1. An apparatus for detecting an edge in a three-dimensional image, comprising: a scan-line approximation unit creating an approximated quadratic curve with regard to each scan-line corresponding to each surface of the three-dimensional image by scanning the three-dimensional image in a set-up direction; a curvature value calculation unit calculating approximated curvature values with regard to each division point estimated as different surfaces of the three-dimensional image on the quadratic curve approximated from the scan-line approximation unit; and an edge decision unit deciding an edge by comparing the approximated curvature values of the division points calculated from the curvature value calculation unit with a predetermined threshold.