1. A three-dimensional (3D) image processing apparatus, comprising: an image processor, comprising: a geometry information analyzer to analyze geometry information of a target region of an image within an input depth image of the 3D image; and a feature point extractor to select at least one feature point from the target region based on the geometry information of the target region, wherein the geometry information comprises a surface normal vector of a pixel included in the target region, and wherein the feature point extractor selects the at least one feature point based on an angle difference between the surface normal vector and a surface normal vector of a neighboring pixel of the pixel.