This paper proposes an approach to compute view-normalized body part trajectories of pedestrians walking on potentially non-linear paths. The proposed approach finds applications in gait modeling, gait biometrics, and in medical gait analysis. Our approach uses the 2D trajectories of both feet and of the head extracted from the tracked silhouettes. On that basis, it computes the apparent walking (sagittal) planes for each detected gait half-cycle. A homography transformation is then computed for each walking plane to make it appear as if walking was observed from a fronto-parallel view. Finally, each homography is applied to head and feet trajectories over each corresponding gait half-cycle. View normalization makes head and feet trajectories appear as if seen from a fronto-parallel viewpoint, which is assumed to be optimal for gait modeling purposes. The proposed approach is fully automatic as it requires neither manual initialization nor camera calibration. An extensive experimental evaluation of the proposed approach confirms the validity of the normalization process.