Region oriented image representation offers several advantages over block-oriented schemes, e.g. adaptation to the local image characteristics, or object motion compensation as opposed to block-wise motion compensation. For the task of image data compression, i.e. image coding, new algorithms are needed which work on arbitrarily shaped image regions, called segments, instead of rectangular image blocks. Based on a generalized moment approach, the luminance function inside the segment is approximated by a weighted sum of basis functions, for example polynomials. A set of basis functions which is orthogonal with respect to the shape of the segment to be coded can be obtained using orthogonalization schemes. This results in the derivation of a generalized shape-adapted transform coder. Suitable coder and decoder structures are introduced which do not necessitate the transmission of the basis functions for each segment. Finally an application of the derived algorithms to image sequence coding at low data rates is shown, which is based on a segmentation of the motion compensated prediction error image.