1. A surgery-assistance apparatus that determines an excision region including an abnormal region of an organ to be removed, the apparatus comprising: a medical image obtainment unit that obtains a medical image representing the organ: an organ region extraction unit that extracts a region of the organ from the obtained medical image; an abnormal region extraction unit that extracts the abnormal region from the extracted region of the organ; an enclosing body setting unit that sets a smallest enclosing body that encloses the extracted abnormal region; a partial region extraction unit that extracts, as a partial region, a part of the organ, and the part belonging to the inside of an elliptic parabolic surface or a circular conic surface that circumscribes the set enclosing body; a structure region extraction unit that extracts a region of a structure dominating the organ from the obtained medical image; a dominance region extraction unit that extracts, as a dominance region, a part of the organ, and the part including the abnormal region and being dominated by a part of the structure extending from a predetermined position in the extracted region of the structure toward the part of the organ including the abnormal region; and an excision region determination unit that determines, based on a predetermined excision region determination condition, the partial region extracted by the partial region extraction unit or the dominance region extracted by the dominance region extraction unit, as the excision region.