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 region-of-interest setting unit that sets a region of interest in the extracted tubular organ region; a branching structure extraction unit that extracts a branching structure of the blood vessel from the extracted blood vessel region; and a dominating blood vessel identification unit that identifies a dominating blood vessel region in the blood vessel region that dominates the region of interest by using a positional relationship between a terminal end point of the extracted branching structure and the set region of interest, wherein the dominating blood vessel identification unit identifies a part of the blood vessel region corresponding to a segment from an edge including a terminal end of the branching structure, and the terminal end being located within a predetermined distance from the region of interest, to a higher edge branching at least once to reach the edge including the terminal end, as the dominating blood vessel region.