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Wireless video sensor networks (WVSNs) have been envisioned for a wide range of important applications, including battlefield intelligence, security monitoring, emergency response, and environmental tracking. Compared to traditional communication system, the WVSN operates under a set of unique resource constraints, including limitations with respect to energy supply, on-board computational capability, and transmission bandwidth. The objective of this paper is to study the resource utilization behavior of a wireless video sensor and analyze its performance under the resource constraints. More specifically, we develop an analytic power-rate-distortion (P-R-D) model to characterize the inherent relationship between the power consumption of a video encoder and its rate-distortion performance. Based on the P-R-D analysis and a simplified model for wireless transmission power, we study the optimum power allocation between video encoding and wireless transmission and introduce a measure called achievable minimum distortion to quantify the distortion under a total power constraint. We consider two scenarios in wireless video sensing, small-delay wireless video monitoring and large-delay wireless video surveillance, and analyze the performance limit of the wireless video sensor in each scenario. The analysis and results obtained in this paper provide an important guideline for practical wireless video sensor design.