This is a presentation done for my project in college.It is not perfect.It is based on the Fisherfaces face recognition system.

1. fisherfaces
Face recognition algorithm
Vishnu K N S5 CSE B 59
Federal Institute of Science and Technology

2. introduction
Face Recognition System
-The input of a face recognition system is always an image or video
stream.
-The output is an identification or verification of the subject or
subjects that appear in the image or video.
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3. fisherfaces

4. working
-The Fisherfaces method learns a class-specifc transformation
matrix, so they do not capture illumination as obviously as the
Eigenfaces method.
-The Discriminant Analysis instead fnds the facial features to
discriminate betweenthe persons.
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5. -It’s important to mention, that the performance of the Fisherfaces
heavily depends on the input data as well.
-Practically said: if you learn the Fisherfaces for well-illuminated
pictures only and you try to recognize faces in bad-illuminated
scenes, then method is likely to fnd the wrong components (just
because those features may not be predominant on bad illuminated
images).
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6. The Fisherfaces allow a reconstruction of the projected image, just
like the Eigenfaces did.
But since we only identifed the features to distinguish between
subjects, you can’t expect a nice reconstruction of the original image.
For the Fisherfaces method we’ll project the sample image onto
each of the Fisherfaces instead.
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7. fisherfaces v/s eigenfaces
-The Eigenface method uses Principal Component Analysis (PCA) to
linearly project the image space to a low dimensional feature space.
-The Fisherface method is an enhancement of the Eigenface method
that it uses Fisher’s Linear Discriminant Analysis (FLDA or LDA) for
the dimensionality reduction.
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8. -The LDA maximizes the ratio of between-class scatter to that of
within-class scatter, therefore, it works better than PCA for purpose
of discrimination.
-The Fisherface is especially useful when facial images have large
variations in illumination and facial expression.
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9. algorithm

10. Let X be a random vector with samples drawn from c classes:
X = {X1, X2, . . . , Xc}
Xi = {x1, x2, . . . , xn}
The scatter matrices SBandSWarecalculatedas :
SB =
c∑
i=1
Ni(µi − µ)(µi − µ)T
SW =
c∑
i=1
∑
xj∈Xi
(xj − µi)(xj − µi)T
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11. , where µisthetotalmean :
µ = 1
N
∑N
i=1 xi
And µiisthemeanofclassi ∈ {1, . . . , c} :
µi = 1
|Xi|
∑
xj∈Xi
xj
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12. Fisher’s classic algorithm now looks for a projection W, that
maximizes the class separability criterion:
Wopt = arg maxW
|WT
SBW|
|WTSWW|
a solution for this optimization problem is given by solving the
General Eigenvalue Problem:
SBvi = λiSwvi
S−1
W SBvi = λivi
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13. The optimization problem can then be rewritten as:
Wpca = arg maxW |WT
STW|
Wfld = arg maxW
|WT
WT
pcaSBWpcaW|
|WTWT
pcaSWWpcaW|
The transformation matrix W, that projects a sample into the
(c-1)-dimensional space is then given by:
W = WT
fldWT
pca
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14. before
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15. after
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16. thank you