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 of an eye based on a result of detecting the face area; a combining position setting unit that sets a combining position, in which the process image selected by the process image selecting unit is to be combined as a catch light, in the original image based on a position of the eye area detected by the eye detecting unit; an image processing unit that performs, on the process image selected by the process image selecting unit, at least any one of trimming processing and transparency processing; 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 set by the combining position setting unit, 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, wherein the image processing unit further performs distortion processing by setting a predetermined position in the process image as a distortion center, and distorting the process image about the distortion center, wherein the eye detecting unit determines an eye direction of the eye based on a result of detecting the eye area, and wherein the image processing unit sets, in accordance with a pupil reference position determined from the eye direction of the eye determined by the eye detecting unit, the distortion center in the process image based on a relative position of the pupil reference position with respect to the eye area in the distortion processing.