We present a novel approach to gait recognition that considers gait sequences as cyclostationary processes on a shape space of simple closed curves. Consequently, gait analysis reduces to quantifying differences between statistics underlying these stochastic processes. The main steps in the proposed approach are: (i) off-line extraction of human silhouettes from IR video data, (ii) use of piecewise-geodesic paths, connecting the observed shapes, to smoothly interpolate between them, (iii) computation of an average gait cycle within class (i.e. associated with a person) using average shapes, (iv) registration of average cycles using linear and nonlinear time scaling, (iv) comparisons of average cycles using geodesic lengths between the corresponding registered shapes. We illustrate this approach on infrared video clips involving 26 subjects.