1. A Review on Decision Fusion Strategies
Data Fusion
A Review on Decision Fusion Strategies
B. Moshiri, Senior Member, IEEE,
School of ECE, University of Tehran

2. 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

3. 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

4. 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
Object identification
Satellite
Surveillance and pattern recognition
Ultrasonic sensor
NDT sensor
Voltage
Materials examination
Sonar
Pulse echo
Obstacle detection
Laser
Pattern recognition
X-ray
Medical

6. Major advantage of ROC curves compared to POD curves:
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.

7. The performance and potential of each used sensor
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

8. Common types of errors -ambiguous -incomplete
Sensor performance
Common types of errors
-ambiguous
-incomplete
- practicality (environment)
-Human error
-Equipment malfunction
-False negative
-False positive
-Incorrect output
-Unreliable
-No output
-incorrect
-Calibration error
-Precision
-Accuracy
-measurement
-random
-systematic
-Inductive error
-Deductive error
-reasoning

9. -Multisensor data integration and fusion center
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]

10. Multisensor data integration and fusion
Data Fusion Models
Data Processing
Assignment of Bayes or Dempster-Shafer Rule of Combination
Sensor Data Selection Y1 Y2 Yn Z1 Z2 Zn
Optimum
Estimation
Decision
Level
Fused
Data
Integration Fusion Integration X1 X2 Xn
Raw
Sensor 1
Processed
Multisensor data integration and fusion
center
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.

11. Three-level fusion paradigm
Data Fusion Models
Three-level fusion paradigm
Level of evidence
Level of Dynamics
Signal Level
Database
Sensors
Data
Fusion
Decision
Features
fusion

12. Distributed (decentralized) signal detection system
Data Fusion Models
Distributed (decentralized) signal detection system
Fusion
Center
Global
Decision
Level
Measurement
Sensor 1
Sensor 2
Sensor N
Feature
Extraction
Local Decision
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.

13. Centralized signal detection system
Data Fusion Models
Centralized signal detection system
Fusion
Center
Decision
Level
Measurement
Sensor 1
Sensor 2
Sensor N
More suitable for fusion of raw data but the association phase can be
difficult .

14. Four major sensor network types
Data Fusion Models
Four major sensor network types
Sensor 1
Sensor 2
Sensor n
-Serial
-Parallel
-Parallel-Serial
-Serial-Parallel

15. Decision Fusion
in a
Parallel Sensor suite

16. A recursive processing structure for enhanced performance with a
Decision fusion in parallel sensor suite
Sensor 1
Sensor 2
Sensor j
Sensor t
Local
processor 1
processor 2
processor j
processor t
Data
set Z1
set Z2
set Zj
set Zt
Decision
Fusion
Processor
Output O1 O2 Oj Ot
Consistent
decision across
the suite?
Yes No
A recursive processing structure for enhanced performance with a
parallel sensor suite B.V. Dasarathy, 1991, IEEE

17. Sensor output can be regarded as a decision array
of n decisions.
The efficiency of each sensor, , is the probability
of correctness of the decision Dj from sensor j, a
measure of the effectiveness of a sensor.
Cj and Wj : the belief that the decisions from sensor
j are correct and wrong (based on the Dempster-Shafer
Theory)
Uj: the ignorance (uncertainty) of a measurand

18. decisions and nondecisions respectively
Decision fusion in parallel sensor suite
ck , wk , uk : incremental probabilities of the joint correct, incorrect
decisions and nondecisions respectively

19. Decision fusion in parallel sensor suite

20. Detection (Binary) Decision Analysis
Decision fusion in parallel sensor suite
Detection (Binary) Decision Analysis

21. A simple decision fusion rules matrix
Decision fusion in parallel sensor suite
Second sensor
Decision
First sensor Decision
Target
Nontarget
Undecided
A simple decision fusion rules matrix

22. Two sensor suite ( t = 2) sensor1 sensor2 Local processor 1
Decision fusion in parallel sensor suite
Two sensor suite ( t = 2)
sensor1
sensor2
Local processor 1
Local processor 2
Decision
Fusion
processor

23. Perfect Sensor Case: ηi = 1 ( i = 1,2 )
Decision fusion in parallel sensor suite
Perfect Sensor Case: ηi = 1 ( i = 1,2 )
η : 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.

24. Bad Sensor Case: ηi = 0 ( i = 1,2 )
Decision fusion in parallel sensor suite
Bad Sensor Case: ηi = 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.

25. Equally Imperfect Sensor Case: ηi = η ( i = 1,2 )
Decision fusion in parallel sensor suite
Equally Imperfect Sensor Case: ηi = η ( i = 1,2 )
Minimum number of recursions needed for the fused decision to be
better than the decision derived by the individual sensor:

26. u1|max=0.5 Initial (c1,w1) and final (Ck |max , Wk |max )
Decision fusion in parallel sensor suite
u1|max=0.5
c,w u
c1,
w1,
Ck |max,
Wk |max η
Fused correct (c1), incorrect (w1) and
non-decision (u1) rates vs. sensor
efficiency (η)
Initial (c1,w1) and final (Ck |max , Wk |max )
fused decision rates vs. sensor efficiency

27. Fused correct decision rate (Ck ) vs.
Decision fusion in parallel sensor suite
η=0.1
η=0.2
η=0.3
η=0.4
η=0.5
η=0.6
η=0.7
η=0.8
η=0.9 Ck Ck k η
Fused correct decision rate (Ck ) vs.
sensor efficiency ( η) at different
numbers of recursions (k)
Fused correct decision rate (Ck ) vs.
recursion number (k) at different sensor
efficiencies (η)

