Image compression is an application of data compression on digital images. Several lossy/lossless transform coding techniques are used for image compression. Discrete cosine transform (DCT) is one such widely used technique. A variation of DCT, known as warped discrete cosine transform (WDCT), is used for 2-D image compression and it is shown to perform better than the DCT at high bit-rates. We extend this concept and develop the 3-D WDCT, a transform that has not been previously investigated. We outline some of its important properties, which make it especially suitable for image compression. We then propose a complete image coding scheme for volumetric data sets based on the 3-D WDCT scheme. It is shown that the 3-D WDCT-based compression scheme performs better than a similar 3-D DCT scheme for volumetric data sets at high bit-rates.