We evaluated some arbitrary-shape ROI (Region of Interest) coding techniques for three-dimensional volumetric images, and through the observation we propose a flexible ROI coding with efficient compression performance. In arbitrary-shape ROI coding, the object in an image is coded with higher fidelity than the rest of the image, together with the shape information, which indicates the region of the object. In our proposed method (named as SA-ROI), in which shape-adaptive wavelet transform and scaling-based ROI coding are incorporated, the samples within the object are transformed with three-dimensional shape-adaptive wavelet transform according to its shape-information. If necessary, the background is also transformed by shape-adaptive wavelet transform independently. Then the samples within the object are scaled up by a certain number of bit-shifts, and encoded from the MSB (Most Significant Bit) plane by plane so that coefficients within the object are encoded earlier and have higher fidelity than the background. Compared with the scaling-based ROI coding using ordinary wavelet transform, which has almost the same ROI coding functionalities, SA-ROI outperforms by 5% in lossless compression ratio. Also in lossy coding, except at very low coding rates, SA-ROI has better compression performance.