This paper introduces a set of techniques for processing video data compressed using JPEG compression at near real-time rates on current generation workstations. Perfor- mance is improved over traditional methods by processing video data in compressed form, avoiding compression and decompression and reducing the amount of data processed. An approximation technique called condensation is devel- oped that further reduces the complexity of the operation. The class of operations that are computable using the tech- niques developed in this paper are called linear, global digi- tal specials effects (LGDSES), and represent those effects where a pixel in the output image is a linear combination of pixels in the input image. Many important video processing problems, including convolution, scaling, rotation, transla- tion, and transcoding can be expressed as LGDSES.