Data Fusion

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Data Fusion A Review on Decision Fusion
Strategies B. Moshiri, Senior Member,
IEEE, School of ECE, University of Tehran
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Layout
1-Benefits of multisensor devices 2-Typical
sensors used in data fusion 3-Sensor
performance 4-Data fusion models 5-Decision
fusion in parallel sensor suite 6-Comparison of
mathematical tools in data fusion
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Benefits of Multiple sensor devices

• Reduction in measurement time
• A downtime reduction and an increase in
  reliability
• Redundant and complementary information
• A higher signal-to-noise ratio
• A reduction in measured uncertainty
• A more complete picture of the environment

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Survey of typical sensors used in Data fusion
Sensor Output format Applications
Optical sensor Image Mobile robot guidance
Radar Pulse signal Target detection and target tracking
Infrared sensor Image Object identification
Satellite Image Surveillance and pattern recognition
Ultrasonic sensor Pulse signal Mobile robot guidance
NDT sensor Voltage Materials examination
Sonar Pulse echo Obstacle detection
Laser Image Pattern recognition
X-ray Image Medical
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Sensor performance
Sensor performance can be statistically
represented using
POD Probability Of Detection PFC Probability
of False Call ROC Receiver Operating
Characteristic (POD versus PFC)
Major advantage of ROC curves compared to POD
curves In ROC curves false calls are taken into
account But In practice, ROC curves are
difficult to realise.
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Sensor performance
The performance and potential of each used sensor
needs to be established in order to assign
weight of evidence,for example, in sensor data
fusion.
The most common sources of uncertainty -little
or no knowledge about measurement -incomplete
measurement (when data are approximated rather
than waiting for complete data which may be
time consuming and costly) -limitations of the
system
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Sensor performance
Common types of errors
-ambiguous
- practicality (environment) -Human
error -Equipment malfunction -False
negative -False positive
-incomplete
-Incorrect output -Unreliable -No output
-incorrect
-Calibration error -Precision -Accuracy
-measurement
-random
-systematic
-Inductive error -Deductive error
-reasoning
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Data Fusion Models
-Multisensor data integration and fusion
center -Three-level fusion paradigm -Centralized
signal detection system -Distributed
(decentralized) signal detection system
X.E. Gros, NDT Data Fusion, 1997
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Data Fusion Models
Measurements from n sensors are integrated, data
is then processed with evidental reasoning,
probabilistic and belief theories, the results
are classified and selected before a decision on
the optimum fused information is made.
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Data Fusion Models
Three-level fusion paradigm
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Data Fusion Models
Fuse identity declarations using Bayesian theory,
the Dempster-Shafer paradigm or Thomopoulos
generalized evidence processing (GEP). The output
from each sensor is a decision which forms the
inputs to a fusion center where association is
performed.
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Data Fusion Models
More suitable for fusion of raw data but the
association phase can be difficult .
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Data Fusion Models
Four major sensor network types
-Serial -Parallel -Parallel-Serial -Serial-Paralle
l
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Decision Fusion in a Parallel Sensor suite
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Decision fusion in parallel sensor suite
A recursive processing structure for enhanced
performance with a parallel sensor suite.
B.V. Dasarathy, 1991, IEEE
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Decision fusion in parallel sensor suite
ck , wk , uk incremental probabilities of the
joint correct, incorrect decisions and
nondecisions respectively
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Decision fusion in parallel sensor suite
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Decision fusion in parallel sensor suite
Detection (Binary) Decision Analysis
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Decision fusion in parallel sensor suite
Second sensor Decision First sensor Decision First sensor Decision First sensor Decision
