Fusion by Biometrics
主講人：李佳明、陳明暘
指導教授：林維暘
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Outline
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Introduction
Score normalization methods
Fusion methods
Experiment Results
Conclusion
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Reference Paper
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A. K. Jain, K. Nandakumar, and A. Ross, “Score
normalization in multimodal biometric
systems," Pattern Recognition , 2005.
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Why score normalization ?
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1. The matching scores at the output of the
individual matchers may not be homogeneous.
2. The outputs of the individual matchers need
not be on the same numerical scale (range).
3. The matching scores at the output of the
matchers may follow different statistical
distributions.
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Why score normalization ?
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Score normalization refers to changing the location and scale
parameters of the matching score distributions at the output
of the individual matchers, so that the matching scores of
different matchers are transformed into a common domain.
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Score normalization
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When the parameters used for normalization
are determined using a fixed training set, it is
referred to as fixed score normalization.
In adaptive score normalization, the
normalization parameters are estimated based
on the current feature vector.
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A good normalization scheme
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Robustness refers to insensitivity to the
presence of outliers.
Efficiency refers to the proximity of the
obtained estimate to the optimal estimate
when the distribution of the data is known.
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Normalization Techniques
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1.
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5.
6.
Min-max
Decimal scaling
z-score
Median and MAD
Double sigmoid function
tanh-estimators
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1. Min-max normalization
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Min-max normalization is best suited for the case where
the bounds (maximum and minimum values) of the
scores produced by a matcher are known.
We usually shift the minimum and maximum scores to 0
and 1.
xk : the kth matching score before normalization
xk’ : the kth matching score after normalization
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1. Min-max normalization
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This method is not robust (i.e., the method is highly sensitive
to outliers in the data used for estimation).
Min-max normalization retains the original distribution of
scores except for a scaling factor and transforms all the
scores into a common range [0, 1].
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2. Decimal scaling
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For example, if one matcher has scores in the
range [0, 1] and the other has scores in the range
[0, 1000], the following normalization could be
applied.
The problems with this approach are lack of
robustness.
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3. z-score
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The most commonly used score normalization technique is
the z-score that is calculated using the arithmetic mean and
standard deviation of the given data.
Both mean and standard deviation are sensitive to outliers
and, hence, this method is not robust.
Z-score normalization does not guarantee a common
numerical range for the normalized scores of the different
matchers.
If the input scores are not Gaussian distributed, z-score
normalization does not retain the input distribution at the
output.
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3. z-score
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4. Median and MAD
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Robust : The median and median absolute
deviation (MAD) are insensitive to outliers and the
points in the extreme tails of the distribution.
This normalization technique does not retain the
input distribution and does not transform the
scores into a common numerical range.
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4. Median and MAD
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5. Double sigmoid function
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The normalized score is given by
where m is the reference operating point and
s1 and s2 denote the left and right edges of the
region
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5. Double sigmoid function
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where the scores in the [0, 300] range are mapped to the [0, 1] range
using m = 200, s1 = 20 and s2 = 30.
Generally, m is chosen to be some value falling in the region of overlap
between the genuine and impostor score distribution, and s1 and s2
are made equal to the extent of overlap between the two distributions
toward the left and right of m, respectively.
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5. Double sigmoid function
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6. tanh-estimators
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The tanh-estimators introduced by Hampel et al. are robust
and highly efficient.
The normalization is given by
Hampel estimators
are based on the following influence ( )function:
where μGH and σGH are the mean and
standard deviation estimates, respectively,
of the genuine score distribution as given by
Hampel estimators
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6. tanh-estimators
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Summary of Normalization Techniques
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Experimental Results
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Database of 100 users with three modalities.
Each user having five biometric templates for each modality.
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Experimental Results
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Experimental Results
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Experimental Results
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Experimental Results
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Experimental Results
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Experimental Results
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Experimental Results
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Feature Level Fusion
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“Biometric A” feature vectors : X
“Biometric B” feature vectors : Y
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Normalization -> X’ , Y’
Dimension reduction
Combine two vector -> Z’ = { X’ , Y’ }
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Reference Paper
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A. Ross and R. Govindarajan. “Feature Level Fusion
Using Hand and Face Biometrics.” In Proc. SPIE Conf.
on Biometric Technology for Human Identication II,
volume 5779, pages 196-204,Orlando, 2005.