28. General Case Decision fusion in parallel sensor suite
η1 and η2 are related by α
Asymptotic fused correct decision
rate( Ck|max ) vs. sensor efficiency
( η ) at different sensor performance
ratios (α )
Ck |max η

29. Suite of t sensors Asymptotic fused decision efficiency ( Ck | max )
Decision fusion in parallel sensor suite
Suite of t sensors
η=0.1
η=0.2
η=0.3
η=0.4
η=0.5
η=0.6
η=0.7
η=0.8
η=0.9
Asymptotic fused decision efficiency ( Ck | max )
vs. number of sensors ( t) for different sensor
efficiencies (η )
Ck |max t

30. Equally Imperfect Sensor Case: ηi = η ( i = 1,2,…,t )
Decision fusion in parallel sensor suite
Equally Imperfect Sensor Case: ηi = η ( i = 1,2,…,t )
Minimum number of recursions needed for the fused decision
to be better than the decision derived by the individual sensor:

31. Multihypothesis Decision Analysis
Decision fusion in parallel sensor suite
Multihypothesis Decision Analysis

32. Suite of t sensors m: the number of hypothesis
Decision fusion in parallel sensor suite
Suite of t sensors
m: the number of hypothesis

33. The minimum number of sensors for the correct
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:

34. Binary Decision making
Decision fusion in parallel sensor suite
Binary Decision making
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
w1 :majority
c1:majority
c1, w1
w1 :consensus
c1 consensus η
Initial fused decision rates vs. sensor efficiency with three sensors
(comparison of the consensus and majority based fusion methods)

35. Multihypothesis Decision making (m=3)
Decision fusion in parallel sensor suite
Multihypothesis Decision making (m=3)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
w1 :majority
c1 majority
c1, w1
w1 :consensus
c1 consensus η
Initial fused decision rates vs. sensor efficiency with three sensors
(comparison of the consensus and majority based fusion methods)

36. Comparison of Mathematical Tools in Data Fusion
Decision fusion in parallel sensor suite
Comparison of
Mathematical
Tools in
Data Fusion

37. The most common data fusion and integration methods
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

38. Likelihood ratio criterion Neyman-Pearson test Bayes criteria
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

39. Compares two probabilities assigned to two hypothesis
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

40. Likelihood ratio criterion
Fusion Methodology
Classical Inference
Likelihood ratio criterion
A test to decide between hypothesis H0 or its alternative Hi .
If Λ(u)>t , 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.
Λ(u) : the degree to which the observation of evidence u influences the
Prior probability of H

41. Neyman-Pearson hypothesis test
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.

42. A cost function based on false alarm and probability of detection is
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(H0|H0) :the probability associated with this decision
- C01 : the cost function assigned to the decision 0 when the true outcome is 1
P(H0|H1) :the probability associated with this decision
- C10 : the cost function assigned to the decision 1 when the true outcome is 0
P(H1|H0) :the probability associated with this decision
- C11 : the cost function assigned to the decision 1 when the true outcome is 1
P(H1|H1) :the probability associated with this decision

43. The expected values of the cost as the risk R is defined as :
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.

44. Uses a priori probability of a hypothesis to produce an a posteriori
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 H0…Hn
that an event E will occur.
The conditional probability p(E|Hi) 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(Hi|E): a posteriori probability of having E given that Hi is true

45. If multiple sensors are used…
Fusion Methodology
Bayesian Inference
If multiple sensors are used…

46. Bayesian Fusion Target location and tracking
Fusion Methodology
Bayesian Fusion
Target location and tracking
Search for formation of targets in a region …

47. Example: Two sensor data fusion x: to be identified (e.g. aircraft)
Fusion Methodology
Example: Two sensor data fusion
x: to be identified (e.g. aircraft)
Latest data set
Old data set
Current measurement

48. Some limitations: Bayesian Inference
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)

49. Frame of discernment Θ={X0, X1 , …Xn}
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 Θ={X0, X1 , …Xn}
Mass probability (basic probability assignment (bpa)) : m(X)

50. Properties of the belief function:
Fusion Methodology
Dempster-Shafer Evidental reasoning
Bel(X) : the degree of support
Properties of the belief function:

51. Dempster rule of combination:
Fusion Methodology
Dempster-Shafer Evidential reasoning
Dempster rule of combination:

52. Geometrical representation of Dempster rule of combination
Fusion Methodology
Dempster-Shafer Evidental reasoning
Geometrical representation of Dempster rule of combination … 1
m2(Xn)
m2(Xj)
m1,2 (Xi,Xj)
m2(X1) 1
m1(X1)
m1(Xi)
m1(Xn)

53. Dempster-Shafer Evidental reasoning
Fusion Methodology
Dempster-Shafer Evidental reasoning
Incertitude
Belief
Disbelief
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

54. Dempster-Shafer Fusion
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
Mobile robot map building (e.g. occupancy grid)
{occupied, empty, unknown} :{O,E,U}
m:confidence in each element
ms:confidence from sensors
mo:confidence from old existing evidence

55. Some features: An overestimation of the final assessment can occur
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

56. Bayesian Fusion vs. Dempster-Shafer Fusion
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.

57. Typical associated values for different elements in fuzzy logic
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

58. Fuzzy logic methods can be very useful to represent uncertainty from
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

59. Combining information from multiple images to improve
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.
Fusion center

60. Artificial Intelligence
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

61. A two-layer neural network, Perceptron
Fusion Methodology
Artificial Intelligence
Weights wi
Input xi
node
Output signal
A two-layer neural network, Perceptron

62. Artificial Intelligence
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.

63. 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 where here is highly appreciated.