1. An image analysis apparatus that analyzes, based on a series of three-dimensional images of lungs at different time phases, a three-dimensional distribution of ventilation volume of the lungs, the apparatus comprising: a lung region extraction unit that extracts a lung region from each of the three-dimensional images; an alignment unit that aligns the lung regions between the series of three-dimensional images and calculates a displacement vector field in the lung region; a function calculation unit that calculates a local ventilation volume function representing a temporal change in ventilation volume at each point in the displacement vector field in each of the three-dimensional images based on the displacement vector field; and a quantification unit that quantifies a difference between the local ventilation volume function and a benchmark ventilation volume function serving as a reference and calculates a quantitative value representing the difference.