We propose a compact description method for image gamut shell shapes. The 3-D image-to-device gamut mapping algorithm (I-D GMA) is an ideal way to map a display image into the inside of a printer gamut, keeping the loss in color information to a minimum. The key point in I-D GMA is to make use of the relation in image and device gamut boundaries along the mapping line. The image gamut surface is shaped into polygon meshes by extracting the most outside points from the random color distributions in the images. A compact gamut boundary descriptor (GBD) attached to the image data is used for executing the I-D GMA flexibly on the user side. In our proposal, the image gamut shell shape is compactly represented by a 2-D monochromatic image, called the r image. Each pixel in the r image denotes the maximum radial vector magnitude extracted from the subdivided segment in discrete polar angle color space. Since the r image is highly correlated spatially when the image has a smooth gamut shell surface, it is easily compressed by applying the conventional transform coding techniques such as the discrete cosine transform (DCT), singular value decomposition, (SVD) or wavelet. The compressed ultra-compact r image is delivered to the users attached to the image data and is used for I-D gamut mapping. We present how the complicated 3-D image gamut shell shape is simply described by the 2-D monochromatic r image and easily reconstructed with its surface colors. In practice, wavelet coding was most efficient in compressing the r image as compared with a DCT-based JPEG. It is shown that the complex shell shapes are well reconstructed from around 400 bytes of compact data compressed by SVD or less by a wavelet.