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MPEG-4 is the first multimedia standard that supports the decoupling of a video object into object shape and object texture information, which consequently brings up the optimal encoding problem for object-based video. In this paper, we present an operational rate-distortion optimal bit allocation scheme between shape and texture for MPEG-4 encoding. Our approach is based on the Lagrange multiplier method, while the adoption of dynamic programming techniques enables its higher efficiency over the exhaustive search algorithm. Our work will not only benefit the further study of joint shape and texture encoding, but also make possible the deeper study of optimal joint source-channel coding of object-based video.