We present a computational approach to analyze the cellular organization during the elongation process of the ovine conceptus. First, we selected a set of mathematical descriptors to quantify cell geometry and cell neighborhood within the external epithelial layer of the conceptus: the trophoblast. Second, we established a hybrid image segmentation framework, and analyzed the extracted features with statistical tools to describe and compare the spatio-temporal dynamics of cellular organization within this epithelium. The main results indicated that the average geometry and neighborhood of the trophoblast cells are relatively stable from a sampling position to another and from a stage of development to another. Further, their elongation axes are randomly distributed. The cellular organization fits the Poisson's process. Moreover, no clustering structures or grid-like regular point patterns are found inside the studied cell population. This suggests that the trophoblast elongation observed in ruminants is not due to the geometrical change of cell shape but might be the consequence of cell addition associated with peculiar plans of cell division or intercalation.