SON, B. and LEE, Y. “The Fusion of Two User-friendly
Biometric Modalities: Iris and Face”, IEICE Transactions
on Information and Systems , 2006.
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Fusion in feature and matching level
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Normalization method : median and MAD
Dimension reduction method : PCA , LDA
Matching score fusion method : sum rule
Consider feature vectors {Xi , Yi} and {Xj , Yj} obtained at
two different time instances i and j.
 Fusion in feature level -> { Zi , Zj }
 Let sX and sY be the normalized match (Euclidean
distance) scores generated by comparing Xi with Xj
and Yi with Yj , respectively.
 smatch = (sX + sY)/2 be the fused match score
obtained using the simple sum rule.
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Experimentation
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A set of 500 face images and hand images were acquired
from 100 users (5 biometric samples per user per biometric)
Each face image was decomposed into its component R, G, B
channels. Further, the grayscale rendition of the color image
- I - was also computed.
The Principal Component Analysis (PCA) and Linear
Discriminant Analysis (LDA) were performed on these
component images (i.e., R, G, B, I) in order to extract
representational features.
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Experimental Results
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Experimental Results
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The Fusion of Two User-friendly Biometric
Modalities: Iris and Face
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Fusion method
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Dimension reduction method :
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Wavelet Transform
LDA
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Experimentation
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Face Databases:
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IISFace : We sampled frontal face images of 100
subjects from the IIS face database. Each subject has 10
images with varying expressions.
Iris Databases:
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Iris1 : This data set consists of 1000 iris images acquired
from 100 individuals. (good quality images)
Iris2 : The Iris2 database consists of 1000 iris images
containing some bad quality ones acquired from 100
individuals.
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Experimental Results
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Experimentation
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Face Databases:
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ORLFace : The ORL data set consists of 400 frontal
faces: 10 tightly cropped images of 40 subjects with
variations in poses, illuminations, facial expressions
and accessories.
Iris Databases:
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Iris3 : The Iris3 database is composed of 400 good
quality images sampled from the Iris1 database to
combine with the ORLFace database.
Iris4 : The Iris4 is composed of 400 iris images
containing some bad quality ones sampled from the
Iris2 database to combine with the ORLFace.
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Experimental Results
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Reference Paper
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M. Indovina, U. Uludag, R. Snelick, A. Mink
and A. Jain, "Multimodal Biometric
Authentication Methods: A COTS Approach",
Proc. MMUA 2003, Workshop on Multimodal
User Authentication, pp. 99-106, Santa
Barbara, CA, December 11-12, 2003.
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abstract
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We examine the performance of multimodal
biometric authentication systems using
Commercial Off-the-Shelf (COTS) fingerprint
and face biometrics.
It introduce novel methods of fusion and
normalization that improve accuracy still
further through population analysis.
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Normalization methods
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a matcher score as s from the set S of all
scores for that matcher and the corresponding
normalized score as n.
Min-Max
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maps the scores to the [0, 1] range.
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Normalization methods
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Z-score
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transforms the scores to a distribution with mean of
0 and standard deviation of 1.
Tanh
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robust statistical techniques.
maps the scores to the (0, 1) range.
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Normalization methods
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Adaptive
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Using an adaptive normalization procedure that
aims to increase the separation of the genuine and
impostor distributions.
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Normalization methods
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Two-Quadrics
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composed of 2 quadratic segments that change
concavity at c.
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Normalization methods
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Logistic
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logistic function
The general shape of the curve is similar to Two-Quadrics
f(0) is equal to the constant Δ, which is selected to be
a small value (0.01 in this study).
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Normalization methods
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Quadric-Line-Quadric
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The overlapped zone, w, is left unchanged while the
other regions are mapped with two quadratic
function segments.
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Fusion methods
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Simple Sum
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Min Score
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Scores for an individual are summed.
Choose the minimum of an individual’s scores.
Max Score
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Choose the maximum of an individual’s scores.
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Fusion methods
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Matcher Weighting
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Matcher weighting-based fusion makes use of the
Equal Error Rate (EER).
the weights are inversely proportional to the
corresponding errors.
The fused score is calculated as
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Fusion methods
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EER
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if the score distributions overlap, the FAR and FRR
intersect at a certain point. The value of the FAR
and the FRR at this point, which is of course the
same for both of them, is called the Equal Error
Rate (EER).
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Fusion methods
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User Weighting
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This method applies weights to individual matchers
differently for every user (individual).
