An important issue in object-based image coding is the efficient description of image segments having an arbitrary shape. This paper outlines a solution to this task using basic principles of transform image coding that are generalized for the case of arbitrarily shaped image segments. The texture inside each region is successively approximated using two-dimensional (2-D) shape-independent basis functions defined on a rectangle circumscribing the given image segment. The resulting texture description exhibits a high energy compactness and is well suited for low bit rate image coding. Unlike other approaches aimed at segment-oriented image coding, the proposed concept does not couple texture description with contour coding. The computational load is kept low, especially for the decoding process.