Container technology is getting popular in cloud environments due to its lightweight feature and convenient deployment. The container registry plays a critical role in container-based clouds, as many container startups involve downloading layer-structured container images from a container registry. However, the container registry is struggling to efficiently manage images (i.e., transfer and store) with the emergence of diverse services and new image formats. The reason is that the container registry manages images uniformly at layer granularity. On the one hand, such uniform layer-level management probably cannot fit the various requirements of different kinds of containerized services well. On the other hand, new image formats organizing data in blocks or files cannot benefit from such uniform layer-level image management. In this paper, we perform the first analysis of image traces at multiple granularities (i.e., image-, layer-, and file-level) for various services and provide an in-depth comparison of different image formats. The traces are collected from a production-level container registry, amounting to 24 million requests and involving more than 184 TB of transferred data. We provide a number of valuable insights, including request patterns of services, file-level access patterns, and bottlenecks associated with different image formats. Based on these insights, we also propose two optimizations to improve image transfer and application deployment.