The 3D-DCT transform: didactic experiment and possible useful tool

Abstract: This article is about an image transform called 3D-DCT, or three-dimensional discrete cosine transform. This is an extension of the well-known 1D and 2D-DCT, which is extensively used, mostly in multimedia coding. A modification of 1D-DCT (MDCT) is used in audio coding, whereas 2D-DCT is the key concept for JPEG standard (still image coding) and also for very popular video coding standards: MPEG-1 and 2, H.261 & H.263. Other, more modern methods like MPEG-4/H.264 and the newest MPEG-H/H.265 use a modified version of 2D-DCT. Nevertheless, 3D-DCT is less known. In this work, a simple implementation for 3D-DCT is constructed and some applications are explored. This is designed as a material for class work but, as it will be shown in this paper, some practical applications can be interesting. 3D-DCT can be applied for creating a video coder much simpler than those following MPEG-x/H.26x and with only slightly less performance. 3D-DCT has also been tested for 3D medical imaging (CT studies) coding, yielding very interesting results.