1. A projection image generating device, comprising: a condition setting section that sets a view point inside a hollow organ and sets a visual line direction from the view point in volume data representing a three-dimensional region including the hollow organ; a clip plane setting section that sets a clip plane crossing an internal cavity of the hollow organ in a position spaced apart in the visual line direction from the view point; a dividing section that sets a portion of the three-dimensional region that is on a distant side of the clip plane from the view point of the three-dimensional region as a visible region, and divides a field of view from the view point into a first field-of-view range in which the inside of the hollow organ is viewed and a second field-of-view range other than the first field-of-view range; and a projection image generation section that projects a portion within the first field-of-view range of the visible region onto a projection plane set corresponding to the view point using a first template in which a relationship between a data value and opacity is defined so that an inner wall surface of the hollow organ is able to be drawn, to thereby acquire a first projection image in the first field-of-view range, projects a portion within the second field-of-view range of the visible region onto the projection plane using a second template in which the relationship between the data value and the opacity is defined so that a contact surface with the inner wall surface of the air region in the hollow organ is able to be drawn, to thereby acquire a second projection image in the second field-of-view range, and generates a projection image in the entire field of view in which the first projection image is connected to the second projection image.