A novel object-based fractal monocular and stereo video compression scheme with quadtree-based motion and disparity compensation is proposed in this paper. Fractal coding is adopted and each object is encoded independently by a prior image segmentation alpha plane, which is defined exactly as in MPEG-4. The first n frames of right video sequence are encoded by using the Circular Prediction Mapping (CPM) and the remaining frames are encoded by using the Non Contractive Interframe Mapping (NCIM). The CPM and NCIM methods accomplish the motion estimation/compensation of right video sequence. According to the different coding or user requirements, the spatial correlations between the left and right frames can be explored by partial or full affine transformation quadtree-based disparity estimation/ compensation, or simply by applying CPM/NCIM on left video sequence.