The present invention relate to methods and codecs for image and video compression. Embodiments of the present invention include a novel shape-adaptive model-based codec (SAM) that supports binary shapes as well as matte and soft segmentation image compression by decomposing input shapes into deterministic and stochastic components for flexible lossy and lossless coding. The present invention can provide inter/intra prediction and flexibly adapts between lossy and lossless modes with various parameters for compression quality control. The compression module can also be adapted with numerous other compression techniques.