1. A computer-implemented method of detecting a facial image, comprising: with a computing device: pre-processing an image; detecting a face region from the pre-processed image to create facial records of the detected face region; and detecting the facial image by creating coordinates of the face and eyes in the input image by using the facial records, the detecting of the facial image: classifying the facial records into face candidates and eye candidates through clustering, calculating an average coordinate of center coordinates of the face candidates and eliminating facial records far from the average coordinate over a preset distance, and calculating an average coordinate of center coordinates of remaining face candidates after the elimination to calculate a final center coordinate of a face.