International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
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Figure 7: Up is VPS as target visibility model in which bright
area of each sphere is the visible directions. Down is model of
fuzzy accessible area for camera positions
In the second main stage it builds, adjusts and examines a fuzzy
inference system including 14 fuzzy rules with equal weights, 8
inputs and 5 outputs implemented by using the fuzzy toolbox of
MATLAB. The normalized membership functions of input and
output parameters of FIS are provided using the trial and error
method in order to placc camera optimally and efficiently. To
do this, the effect of each input parameter on all output
parameters is studied through their rules and membership
functions. The fuzzy operator setting in the FIS is as following:
'min' for fuzzy AND, 'max' for fuzzy OR, 'min' for implication,
'sum' for aggregation, and 'centroid' for defuzzification.
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Figure 8: four states of camera placement optimization by
proposed FIS
4.2 System Experiment
The FIS is utilized to optimally design a camera station around
a weak point. To optimize our design, it is necessary to define a
fitness function in the design process (Figure 7) in order 10
compare states and select the best one with highest fitness
function valuc. To define an optimization criterion, a fitness
function F (0<F<1) is computed as relation 1 in which d, p, v, a,
m, and u are constraints of distribution and number of image
points, visibility, accessibility, their average, and accuracy
enhancement factor respectively. All these parameters are
normalized to the range between zero and one.
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w is the weight parameter which balances the attention to
constraint satisfaction versus accuracy enhancement and equal
with the number of unsatisfied constraints plus one. At first that
usually any constraint is satisfied, w = 5 so the attention to
satisfy all constraints is five times more than accuracy
enhancement. When FIS satisfies constraints one by one, the
attention is gradually decreased till FIS satisfies all constraints
e.g. w = 1. It means accuracy enhancement and constraint
satisfaction has same importance for FIS and if accuracy has
been enhanced significantly, it is enough to stop the loop and
consider the last state as the optimal final answer. To find
weather a constraint has been satisfied, it should be defined a
satisfaction threshold for each one. Satisfaction threshold is the
difficulty or importance level of satisfying constraint. In our
tests, we sct thresholds 0.6, 0.6, 0.7, and 0.6 for d, p, v, and a
correspondingly.
To study the optimization process, Figure 8 illustrates the four
states of camera placement. Left column shows the progress of
satisfying the number and distribution of image points into
camera format border. The visibility constraint that is satisfied
through above iterations is illustrated in middle column. Right
column displays the position and situation of designed camera
station which moves toward existing camera stations to satisfy
accessibility constraint.
5. CONCLUSIONS
Based on the assumption that no simulated 3D model of object
and workspace is available a fuzzy based camera placement
concept is proposed using vision constraints. Incidence angle,
visibility and accessibility constraints are introduced in a fuzzy
inference system due to their high level of uncertainty. The
developed fuzzy inference system (FIS) automatically designs a
multi image convergent photogrammetric network based on the
fuzzy model of vision constraints. The fuzzy rules of our FIS
control three parameters of distance, direction and rotation. This
method optimizes the camera station in cases of a high conflict
among vision constraints and accuracy. Experimental
investigations are carried out to examine our FIS with a real
world example. Steps of camera placement by our FIS are
discussed in the paper and illustrate the FIS process and results.
The results demonstrate the efficiency and capability of our
fuzzy inference system in camera placement.
Internationc
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