Understanding the cellular and mechanical processes that underlie the shape changes of individual cells and their collective behaviors in a tissue during dynamic and complex morphogenetic events is currently one of the major frontiers in developmental biology. The advent of high-speed time-lapse microscopy and its use in monitoring the cellular events in fluorescently labeled developing organisms demonstrate tremendous promise in establishing detailed descriptions of these events and could potentially provide a foundation for subsequent hypothesis-driven research strategies. However, obtaining quantitative measurements of dynamic shapes and behaviors of cells and tissues in a rapidly developing metazoan embryo using time-lapse 3D microscopy remains technically challenging, with the main hurdle being the shortage of robust imaging processing and analysis tools. We have developed EDGE4D, a software tool for segmenting and tracking membrane-labeled cells using multi-photon microscopy data. Our results demonstrate that EDGE4D enables quantification of the dynamics of cell shape changes, cell interfaces and neighbor relations at single-cell resolution during a complex epithelial folding event in the early Drosophila embryo. We expect this tool to be broadly useful for the analysis of epithelial cell geometries and movements in a wide variety of developmental contexts.