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 authentication, access control, and surveillance. Human face image appearance has potentially very large intra-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 representation.

Independent Components Analysis ICA assumes a statistical model whereby the observed multivariate 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 independent, 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 function, 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

Where is an estimation of the N sources . Where A represents a linear mixture called the mixing matrix. To achieve the separation, one must estimate the separating matrix W that verifies: Where is an estimation of the N sources . if mixing matrix A is the inverse matrix of separating matrix W, WA is an identity matrix and the independent sources can be recovered accurately.

ICA估計的原理 ICA 模型：x = As s=A-1x 令y=wTx.z=ATw, 则 y=wTx=wT As=zTs 這樣的話y 是s的線性組合，y應該比s更具有高斯性，除非wT接近A-1。此時，y=wTx=A-1x=s。 也就是說y=s時，y具有最大非高斯性。 問題轉化為求解w，它最大化wTx的non-Gaussianity性。

Negentropy 基於信息中熵的概念 定理：在所有隨機變量，高斯分布的變量有最大熵。 定義Negentropy J为： yGauss是和y有相同協方差矩陣的高斯隨機變量。 y為高斯分布时， Negentropy為零，其它分布時不為零。 計算起來太複雜，需要引入其近似值。

PCA&ICA 兩者都是線性變換都可以看作一些分量的组合。 不同的是 PCA而言，各分量不相關 ICA而言， 各分量獨立

Image data The face images employed for this research are two subset 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 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 our experiments are the Euclidean distance measure euc δ and the cosine similarity measure cos δ , which are defined as follows:

Image data

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

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

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.

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.

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