1. A feature identification apparatus comprising: a labeling processing unit for extracting a point cloud continuing from a position of a point cloud of a road surface shape model which is a three-dimensional point cloud model generated based on distance and orientation data showing distance and orientation for the feature measured from a running vehicle, and for grouping the point cloud of the road surface shape model; an edge determining unit for determining an edge part from a line segment formed by a point cloud for each group grouped by the labeling processing unit, and for grouping the group using the edge part as a border; and a feature identifying unit for determining 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.