A New Biased Discriminant Analysis Using Composite Vectors for Eye Detection

We propose a new biased discriminant analysis (BDA) using composite vectors for eye detection. A composite vector consists of several pixels inside a window on an image. The covariance of composite vectors is obtained from their inner product and can be considered as a generalization of the covariance of pixels. The proposed composite BDA (C-BDA) method is a BDA using the covariance of composite vectors. We construct a hybrid cascade detector for eye detection, using Haar-like features in the earlier stages and composite features obtained from C-BDA in the later stages. The proposed detector runs in real time; its execution time is 5.5 ms on a typical PC. The experimental results for the CMU PIE database and our own real-world data set show that the proposed detector provides robust performance to several kinds of variations such as facial pose, illumination, eyeglasses, and partial occlusion. On the whole, the detection rate per pair of eyes is 98.0% for the 3604 face images of the CMU PIE database and 95.1% for the 2331 face images of the real-world data set. In particular, it provides a 99.7% detection rate for the 2120 CMU PIE images without glasses. Face recognition performance is also investigated using the eye coordinates from the proposed detector. The recognition results for the real-world data set show that the proposed detector gives similar performance to the method using manually located eye coordinates, showing that the accuracy of the proposed eye detector is comparable with that of the ground-truth data.