1. An apparatus for detecting a vertex of an image, the apparatus comprising: a UI part used to display an image and input a vertex position of the image; an ROI setting part to set an ROI including the input vertex position; an edge detector to detect a plurality of edges from an image in the ROI, and to detect a candidate straight line group based on the edges; and a vertex detector to remove a candidate straight line, which forms an angle less than a critical angle with respect to a base candidate straight line set from the candidate straight line group, and to determine an intersection point between a remaining candidate straight line and the base candidate straight line, which is provided at a position making a minimum distance from the input vertex position, as an optimal vertex.