Using Composite Features
Chunghoon Kim and Matthew Turk
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.
Recently, several studies have been done on eye detection as a preprocessing step for face recognition. 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. According to recent results in the field of face recognition, state-of-the-art methods provide a recognition rate reaching almost 100% even under variations in facial expression and illumination. In those experiments, the eye coordinates were manually located. When these coordinates were shifted randomly, the recognition rates degraded rapidly. From these results, we can see that eye detection is very important in face recognition systems.
In this project, we propose a new biased discriminant analysis using composite vectors, called C-BDA, for eye detection. C-BDA is derived from biased discriminant analysis, by using the covariance of composite vectors instead of the covariance of pixels. Figure 1 shows the schematic diagram of C-BDA. In this case, the size of A(k) is 40*40, the size of the composite vector l is 16. In C-BDA, 16 images are used for making scatter matrices as if they are individual samples. If l becomes larger, more images with a larger variation are used for making scatter matrices, and vice versa. The projection vector is obtained by C-BDA and is represented as an image in the figure. Note that the composite feature has the same size as the composite vector and is further reduced by applying a downscaling operator. In this case, the downscaling factor is 16.
Figure1. Schematic diagram of C-BDA
When detecting the eye coordinates in a face image, we construct a hybrid cascade detector. At the earlier stages in the hybrid cascade detector, Haar-like features are used to remove majority of non-eyes. At the later stages, composite features obtained from C-BDA are used to discriminate between eyes and non-eyes, which are difficult to discriminate by Haar-like features. Table 1 shows the detection results for the CMU PIE database. As can be seen in the table, the proposed detector gives robust performance to several kinds of variations such as facial pose, illumination, and closed eyes. It provides a 99.4% detection rate for the images without glasses. Figure 2 shows some examples of the correct and incorrect detections. Incorrect detections are mainly caused by glare on glasses. In Fig. 2(b), the normalized error of each image from left to right is 0.129, 0.141, 0.167, and 0.212, respectively.
Table 1. Eye detection results for the CMU PIE database
(a) correct detections
(b) incorrect detections
Figure 2. Examples of the correct and incorrect detections