1. A vehicular periphery monitoring apparatus configured to monitor a periphery of a vehicle according to an image acquired from a single imaging device mounted in the vehicle to denote the periphery of the vehicle, comprising: a first processing element configured to: set a region in the image where an object is present as an object region; determine the type of the object; retrieve a motion cycle time corresponding to the object from a storing device; and set the motion cycle time as a specified interval; and a second processing element configured to: calculate a change rate of the size of the object region between two times separated by the specified interval; and determine a distance from the vehicle to the object according to the specified interval and the change rate of the size of the object region, wherein the object preforms movement that changes a shape or a posture thereof cyclically according to the motion cycle time, wherein the motion cycle time corresponds to a length of time in which it takes an object a transform between a first shape or posture, one or more interim shapes or postures, and a return to the first shape or posture.