Second sensor Decision Target Nontarget Undecided
Target Target Undecided Undecided
Nontarget Undecided Nontarget Undecided
Undecided Undecided Undecided Undecided
A simple decision fusion rules matrix
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Decision fusion in parallel sensor suite
Two sensor suite ( t 2)
Decision Fusion processor
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Decision fusion in parallel sensor suite
Perfect Sensor Case ?i 1 ( i 1,2 )
? the efficiency of the imperfect sensor
The fused decision approaches the correct
decision asymptotically even though one of the
sensors may remain imperfect and the user does
not know which one it is.
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Decision fusion in parallel sensor suite
Bad Sensor Case ?i 0 ( i 1,2 )
Fusion leads to complete failure of the
system. Therefore no totally faulty sensor can
be allowed to operate indefinitely in a
two-sensor fusion system of this type.
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Decision fusion in parallel sensor suite
Equally Imperfect Sensor Case ?i ? ( i 1,2 )
Minimum number of recursions needed for the fused
decision to be better than the decision derived
by the individual sensor
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Decision fusion in parallel sensor suite
u1max0.5
Initial (c1,w1) and final (Ck max , Wk max
) fused decision rates vs. sensor efficiency
Fused correct (c1), incorrect (w1) and
non-decision (u1) rates vs. sensor efficiency (?)
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Decision fusion in parallel sensor suite
?0.1 ?0.2 ?0.3 ?0.4 ?0.5 ?0.6 ?0.7 ?0.8 ?
0.9
Ck
Ck
k
?
Fused correct decision rate (Ck ) vs. sensor
efficiency ( ?) at different numbers of
recursions (k)
Fused correct decision rate (Ck ) vs. recursion
number (k) at different sensor efficiencies (?)
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Decision fusion in parallel sensor suite
General Case
?1 and ?2 are related by a
Asymptotic fused correct decision rate( Ckmax )
vs. sensor efficiency ( ? ) at different sensor
performance ratios (a )
Ck max
?
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Decision fusion in parallel sensor suite
Suite of t sensors
?0.1 ?0.2 ?0.3 ?0.4 ?0.5 ?0.6 ?0.7 ?0.8 ?
0.9
Asymptotic fused decision efficiency ( Ck max
) vs. number of sensors ( t) for different
sensor efficiencies (? )
Ck max
t
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Decision fusion in parallel sensor suite
Equally Imperfect Sensor Case ?i ? ( i
1,2,,t )
Minimum number of recursions needed for the fused
decision to be better than the decision derived
by the individual sensor
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Decision fusion in parallel sensor suite
Multihypothesis Decision Analysis
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Decision fusion in parallel sensor suite
Suite of t sensors
m the number of hypothesis
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Decision fusion in parallel sensor suite
The minimum number of sensors for the correct
fused decision rate to exceed the incorrect
fused decision rate
The asymptotic values of the fused decision rates
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Decision fusion in parallel sensor suite
Binary Decision making
w1 majority
c1majority
c1, w1
w1 consensus
c1 consensus
?
Initial fused decision rates vs. sensor
efficiency with three sensors (comparison of the
consensus and majority based fusion methods)
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Decision fusion in parallel sensor suite
Multihypothesis Decision making (m3)
w1 majority
c1 majority
c1, w1
w1 consensus
c1 consensus
?
Initial fused decision rates vs. sensor
efficiency with three sensors (comparison of the
consensus and majority based fusion methods)
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Decision fusion in parallel sensor suite
Comparison of Mathematical Tools in Data Fusion
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Fusion Methodology
The most common data fusion and integration
methods
Fusion method Applications
Pixel level fusion Image processing, image segmentation
Bayesian theory Decision making between multiple hypotheses
Demspter-Shafer theory of evidence Decision making, Beliefs intervals
Neural Network Signal interpretation
Neyman-Pearson criteria Decision making
Fuzzy Logic Handle vagueness
Knowledge based system Pattern recognition
Markov random field Image processing
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Fusion Methodology
Classical Inference
The most common inference approaches based on an
observed sample of data for acceptance or
rejection of a hypothesis

• -Maximum a posteriori
• Likelihood ratio criterion
• Neyman-Pearson test
• Bayes criteria

