1. A projection image generation apparatus, comprising: a virtual endoscopic image generator that generates, based on three dimensional data representing an interior of a subject having a lumen captured by an imaging device, a virtual endoscopic image, which is a pseudo three dimensional image, for visualizing an interior of the lumen by volume rendering; an opacity curve setter that sets, in the virtual endoscopic image generator, an opacity curve which defines a relationship between pixel values of the three dimensional data and opacity values and is used in the volume rendering; a viewpoint position setter that sets a viewpoint position corresponding to a camera position of the virtual endoscopic image within the interior of the lumen in the virtual endoscopic image generator, and is capable of setting different viewpoints in the extension direction of the lumen; and a movement amount determination device that determines a movement amount of the opacity curve for the viewpoint position set by the viewpoint position setter with respect to the opacity curve at a reference viewpoint position in the case that the viewpoint position set by the viewpoint position setter is changed in the extension direction of the lumen from the reference viewpoint position, after the change in the viewpoint position, wherein a viewpoint position change is made by the viewpoint position setter, the opacity curve setter automatically moves the opacity curve at the reference viewpoint position by the movement amount determined by the movement amount determination device for the viewpoint position after the change, and sets the moved opacity curve in the virtual endoscopic image generator.