We investigate energy allocation strategies in image sensor networks for the purpose of maximizing the network operational lifetime. For the application scenarios that we consider, visual coverage over a monitored region is obtained by deploying wireless, battery-powered image sensors. Each sensor camera provides coverage over a part of the monitored region and a central processor coordinates the sensors in order to gather required visual data. We characterize the network lifetime as a stochastic random variable that depends upon the coverage geometry for the sensors and the distribution of data requests over the monitored region. Using this characterization we consider optimized strategies for energy allocation among the sensors that maximize the expected network lifetime. The formulation naturally leads to a max-min optimization problem that aims to maximize the duration of coverage for the most critical region for which the available energy is the least. We transform this problem i...