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Most existing works on routing for video transmission over multihop wireless networks only focus on how to satisfy the network-oriented quality-of-service (QoS), such as through put, delay, and packet loss rate rather than application-oriented QoS such as the user-perceived video quality. Although there are some research efforts which use application-centric video quality as the routing metric, they either calculate the video quality based on some predefined rate-distortion function or model without considering the impact of video coding and decoding (including error concealment) on routing, or use exhaustive search or heuristic methods to find the optimal path, leading to high computational complexity and/or suboptimal solutions. In this paper, we propose an application-centric routing framework for real-time video transmission in multihop wireless networks, where expected video distortion is adopted as the routing metric. The major contributions of this paper are: 1) the development of an efficient routing algorithm with the routing metric expressed in terms of the expected video distortion and being calculated on-the-fly, and 2) the development of a quality-driven cross-layer optimization framework to enhance the flexibility and robustness of routing by the joint optimization of routing path selection and video coding, thereby maximizing the user-perceived video quality under a given video playback delay constraint. Both theoretical and experimental results demonstrate that the proposed quality-driven application-centric routing approach can achieve a superior performance over existing network-centric routing approaches.