1. A method of detecting eyes comprising: (a) extracting a symmetric face region from a face image based on magnitude and phase of gradient in each pixel of the face image, (a1) calculating the magnitude and phase of gradient in each pixel of the face image; (a2) creating a certain-sized window smaller than the face image and comparing an magnitude and phase of gradient in each pixel, which are calculated with reference to a center pixel in the window, with a critical value, and marking pixels which have greater magnitude and phases of gradient than the critical value as symmetric points; and (a3) applying a symmetric filter obtained from the face image in which the symmetric points are marked to the face image and extracting the symmetric face region from the face image, wherein illumination effects are removed from the face image prior to calculating the magnitude and phase of gradient in the each pixel of the face region; (b) detecting available eye positions based on brightness information of the extracted face region, where the detecting available eye position is done after the illumination effects have been removed from the face image; (c) verifying regions around each of the detected eye positions with a classifier which determines whether an input image is an eye image using information obtained by supervised learning on sample images, wherein the verifying regions around each of the detected eye positions with the classifier is done after the illumination effects have been removed from the face image.