Cloud-edge collaborative computing paradigm is a promising solution to high-resolution video analytics systems. The key lies in reducing redundant data and managing fluctuating inference workloads effectively. Previous work has focused on extracting regions of interest (RoIs) from videos and transmitting them to the cloud for processing. However, a naive Infrastructure as a Service (IaaS) resource configuration falls short in handling highly fluctuating workloads, leading to violations of Service Level Objectives (SLOs) and inefficient resource utilization. Besides, these methods neglect the potential benefits of RoIs batching to leverage parallel processing. In this work, we introduce Tangram, an efficient serverless cloud-edge video analytics system fully optimized for both communication and computation. Tangram adaptively aligns the RoIs into patches and transmits them to the scheduler in the cloud. The system employs a unique ``stitching'' method to batch the patches with various sizes from the edge cameras. Additionally, we develop an online SLO-aware batching algorithm that judiciously determines the optimal invoking time of the serverless function. Experiments on our prototype reveal that Tangram can reduce bandwidth consumption and computation cost up to 74.30\% and 66.35\%, respectively, while maintaining SLO violations within 5\% and the accuracy loss negligible.