The region-based description of multispectral images enables important high-level tasks such as data mining and retrieval, and region-of-interest selection. In order to obtain an efficient representation of such images we resort to adaptive transform coding techniques. Such techniques, however, require a considerable information overhead, which must be carefully managed to obtain a satisfactory rate-distortion performance. In this work we develop several region-based coding schemes and compare them with conventional (non-adaptive) and class-based schemes, so as to single out the rate-distortion gains/losses of this approach.