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Fusion Methodology
Classical Inference
Maximum a posteriori
Compares two probabilities assigned to two
hypothesis and favors either one or the other
depending only on their chance of occurrence.
y is an observation from a sensor and Hi a
hypothesis i
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Fusion Methodology
Classical Inference
Likelihood ratio criterion
A test to decide between hypothesis H0 or its
alternative Hi . If ?(u)gtt , H0 is true
otherwise, H1 is true..
Likelihood ratio (level of sufficiency)
H0 and H1 are hypothesis 0 and 1, n the number of
sensors, ui random observed sample data and t,
the threshold (significance level) determined
from experiment.
?(u) the degree to which the observation of
evidence u influences the Prior probability of H
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Fusion Methodology
Classical Inference
Neyman-Pearson hypothesis test
A general theory used to make a decision between
two hypothesis. Hypothesis H0 is rejected if the
following equation is verified
The threshold t is chosen depending on the risk
the user is prepared to take to accept or reject
H. the smaller the value of t, the lower the
risk.
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Fusion Methodology
Classical Inference
Bayes criteria
A cost function based on false alarm and
probability of detection is used to select
between two hypotheses H0 and H1. P0 and P1 are
a priori probabilities which govern the decision
output.

• The cost function C for each decision outcome
• C00 the cost function assigned to the decision
  0 when the true outcome is 0
• P(H0H0) the probability associated with this
  decision
• - C01 the cost function assigned to the
  decision 0 when the true outcome is 1
• P(H0H1) the probability associated with this
  decision
• - C10 the cost function assigned to the
  decision 1 when the true outcome is 0
• P(H1H0) the probability associated with this
  decision
• - C11 the cost function assigned to the
  decision 1 when the true outcome is 1
• P(H1H1) the probability associated with this
  decision

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Fusion Methodology
Classical Inference
Bayes criteria
The expected values of the cost as the risk R is
defined as
The decision intervals are defined as
Where the right hand side is the threshold of the
test and should be such that the cost is as
small as possible.
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Fusion Methodology
Bayesian Inference
Used to estimate the degree of certainty of
multiple sensors providing information about a
measurand.
Uses a priori probability of a hypothesis to
produce an a posteriori Probability of this
hypothesis.
Suppose there are n mutually exclusive and
exhaustive hypotheses H0Hn that an event E will
occur. The conditional probability p(EHi) states
the probability of an event E that Hi is true
and is given by
p(Hi) a priori probability of the hypothesis
Hi p(HiE) a posteriori probability of having E
given that Hi is true
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Fusion Methodology
Bayesian Inference
If multiple sensors are used
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Fusion Methodology
Bayesian Fusion

• Target location and tracking
• Search for formation of targets in a region

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Fusion Methodology
Example Two sensor data fusion x to be
identified (e.g. aircraft)
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Fusion Methodology
Bayesian Inference
Some limitations
-no representation of ignorance is
possible -prior probability may be difficult to
define -result depends on choice of prior
probability -it assumes coherent sources of
information -adequate for human assessment (more
difficult for machine-driven decision
making) -complex with large number of
hypotheses -poor performance with non-informative
prior probability (relies on experimental data
only)
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Fusion Methodology
Dempster-Shafer Evidental reasoning
Often described as an extension of the
probability theory or a Generalization of the
Bayesian inference method.
Frame of discernment TX0, X1 , Xn Mass
probability (basic probability assignment (bpa))
m(X)
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Fusion Methodology
Dempster-Shafer Evidental reasoning
Bel(X) the degree of support
Properties of the belief function
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Fusion Methodology
Dempster-Shafer Evidential reasoning
Dempster rule of combination
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Fusion Methodology
Dempster-Shafer Evidental reasoning
Geometrical representation of Dempster rule of
combination

