1. A medical image processing apparatus which shows an image of an extracted region of interest of three-dimensional volume data representing an inside of a living body, said apparatus comprising: a display unit which has a first display area and a second display area, and displays said medical image in at least one of said display areas; a subtraction point specifying unit which accepts designation of a point on said first display area as a subtraction input point and specifies subtraction coordinates indicating a position in said three-dimensional volume data corresponding to said subtraction input point; a first region specifying unit which specifies a first closed continuous region including said subtraction coordinates; a first display control unit which generates an image from said three-dimensional volume data indicating a region after subtracting said first closed continuous region from said three-dimensional volume data on said first display area and generates an image from said three-dimensional volume data, indicating said first closed continuous region on said second display area; an addition point specifying unit which accepts designation of an addition point on said second display area and specifies addition coordinates indicating a position in said three-dimensional volume data corresponding to said addition input point; a second region specifying unit which specifies a second closed continuous region which does not include said subtraction coordinates while including the addition coordinates; and a second display control unit which generates an image from said three-dimensional volume data indicating a third region after subtracting said second closed continuous region from said first closed continuous region for display on said second display area and generates an image from said three-dimensional volume data indicating the region of interest after subtracting said third region from said three-dimensional volume data on said first display area.