1. An image-based diagnosis assistance apparatus, comprising: a central processor; a non-volatile data storage device; and a memory device in connection with said central processor, said memory device having stored therein computer-executable instruction code that causes the central processor to operate as: an image storage unit that stores a function image, representing a function level at each position in an organ, and a morphology image, representing a morphology of the organ including a tubular structure in an inside thereof; a structure region extraction unit configured to extract a structure region representing a structure dominating the organ from the morphology image; a partial region determination unit configured to determine and store a specific partial region in the extracted structure region; and a dominated region determination unit configured to determine and store a dominated region in the organ, and the dominated region being dominated by a structure in the determined partial region, wherein at least one of the determination of the partial region by the partial region determination unit and the determination of the dominated region by the dominated region determination unit is performed using the function image, wherein the dominated region determination unit carries out the determination of the dominated region as a function of a distance determined between each part of the organ and the determined partial region in the morphology image, and wherein said distance between each part of the organ and the determined partial region in the morphology image is weighted based on a function level at each position of the organ on a shortest path.