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Object-based video coding is a relatively new technique to meet the fast growing demand for interactive multimedia applications. Compared with conventional frame-based video coding, it consists of two types of source data: shape information and texture information. Recently, joint source-channel coding for multimedia communications has gained increased popularity. However, very limited work has been conducted to address the problem of joint source-channel coding for object-based video. In this paper, we propose a cost-distortion optimal unequal error protection (UEP) scheme for object-based video communications. Our goal is to achieve the best video quality (minimum total expected distortion) with constraints on transmission cost and delay in a lossy network environment. The problem is solved using Lagrangian relaxation and dynamic programming. The performance of the proposed scheme is tested using simulations of a narrow-band block-fading wireless channel with additive white Gaussian noise and a simplified differentiated services Internet channel. Experimental results indicate that the proposed UEP scheme can significantly outperform equal error protection methods.