At least one specified position and, if necessary, a cutting surface are specified in a three-dimensional medical image. Plural anatomical structures present within a predetermined range from the specified position are extracted, as structures to be separated, by referring to a structure information storage unit that stores plural anatomical structures and a separation condition storage unit that stores a separation condition for each anatomical structure of a subject to determine, based on the specified position, a boundary surface and, if necessary, a cutting surface for separately displaying the plural anatomical structures. The boundary surface corresponding to the structures to be separated and the specified position and, if necessary, the cutting surface are set based on the separation condition. A three-dimensional medical image in which the structures to be separated are separated by the boundary surface and, if necessary, by the cutting surface is generated, and displayed.