1. An image pickup apparatus comprising: an image pickup unit that picks up images to acquire picked-up images; an original image selecting unit that selects, as an original image, a picked-up image of a subject including a face from the picked-up images acquired by the image pickup unit; a process image selecting unit that selects, as a process image, a picked-up image to be combined with the original image from the picked-up images acquired by the image pickup unit; an image combining instructing unit that issues an instruction to combine the process image with the original image; an eye detecting unit that detects a face area from the original image, and detects an eye area based on a result of detecting the face area; a combining position setting unit that sets a combining position in the original image based on a position of the eye area detected by the eye detecting unit; an image processing unit that processes the process image; an image combining unit that combines the process image processed by the image processing unit with the original image in the combining position in the original image, and generates a composite image; an image display unit that display the composite image; and a composite image display control unit that performs control such that the composite image is displayed on the image display unit.