  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.
