1. A road shape estimation apparatus, mounted to a vehicle, for estimating a shape of a road on which the vehicle runs, the road shape estimation apparatus comprising: an object detection section for detecting, as a plurality of detected points, a position of a stationary object which is around the vehicle; a starting point candidate selection section for selecting, as starting point candidates, points that satisfy predetermined conditions, from among the detected points; a starting point determination section for determining, as a starting point, a point closest to the vehicle in distance, by selecting from among the starting point candidates; a detected point connection section for sequentially connecting between the starting point and one of the detected points that is a point to be connected, so as to start from the starting point, and for thus grouping detected points; a road shape estimation section for estimating, as a shape of the road, a shape of a connection line obtained by grouping the detected points; a storage section for storing information of the detected points detected by the object detection section; and an extrapolation processing section for extrapolating, based on information of the detected points which have been previously obtained and stored in the storage section, current positions of the detected points which have been previously obtained, as the detected points, wherein the starting point candidate selection section includes a reliability determination section for calculating a reliability representing a possibility that each detected point represents a roadside stationary object positioned along the road, based on previous positions of the detected points which are stored in the storage section, and determining whether or not the reliability represents a value greater than or equal to a predetermined threshold value, and selects, as the starting point candidates, each detected point that satisfies, as one of the predetermined conditions, a condition that the reliability of said detected point is determined, by the reliability determination section, to represent a value greater than or equal to the predetermined threshold value, from among the detected points that have been actually detected by the object detection section, and the detected points that have been extrapolated by the extrapolation processing section, the reliability determination section calculates the reliability of each detected point as a relatively small value when the detected points are points extrapolated by the extrapolation processing section, and the reliability determination section calculates the reliability of each detected point as a relatively great value when the detected points are points that are actually detected by the object detection section.