1. A vehicle periphery monitoring apparatus comprising: a camera installed in a front or rear of a vehicle, for picking up images of a side view of the vehicle; feature point detecting means for detecting feature points in the side images and calculating motion vectors of the detected feature points; approaching object detecting means for detecting an object having a vector in such a direction as to approach the vehicle in the side images as an approaching object based on the calculated motion vectors of the feature points; feature point tracking means for tracking the feature points of the detected approaching object; and passage time calculating means for calculating a time at which the approaching object passes the front or rear of the vehicle from the feature points of the approaching object tracked by said feature point tracking means.