1. A cutting-edge position detecting method comprising: determining a measurement reference point for measuring a position of a cutting edge of a tool; under a condition in which the cutting edge of the tool is positioned in an image that is taken by a camera, performing first sampling scanning operations for the image in a predetermined scanning direction at predetermined first intervals, and recognizing points on an upper edge line of the cutting edge of the tool and points on a lower edge line thereof, based on brightness changing points upon the first scanning operations; connecting the recognized points on the respective two edge lines, so as to obtain two first-level approximate linear lines by a least-squares method; performing second sampling scanning operations for the respective two first-level approximate linear lines in directions perpendicular thereto at predetermined second intervals, and newly recognizing points on the upper edge line of the cutting edge of the tool and points on the lower edge line thereof, based on brightness changing points upon the second scanning operations; connecting the newly recognized points on the respective two edge lines, so as to obtain two second-level approximate linear lines by a least-squares method; and obtaining a coordinate of an intersection of the second-level approximate linear lines, as the position of the cutting edge of the tool, with respect to the measurement reference point.