1
m2(Xn)
m1,2 (Xi,Xj)
m2(Xj)
m2(X1)
0
1
0
m1(Xn)
m1(Xi)
m1(X1)
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Fusion Methodology
Dempster-Shafer Evidental reasoning
Incertitude
0 Belief
Disbelief 1
Plausibility
Bel(X),Pls(X) Decision
0,1 Total ignorance, no belief in support of X
1,1 Proposition X is completely true
0,0 Proposition X is completely false
0.4,1 Partial belief, tends to support X
0,0.7 Partial disbelief, tends to refute X
0.3,0.5 Both support and refute X
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Fusion Methodology
Dempster-Shafer Fusion
Gives a rule for calculating the confidence
measure of each state,based on data from both
new and old evidence. Assigns its masses to all
of the subsets of the entities that comprise a
system
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Fusion Methodology
Dempster-Shafer Evidental reasoning
Some features

• An overestimation of the final assessment can
  occur
• Small changes in input can cause important
  changes
• in output
• High efficiency with bodies of evidence in
• pseudo-agreement
• Lower efficiency with bodies of evidence in
  conflict

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Fusion Methodology
Bayesian Fusion vs. Dempster-Shafer Fusion

• Bayes
• Works with probabilities, numbers that reflect
  how often
• an event will occur
• Less calculations.
• Dempster-Shafer
• Considers a space of elements that each reflect
  not what Nature
• chooses, but rather the state of our knowledge
  after making
• a measurement.
• Calculations tend to be longer.
• Allows more explicitly for an undecided state of
  our knowledge.
• (in military it is sometimes far safer to be
  undecided than to decide
• wrongly)
• Sometimes fails to give an acceptable solution.

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Fusion Methodology
Fuzzy Logic Inference Technique
Is very flexible and there is no universal rule
of formalism which can be associated with it.
Fuzzy logic evaluates qualitatively a signal from
a sensor and fuzzy sets associate a grade
(numerical value) to each element.
Typical associated values for different elements
in fuzzy logic
Element Associated value Associated reliability
Signal high 1.0,0.7 Certain
Signal medium 0.7,0.3 Uncertain
Signal low 0.3,0.0 Incorrect
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Fusion Methodology
Fuzzy Logic Inference Technique
Fuzzy logic methods can be very useful to
represent uncertainty from multiple sensors and
to handle vagueness.
A multilevel system to handle vagueness -sensor
level -data fusion level -reasoning level
Produce information
Integrate information
Generates a decision making use of
artificial intelligent systems
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Fusion Methodology
Fuzzy Logic Inference Technique
Combining information from multiple images to
improve classification accuracy of a scene
where images are processed at the pixel level
using segmentation algorithm .
Can be performed for image processing and
image smoothing image segmentation to
combine information perceived by visual
sensors.
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Fusion Methodology
Artificial Intelligence
AI techniques developed for data association make
use of expert systems and neural networks
Artificial Neural networks (NNs) are software
simulated processing units or nodes, which are
trained in order to solve problems.
NNs can be very useful to solve problems in
applications where it is difficult to specify an
algorithm. They are composed of interconnected
nodes that act as independent processing units
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Fusion Methodology
Artificial Intelligence
Weights wi
Input xi
node
Output signal
A two-layer neural network, Perceptron
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Fusion Methodology
Artificial Intelligence

• Some NN applications in data fusion
• For sensor data fusion for detection and correct
• classification of space object maneuvers
  observed by radar
• of different frequencies and resolution.
• -Used in decision systems for target tracking,
  object detection, recognition
• and classification in defence applications
• -In image processing operations such as filtering
  and segmentation
• -To select matching pixel based fusion from
  sensors for robotics application.
• To perform pixel-to-pixel image association for
  object identification
• Applied to non-destructive examination for eddy
  current signal
• classification and automatic tube
  inspection,defect characterisation,
• classification of weld defects and signal
  interpretation.

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A Review on Decision Fusion Strategies

• Acknowledgements
• This powerpoint presentation was prepared by Miss
  Mahdavi and Miss Bahari former M.Sc. Students at
  School of ECE , University of Tehran in Dec. 2005
  where here is highly appreciated.