1. An image diagnosis support apparatus comprising: a three-dimensional medical image data storage unit that stores three-dimensional medical image data of a subject; a display unit that displays a three-dimensional medical image based on the stored three-dimensional medical image data; a structure information storage unit that stores a plurality of anatomical structures included in the three-dimensional medical image data; a specifying unit that specifies, in the three-dimensional medical image displayed by the display unit, at least one specified position and, if necessary, a cutting surface for separating the plurality of anatomical structures included in the three-dimensional medical image; a separation condition storage unit that stores a separation condition for each anatomical structure of the subject to determine, based on the specified position specified by the specifying unit, a boundary surface and, if necessary, a cutting surface for separately displaying the plurality of anatomical structures; a setting unit that extracts, as structures to be separated, the plurality of anatomical structures present within a predetermined range from the specified position that has been specified, and that sets, based on the separation condition, the boundary surface corresponding to the extracted structures to be separated and the specified position that has been specified, and that sets the cutting surface if necessary; and a separate image generation unit that generates, based on the boundary surface and, if necessary, the cutting surface as well as based on the three-dimensional medical image data, 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, and that makes the display unit display the three-dimensional medical image.