Facial Feature Extraction by Kernel Independent Component Analysis

學生 : 許維傑

Outline

Introduction Independent Components

Analysis Image data Experimental results References

Introduction It has a wide range of applications such as identity authentic

ation, access control, and surveillance. Human face image appearance has potentially very large intr

a-subject variations due to 3D head pose,illumination, facial expression, occlusion due to other objects or accessories facial hair. On the other hand, the inter-subject variations are small due to the similarity of individual appearances. This makes face recognition a great challenge. Two issues are central:

1) what features to use to represent a face and 2) how to classify a new face image based on the chosen repr

esentation.

Independent Components Analysis ICA assumes a statistical model whereby the observed multiv

ariate data, typically given as a large database of samples, are assumed to be linear or nonlinear mixtures of some unknown latent variables.

The mixing coefficients are also unknown. The latent variables are nongaussian and mutually independe

nt, and they are called the independent components of the observed data.

Independent Components Analysis FastICA proposed in 1999 by Hyvärinen is a fast ICA algorithm.

It is based on fixed point recursion and is applicable to data of any type. Because of its fast convergence and self adaptation, it is the most commonly used ICA algorithm

Independent Components Analysis The Kernel-ICA problem based not on a single nonlinear func

tion, but on an entire function space of candidate nonlinearities. In particular, make use of the “kernel trick” to search over this space efficiently. The use of this function space makes it possible to adapt to a variety of sources and thus makes this algorithm more robust to varying source distributions.

Independent Components Analysis

Model of ICA

Observations, as a N dimensional random vector are assumed to be a linear mixture of mutually statistically independent sources

NX

MS

MN ASX

Where A represents a linear mixture called the mixing matrix. To achieve the separation, one must estimate the separating matrix W that verifies:

NX

NM WXY

Where is an estimation of the N sources .MY

MM WASY if mixing matrix A is the inverse matrix ofseparating matrix W, WA is an identity matrix and theindependent sources can be recovered accurately.

MS

Image data

The face images employed for this research are twosubset of the FERET and ORL face databases.

Coordinates for eye and mouth locations are provided with the FERET database. These coordinates are used to center the face images, and then crop and scale to 240×200 pixels. Scaling is based on the area of triangle defined by the eyes and mouth. At last, we apply the Histogram Equalization to improve the contrast.

Image data

All the 400 images from the ORL database are used to evaluate the face recognition performance of our Kernel ICA method. Five images are randomly chosen from the ten images available for each subject for training, while the remaining five images (unseen during training) are used for testing.

Image data

ktestktest bMb 0,

Face recognition performance is evaluated by thenearest neighbor algorithm (to the mean), which isdefined as follows:

where is the mean of the training samples for class . Therefore, the image feature vector btest is classified to the class of the closest mean based onδ the similarity measure δ . Similarity measures used in ourexperiments are the Euclidean distance measure euc δ andthe cosine similarity measure cos δ , which are defined asfollows:

0kM k

0kM

Image data

2,, i

traintesttraintesteuc iibbbb

traintest

trainT

testtraimtest

bb

bbbb

,cos

Experimental results

Recognition performance of the Kernel ICA, ICA factorial code representations and PCA representations using 36 coefficients corresponding to the similarity measure.

Euc

Experimental results

Recognition performance of the Kernel ICA, ICA factorial code representations and PCA representations using 36 coefficients corresponding to the similarity measure.cos

Experimental results

Recognition performance of the Kernel ICA, ICA factorial code representations and PCA representations using 30, 60, 120, 180 coefficients corresponding to the similarity measure.

Euc

Experimental results

Recognition performance of the Kernel ICA, ICA factorial code representations and PCA representations using 30,60, 120, 180 coefficients corresponding to the similaritymeasure.

cos

References

Bartlett, M.S., Movellan, J.R., T.J., Sejnowski.; Face Recognition by Independent Component Analysis. IEEE Transactions on Neural Networks, vol. 13, NO. 6, November 2002