2-D transform-domain resolution translation

The extensive use of discrete transforms in image and video coding suggests the investigation on filtering before downsampling (FBDS) and filtering after upsampling (FAUS) methods directly acting on the transform domain. We describe the "transform-damain resolution translation" technique that gives flexibility to resize windows of each video conferencing session for a server compositing without explicit decompression, spatial domain processing, and compression. We generalize transform-domain filtering (TDF) to include nonuniform and multirate cases to implement the transform-domain resolution translator. The former is defined as a TDF problem in which the original transform-domain is of different size from the target one, while the latter considers the implementation of sampling rate conversion in the transform-domain. The implementation architecture is based on a pipeline that involves matrix-vector product blocks and vector addition, but is not limited to particular hardware. Such techniques are particularly useful for fast algorithms for processing compressed images and video where transform coding is extensively used (e.g., in JPEG, H.261, MPEG-1, MPEG-2, and H.363).