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In this paper, an optimal framework is proposed for the joint encoding of the shape and texture information in object based video. The solution is optimal in the operational rate distortion sense, i.e, given the coding setup, the solution guarantees the smallest possible distortion for a given rate. The shape is approximated using polygons or higher order curves. We also consider biasing the cost function to favor horizontal and vertical edges, for the case of polygon approximation (biased polygon approximation). The texture is encoded using shape adaptive discrete cosine transform (SA-DCT) or shape adaptive discrete wavelet transform (SA-DWT) of the MPEG-4 video codec. A comparison is drawn between the two techniques. Both a fixed-width and a variable-width tolerance band for shape coding are considered. The variable width of the tolerance band is a function of the texture profile, i.e, the width is inversely proportional to the magnitude of the image gradient. Experimental results are presented and conclusions are drawn.