1. A feature identification apparatus comprising: a labeling processing unit that extracts, via a processor, a point cloud continuing from a position within a point cloud of a road surface shape model, the road surface shape model being a three-dimensional point cloud model generated based on distance and orientation data showing distance and orientation for a feature measured from a running vehicle, and forms groups within the point cloud of the road surface shape model; an edge determining unit that determines an edge part from a line segment formed by a point cloud for each group grouped by the labeling processing unit, and groups the group using the edge part as a border; and a feature identifying unit that determines a type of feature represented by a point cloud of each group based on a position and a shape shown by a point cloud for each group grouped by the edge determining unit, wherein the groups formed by the labeling processing unit include a first group that is grouped into a first sub-group, second sub-group and third sub-group, the first sub-group having a point cloud corresponding to a position of the running vehicle, the second sub-group having one or more point clouds located higher than the first sub-group within a predetermined range and being continuous in vertical and horizontal directions, and the third-sub group having one or more point clouds continuous in the vertical direction.