1. A noncontact biometric identification device, comprising: a sensor that detects feature data including a feature of a part of a living body at a plurality of positions in a range defined in advance in a real space when the part of the living body moves in the range to acquire enrollment data, wherein the feature data is linked to position data relating to the plurality of the positions in the range and to posture data about a posture of the part of the living body at the plurality of positions while detection; a processor that arranges a specified number of hyperspheres in a comparison range defined in advance in a feature space along a line defined by a locus of the living body in the real space, wherein the feature space is spanned by a coordinate specifying a position of the part of the living body in the real space and a variable specifying the posture of the part of the living body, and the comparison range includes a space corresponding to the range in the real space and a space corresponding to a space covered by the posture detected by the sensor, such that the hyperspheres run over the comparison range, do not overlap one another, and have maximum radii, and then selects the feature data detected at one of the positions in the real space closest to the position corresponding to the center of one of the hyperspheres as the enrollment data with top priority; and a memory that stores the enrollment data with a variable specifying the position in the real space detected by the sensor, and the posture of the part of the living body.