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Face Recognition Image database: A: 2 F:

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G: B: C: D: E: Test image: Who is this guy?

Characteristics of FR:

•

A mode of biometric identification

•

Easy for human, hard for machine

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Biometric Identification Identification of people from their physical characteristics, such as

• • • • • • •

faces voices fingerprints palm prints hand vein distributions hand shapes and sizes retinal scans 3

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FR via PCA

First paper:

•

M. Turk and A. Pentland, "Eigenfaces for Recognition", Journal of Cognitive Neuroscience, vol. 3, no. 1, pp. 71-86, 1991 Characteristics

• • •

Efficient computation Proven mathematics Applicable to face detection

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Problem Definition

Input

• •

A dataset of face images of n person An unknown person’s face image Output:

•

Determine the identity of the unknown person

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ATT Face Dataset 6

Origin

•

Olivetti Research Laboratory, 1992~1994 Stats:

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40 subjects, each with 10 images Characteristics

•

Same-size photos of black and white

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Centered faces of different poses

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Face Recognition via PCA

Compute Mean Face Compute Eigenvectors (Eigenfaces) Select 6 Principal Eigenfaces Subtract Facial Signatures

f



i

6   1

w i u i

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8 Steps of Feature Extraction via PCA

3 simple steps:

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1. Data preprocessing

Each sample image is rearranged into a column vector of length 112*92=10304. All images are put into a matrix F of size 10304x400.

Mean face is subtracted from each column.

2. PCA

Find the eigenvectors of F*F’.

3. Projection

Select top k eigenvectors with k largest eigenvalues  k eigenfaces!

Do projection along these eigenfaces to find new features for classification 8

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Details for Step 2: PCA

Problem: is large,10304x10304! (849MB!) How to compute the eigenvectors of ?

Observation:

• •

If u is the eigenvector of F’F, then Fu is the eigenvector of FF’.

If

l

is the eigenvalue eigenvalue of FF’.

of F’F, then

l

is also the

F

'

Fu

 l

u



FF

'

Fu

 l

Fu



FF

'

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Note that:

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FF’ has 10304 eigenvalues.

F’F has 400 eigenvalues, corresponding to the 400 largest eigenvalues of FF’.

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Details for Step 3: Projection (1/2)

Each face (minus the mean) in the training set can be represented as a linear combination of the best k eigenvectors:

f



f mean



i k

  1

w i u i

Typical eigenfaces when k=4:

u

1

u

2

u

3

u

4

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Scientific Computing

Details for Step 3: Projection (2/2)

 

face (after mean subtraction) can be represented by this basis:

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The feature vector of the face is then the new coordinates obtained by:

T U f



u

 

u

2

u

3

f

u

4

  

T

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Classification

Once the features for images are extracted, we can then apply any classification methods to obtain the final recognition results, including

• • • • •

Minimum distance classifier Support vector machines Neural networks Quadratic classifier Gaussian mixture models

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Face Detection Using Eigenfaces 13

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Distance from Face Space (DFFS) 14

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PCA for ATT Dataset Variance vs. no. of eigenvalues used 16 eigenfaces 15

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PCA for ATT Dataset: Accuracy Accuracy vs. no. of eigenvalues used



Accuracy of 98.50% is achieved when the dimensionality is 28.

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PCA for ATT Dataset: DFFS 17

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PCA for ATT Dataset: Similarity 18

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PCA for ATT Dataset: Demo Face Recognition via PCA (eigenfaces)

load faceData.mat frOpt.method='pca'; frOpt.pcaDim=7; frOpt.plot=1; faceRecogDemo(faceData, frOpt);

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PCA+LDA for FR Steps for FR via fisherfaces: 1.

2.

Perform PCA to reduce to 60 dimensions Perform LDA to find the best dimensionality



99.00% when the dimensionality is 14.

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