Embryonic heart morphogenesis (EHM) is a complex and dynamic process where the heart transforms from a single tube into a four-chambered pump. This process is of great biological and clinical interest but is still poorly understood for two main reasons. On the one hand, the existing imaging modalities for investigating EHM suffered from either limited penetration depth or limited spatial resolution. On the other hand, current works typically adopted manual segmentation, which was tedious, subjective, and time consuming considering the complexity of developing heart geometry and the large size of images. In this paper, we propose to utilize confocal microscopy imaging with tissue optical immersion clearing technique to image the heart at different stages of development for EHM study. The imaging method is able to produce high spatial resolution images and achieve large penetration depth at the same time. Furthermore, we propose a novel convex active contour model for automatic image segmentation. The model has the ability to deal with intensity fall-off in depth which is characterized by confocal microscopy images. We acquired the images of embryonic quail hearts from day 6 to day 14 of incubation for EHM study. The experimental results were promising and provided us with an insight view of early heart growth pattern and also paved the road for data-driven heart growth modeling.