Gesture Recognition : a Survey

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  • Topic: Facial recognition system, Matrix, Covariance matrix
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Biased Discriminant Analysis Using Composite Vectors for Eye Detection Chunghoon Kim, Matthew Turk
Computer Science Department
University of California, Santa Barbara
{chkim, mturk}@cs.ucsb.edu
Chong-Ho Choi
Electrical Engineering and Computer Science
Seoul National University, Seoul, Korea
chchoi@csl.snu.ac.kr
Abstract
We propose a new discriminant analysis using composite
vectors for eye detection. A composite vector consists of
a number of pixels inside a window on an image. The covariance of composite vectors is obtained from their inner
product and can be considered as a generalized form of the
covariance of pixels. The proposed C-BDA is a biased discriminant analysis using the covariance of composite vectors.
In the hybrid cascade detector constructed for eye detection, Haar-like features are used in the earlier stages and
composite features obtained from C-BDA are used in the
later stages. The experimental results for the CMU and Yale
databases show that the proposed detector provides robust
performance to several kinds of variations such as facial
pose, illumination, and closed eyes. In particular, it provides a 99.4% detection rate for the CMU images without
glasses.
1. Introduction
Recently, several studies have been done on eye detection
as a preprocessing step for face recognition [3, 10, 11,
13,15,16]. After detecting faces in an image, it is necessary to align faces for face recognition. Face alignment is usually performed by using the coordinates of the left and right
eyes, and the accuracy of the eye coordinates affects the performance of a face recognition system [7, 13, 15]. According
to recent results in the field of face recognition, state-ofthe- art methods provide a recognition rate reaching almost
100% even under variations in facial expression and illumination [7,9]. In those experiments, the eye coordinates were
manually located. When these coordinates were shifted randomly, the recognition rates degraded rapidly [7, 15]. From
these results, we can see that eye detection is very important in face recognition systems.
In the previous studies, several kinds of features were
used to discriminate between eyes and non-eyes. Pentland
et al. used the Eigeneyes based on principal component
analysis (PCA) [11]. Huang and Wechsler used wavelet
packets for eye representation and radial basis functions for classification of eyes and non-eyes [3]. Ma et al. used Haarlike features to find the possible eyes [10]. Wang and Ji used
features obtained from the recursive nonparametric discriminant analysis to find the face and eyes [15, 16].
On the other hand, Kim and Choi introduced a new
method of extracting composite features for classification
problems [6, 7]. In their study, a composite vector is composed of a number of primitive variables which correspond
to pixels inside a window on an image. The covariance of
composite vectors is obtained from their inner product, and
a new linear discriminant analysis technique (C-LDA) is derived by using the covariance of composite vectors. In CLDA,
features are obtained by linear combinations of the
composite vectors and these features are called composite
features because each feature is a vector whose dimension
is equal to the dimension of the composite vector. According to their results, C-LDA showed good performance when
adjacent primitive variables are strongly correlated as in image data sets and the Sonar data set [6, 7].
However, it is inappropriate to apply C-LDA to eye detection directly. C-LDA is an effective method when samples
in each class are normally distributed. In eye detection,
positive samples for eyes are similar and they can be assumed to be normally distributed, while negative samples
are not. In this case, it is better to use the objective function in biased discriminant analysis (BDA) [18]. BDA tries to
find a linear transform that makes the scatter of the positive samples as small as possible while...
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