EE 566 - Pattern Recognition Project

7/28/2019 EE 566 - Pattern Recognition Project

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Comparison of Dimensionality ReductionTechniques for Face Recognition

Berkay Topu 6950Sabanci University


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Outline Motivation

Face Detection

Database (M2VTS) Different Dimensionality Reduction Techniques

PCA, LDA, aPAC, Normalized PCA, Normalized LDA

Classification Results

Conclusion


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Motivation Face recognition: active research area specialising on

how to recognize faces within images or videos

Dimensionality reduction: to be able torepresent/classify with less amount of data

Linear Transforms


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Overall System

Dimensionality Reduction

FaceDetection

PCADimensionReduction

Classification

Pattern

Recognition


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Face Detection Automatic face detection of OpenCV library

Using Haar-like features

Resized to 64x48


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Database M2VTS database used for Audio-visual

speech recognition

Lip detection suitable for face recognition


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Database 40 pictures of each 37 subjects

32 pics for training & 8 pics for testing

64x48 pixels 3072 pixels Unnecessary to use the whole image in

recognition system

Is it possible to represent with less information?


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PCA (Principal Component

Analysis) Weaknesses:

Translation variant

Scale variant Background variant

Lighting variant

Advantages:

Fast and needs lesser amount of memory


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PCA (Principal Component

Analysis) Principal component analysis (PCA) seeks a

computational model that best describes a face byextracting the most relevant information contained inthat face.

Finds a lower dimensional subspace whose basisvectors correspond to the maximum variancedirection in the original image space.

Solution is the eigenvectors of the scatter matrix


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LDA (Linear Discriminant

Analysis) Finds the vectors in the underlying space that best

discriminate among classes.

The goal is to maximize between-class scatter(covariance) while minimizing within-class scatter.

maximize the ratio

Solution is the eigenvectors of

W

B

S

S

det

det

BW SS 1


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aPAC (Approximate Pairwise

Accuracy Criterion) Drawbacks of LDA:

Maximizing the squared distances between pairs of classes,outliers dominate the eigenvalue decomposition.

So, LDA tends to over-weight the influence of classes thatare already well seperated.

Solution is generalization of LDA by weighting thecontribution of each class due to Mahanalobis

distance between classes.


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aPAC (Approximate Pairwise

Accuracy Criterion) K-class LDA can be decomposed into

two-class LDA.

Introducing a weighting of the contributions ofindividual class pairs to the overall criterion.

Weighting function depends on the Bayes error rate*between classes.

Altough it is generalization of LDA, no additionalcomplexity in computation.

* Bayes error rate: theoretical minimum to the error any classifiercan make.

)1(2

1KK


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nPCA (Normalized PCA) PCA computes the projection that maximizes the

preservation of pairwise distances in the projectedspace.

Weighting this sum of the squared distances byintroducing symmetric pairwise dissimilarities.

Proposed weights:

spaceoriginalin thedistanceEuclidean:

where1

ij

ij

ij

dist

distd


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nPCA (Normalized PCA)Solution is the eigenvectors of where is a

matrix containing pairwise dissimilarities.

XLX dT dL


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nLDA (Normalized LDA) Drawbacks of the LDA can be overcome by

Appropriately chosen weights to reduce the dominance oflarge distances

Pairwise similarities together with the pairwise dissimilarities

Attraction between elements of the same class and

repulsion between elements of different classes.


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Classification (Training &Testing)

Classification in MATLAB PrTools (PatternRecognition Toolbox)

Nearest Mean Classifier (nmc) & LinearClassifier (ldc)

40 images from 37 subject 1480 images

32x37 = 1184 images for training

8x37 = 296 images for testing


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Training and Testing

Dimension

Reduction

DimensionReduction

Detected

faces fromdifferentpeople

Classifier

Training

Scorecalculation foreach method

Statictical

data forface images

Unknowndetected

faces

Training

Testing

RecognitionRates


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Test Results

Reduced dimension = 32

Reduced dimension = 16

Recognition rate prior to dimension reduction (using all pixels) is 79.05

PCA(128) LDA aPAC nPCA nLDA

nmc 77.7 % 89.19 % 87.84 % 71.62 % 88.85 %

ldc 61.15 % 88.85 % 87.84 % 86.15 % 88.85 %

PCA(128) LDA aPAC nPCA nLDA

nmc 77.7 % 83.11 % 85.47 % 66.89 % 86.15 %

ldc 61.15 % 84.46 % 85.47 % 79.73 % 84.46 %


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Conclusion

Face recognition in the lower dimension

Improved recognition rates for several

dimensionality reduction techniques Further work:

Analysis of low recognition rates in some cases

Block PCA and LDA

EE 566 - Pattern Recognition Project

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