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w=
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As a general rule, in the open workspaces with low obstructions
a high value for D, and a low value for n are proper. Notably, a
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