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; 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; and a center line extraction unit that extracts a center line of the tubular organ region, wherein the dominated region identification unit determines a corresponding point on the center line corresponding to each of the plurality of terminal end points by using positional relationships between the plurality of terminal end points and the center line, and obtains cross sections that pass through two outermost corresponding points of the determined plurality of corresponding points, respectively, or points in the vicinities of the outermost corresponding points, respectively, and that are orthogonal to the center line, and identifies a part of the tubular organ region between the cross sections, as the dominated region.