1. A periphery surveillance apparatus comprising: a storage section that stores captured image data output from a capturing section for capturing an image of a region including a road surface and a region upward from the road surface, in a traveling direction of a vehicle; a display section that selectively displays at least one of a past image and a present image among pieces of captured image data which are stored in the storage section, the past image based on captured image data corresponding to a current underfloor area of the vehicle, and the present image based on new captured image data which is captured and output by the capturing section; and a control section that performs switching to the past image when a permission condition for permitting display of the past image is established during a time when the present image is displayed in the display section and performs switching to the present image when a recovery condition for performing recovery to the present image is established during a time of displaying the past image is displayed in the display section.