1. A surgery assistance apparatus comprising: an organ region extraction unit that extracts a tubular organ region from a three-dimensional image obtained by imaging a tubular organ and a blood vessel dominating the tubular organ; a blood vessel region extraction unit that extracts a blood vessel region dominating the tubular organ from the three-dimensional image; a branching structure extraction unit that extracts a branching structure of the blood vessel from the extracted blood vessel region; and a dominated region identification unit that identifies, with respect to an arbitrary partial blood vessel corresponding to an upper edge branching at least once to reach an edge including a terminal end of the extracted branching structure, a dominated region in the tubular organ region that is dominated by the arbitrary partial blood vessel by using positional relationships between a plurality of terminal end points present after the edge of the arbitrary partial blood vessel branches last and the tubular organ region.