1. An image processing apparatus that morphs at least part of a face of a subject in an input image, comprising: an image acquiring unit that acquires the input image; an object specifying unit that specifies an object that is included in the input image and is to be morphed, wherein the object is the at least part of the face of the subject in the input image; a map storage unit in which a shift amount map is stored, wherein the shift amount map defines a target point and shift amounts of pixels in a two-dimensional plane along a direction from a position of the pixels to the target point and represents shift amount peaks as a predetermined shape; a map morphing unit that morphs an entirety of the shift amount map such that the predetermined shape of the shift amount peaks in the map matches a shape of the object to be morphed; an image morphing unit that morphs the image by: matching the target point in the morphed shift amount map with a target point in the object to be morphed; converting a resolution of the morphed shift amount map so as to match with a resolution of the input image; and determining a pixel value of a target pixel that corresponds to the object as a pixel value of a pixel that is located in a straight line connecting the target point and the target pixel in the input image, the pixel also being located away from the target pixel by a shift amount defined for the target pixel in the morphed shift amount map; and a display that displays the morphed image, wherein the image acquiring unit, the object specifying unit, the map morphing unit, and the image morphing unit are components of an image capturing apparatus, and wherein the predetermined shape is a closed loop.