Data compression of stereo images and video EdirisingheEran 2020 One of the amazing properties of human vision is its ability to feel the depth of the scenes being viewed. This is made possible by a process named stereopsis, which is the ability of our brain to fuse together the stereo image pair seen by two eyes. As a stereo image pair is a direct result of the same scene being viewed by a slightly different perspective they open up a new paradigm where spatial redundancy could be exploited for efficient transmission and storage of stereo image data. This thesis introduces three novel algorithms for stereo image compression. The first algorithm improves compression by exploiting the redundancies present in the so-called disparity field of a stereo image pair. The second algorithm uses a pioneering block coding strategy to simultaneously exploit the inter-frame and intra-frame redundancy of a stereo image pair, eliminating the need of coding the disparity field. The basic idea behind the development of the third algorithm is the efficient exploitation of redundancy in smoothly textured areas that are present in both frames, but are relatively displaced from each other due to binocular parallax. Extra compression gains of up to 20% have been achieved by the use of these techniques. The thesis also includes research work related to the improvement of the MPEG-4 video coding standard, which is the first audiovisual representation standard that understands a scene as a composition of audio-visual objects. A linear extrapolation based padding technique that makes use of the trend of pixel value variation often present near object boundaries, in padding the exterior pixels of the reference video object has been proposed. Coding gains of up to 7% have been achieved for coding boundary blocks of video objects. Finally a contour analysis based approach has been proposed for MPEG-4 video object extraction.