1. A method of automatically identifying a point of interest on a viewed object, the method comprising the steps of: displaying on a monitor an image of the viewed object; determining the three-dimensional coordinates of a plurality of points on a surface of the viewed object using a central processor unit; selecting a first reference line positioning point using a pointing device; selecting a second reference line positioning point using a pointing device; determining a reference surface based on a plurality of points on the surface of the viewed object associated with the first reference line positioning point and the second reference line positioning point using the central processor unit; determining a first slice plane that is normal to the reference surface and includes a point on the surface of the viewed object associated with the first reference line positioning point and a point on the surface of the viewed object associated with the second reference line positioning point using the central processor unit; determining a first surface contour line that includes a plurality of points on the surface of the viewed object proximate to the first slice plane using the central processor unit; selecting an offset reference line positioning point using a pointing device; determining an offset slice plane that includes a point on the surface of the viewed object associated with the offset reference line positioning point using the central processor unit; determining an offset surface contour line that includes a plurality of points on the surface of the viewed object proximate to the offset slice plane using the central processor unit; determining a plurality of profile surface contour lines between the first surface contour line and the offset surface contour line using the central processor unit; and determining the point of interest as the deepest or highest point on any of the plurality of profile surface contour lines using the central processor unit.