The calculation of these user-dependent
weights make use of the wolf-lamb concept
introduced by Doddington, et al.
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Fusion methods
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We assume that for every (i, m) pair, the mean
and standard deviation of the associated
genuine and impostor distributions are known.
use the d-prime metric as a measure of the
separation of these two distributions.
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Experiment Results
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The best EER values in individual columns are
indicated with bold typeface; the best EER
values in individual rows are indicated with a
star (*) symbol.
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Experiment Results
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Normalization: varied, fusion: Simple Sum
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Experiment Results
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Normalization: varied, fusion: Min Score
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Experiment Results
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Normalization: varied, fusion: Max Score
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Experiment Results
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Normalization: varied, fusion: Matcher weight
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Experiment Results
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Normalization: varied, fusion: User weight
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Experiment Results
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Normalization: Min-Max, fusion: varied
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Experiment Results
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Normalization: Z-score, fusion: varied
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Experiment Results
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Normalization: Tanh, fusion: varied
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Experiment Results
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Normalization: Quadric-Line-Quadric, fusion:
varied
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Experiment Results
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Normalization: Quadric-Line-Quadric, fusion:
Simple Sum
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Reference Paper
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Y. Wang, T. Tan and A. K. Jain, "Combining
Face and Iris Biometrics for Identity
Verification", Proc. of 4th Int'l Conf. on Audio-
and Video-Based Biometric Person
Authentication (AVBPA), pp. 805-813,
Guildford, UK, June 9-11, 2003.
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abstract
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Combining Face and Iris to improve verification
performance.
Fusing in scores level.
We use two different strategies.
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The first strategy is to compute either an
unweighted or weighted sum .
The second strategy is to treat the matching
distances of face and iris classifiers as a twodimensional feature vector and to use a classifier
such as Fisher’s discriminant analysis.
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Fusion methods
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Weighted Sum Rule
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Fusion methods
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Fisher Discriminant Analysis
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we treat the face and iris matcher outputs x1 and
x2 as a feature vector X = (x1 ,x2).
Decision Rule
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Experiment Results
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Distribution of matching distances
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Experiment Results
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Total error rate
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Reference Paper
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Michalis Petrakos, Jon Atli Benediktsson, and
Ioannis Kanellopoulos,” The Effect of Classifier
Agreement on the Accuracy of the Combined
Classifier in Decision Level Fusion”, IEEE
TRANSACTIONS ON GEOSCIENCE AND
REMOTE SENSING, VOL. 39, NO. 11,
NOVEMBER 2001
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abstract
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Agreement among classifiers can inhibit the
gains obtained regardless of the method used
to combine them. In this work, the level of
agreement between different classifiers used in
remote sensing is assessed based on statistical
measures.
A study is performed in which an image is
classified by several methods with different
degrees of agreement between them.
As stated previously, the LOP and the LOGP
are widely used decision fusion approaches.
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Fusion methods
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LOP (Linear Opinion Pool)
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LOGP (Logarithmic Opinion Pool)
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Fusion methods
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Then we can combine LOP/LOGP and neural
network.
Their combination schemes were considered to
be two stage processes: statistical classifiers in
stage one, and a single neural network in
stage two.
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Fusion methods
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Their suggested voting schemes were:
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Majority Voting: When the majority of the
individual agree on the classification of a sample,
the sample is classified to that class.
Complete Agreement: When all the individual
source-specific classifiers agree on the classification
of a sample, the sample is classified to that class.
CONSNN-NN: A neural network and a LOGP
classifier are trained separately on all the data.
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Experiment Results
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Database
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Experiment Results
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The minimum distance (MD) computes the Mahalanobis
distance with every one of the 12 land-use classes for
each sample, and assigns the sample to the class with
the smallest distance.
Linear discriminant analysis (LDA) assigns a sample to
the class with the maximum posterior probability given
that all classes have a common (pooled) covariance
matrix.
Quadratic discriminant analysis (QDA) assigns a sample
to the class with the maximum posterior probability. In
this case, each class has its own covariance matrix.
A conjugate gradient neural network (CGNN) with 13
inputs, one hidden layer containing 20 neurons, and 12
outputs.
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Experiment Results
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Experiment Results
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Conclusion
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Some fusion methods are the best in a
biometric system, but they maybe not the best
in other biometric system.
The effects of different score normalization
techniques in a multimodal biometric system
have been studied.
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