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In this letter, we explore the rate-distortion (R-D) characteristics of binary shape information in the MPEG-4 standard. The shape coding scheme is a block-based context-based arithmetic encoding approach and distortion is introduced by down and up sampling. Generally, the shape bit rate and nonnormalized distortion increase in proportion with the number of border blocks. At any given resolution scale, the more complex an object, the more distortion that is introduced. Consequently, we propose an R-D model based on the parameters derived from the border blocks and a block-based shape complexity for the video object. The computational complexity is much lower than other existing methods. Experimental results show that it can accurately predict the bit rate and distortion of the binary shape for rate control purposes.