Video processing plays an essential role in a wide range of cloud-based applications. It typically involves multiple pipelined stages, which well fits the latest fine-grained serverless computing paradigm if properly configured to match the cost and delay constraints of video. Existing configuration tools, however, are primarily developed for traditional virtual machine clusters with general workloads. This paper presents CharmSeeker, an automated configuration tuning tool for serverless video processing pipelines. We first carefully examine the key steps and the performance bottlenecks for video processing over modern serverless platforms. Then, we identify the configuration space for processing pipelines and leverage a carefully designed Sequential Bayesian Optimization search scheme to identify promising configurations. We further address the practical challenges toward integrating our solution into real-world systems and develop a prototype with AWS Lambda. Evaluation results show that CharmSeeker can find out the optimal or near-optimal configurations that improve the relative processing time up to 408.77%. It is also more robust and scalable to various video processing pipelines compared with state-of-the-art solutions.