We describe an approach to characterize the signatures generated by walking humans in spatio-temporal domain. To describe the computational model for this periodic pattern, we take the mathematical theory of Geometry Group Theory, which is widely used in crystallographic structure research. Both empirical and theoretical analysis prove that spatio-temporal helical patterns generated by legs belong to the Frieze Groups because they can be characterized by a repetitive motif along the direction of walking. The theory is applied to an automatic detection-and-tracking system capable of counting heads and handling occlusion by recognizing such patterns. Experimental results for videos acquired from both static and moving ground sensors are presented. Our algorithm demonstrates robustness to nonrigid human deformation as well as background clutter.