1. An image capturing apparatus, comprising: a processor; and an image capturing section which comprises an image sensor, and which, under control of the processor, sequentially outputs plural pieces of image data, wherein the plural pieces of the image data are captured in a single continuous shooting operation during which the image capturing section is moved in a predetermined panoramic direction, and wherein adjacent pieces of the captured image data which are adjacent to each other in the predetermined panoramic direction each include corresponding overlapping regions which are captured over a same range in the predetermined panoramic direction, such that one piece of the image data includes (i) a first overlapping region which overlaps a second overlapping region of a preceding adjacent piece of the image data, wherein the first overlapping region of the one piece of the image data and the second overlapping region of the preceding adjacent piece of the image data are captured over a first range in the predetermined panoramic direction, and (ii) a second overlapping region which overlaps a first overlapping region of a succeeding adjacent piece of the image data, wherein the second overlapping region of the one piece of the image data and the first overlapping region of the succeeding adjacent piece of the image data are captured over a second range in the predetermined panoramic direction; wherein the processor is further configured to perform control to realize functions of: a control section which performs control to change, at predetermined timings in the single continuous shooting operation, luminances of the plural pieces of the image data such that the adjacent pieces of the image data which are adjacent to each other have respective different luminances; a specification section which specifies, for the adjacent pieces of the image data, plural sets of corresponding overlapping regions of the adjacent pieces of the image data as targets for composite processing, wherein said plural sets include a first set comprising the first overlapping region of the one piece of the image data and the corresponding second overlapping region of the preceding adjacent piece of the image data, and a second set comprising the second overlapping region of the one piece of image data and the corresponding first overlapping region of the succeeding adjacent piece of the image data, and wherein, in each of the plural sets, the first and second overlapping regions have respective different luminances; and a panoramic image composing section which combines the plural sets of the corresponding overlapping regions into a piece of panoramic image data.