||OC-DSSr is a digital straight line segment (DSS) recognition method in 3D non-Cartesian point lattices. A brief overview of image analysis is given, along with its relationship to digital geometry and non-Cartesian cubic lattices. The Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices are reviewed. A digitization method-dependent definition of a DSS is used to develop OC-DSSr. The supercover digitization is used to digitize curves on non-Cartesian lattices. An extension to the supercover is proposed to achieve alpha-connectivity in non-Cartesian lattices. A new independent definition of a DSS is proposed, based on the presented recognition method.