A hypergraphs-based image representation is already used for 2D lossless image compression. In this paper we extend this hypergraph representation on 3D-image and we add an α-tolerance. This extended representation conducts to a generalisation of the HLC lossless compression algorithm [2] for near-lossless 3D-image compression. We present an algorithm performing that compression and we give some experimental results proving its efficiency. This paper is a detailled version of the poster [3].