1. A surgery-assistance apparatus that determines an excision region including an abnormal region of an organ to be removed, the apparatus comprising: a non-transitory computer readable medium storing computer-executable instructions; and a processor executing the instructions comprising: obtaining a medical image representing the organ; extracting a region of the organ from the obtained medical image; extracting the abnormal region from the extracted region of the organ; setting a smallest enclosing body that encloses the extracted abnormal region; extracting, 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; extracting a region of a structure dominating the organ from the obtained medical image; extracting, 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 determining, based on a predetermined excision region determination condition, the partial region or the dominance region, as the excision region.