Analyzing and modelling a person's gait with computer vision algorithms has indeed some interesting advantages over more traditional biometrics. For instance, gait can be analyzed and modelled at a distance by observing the person with a camera, which means that no markers or sensors have to be worn by the person. Moreover, gait analysis and modelling using computer vision algorithms does not require the cooperation of the observed people, which thus allows for using gait as a biometric in surveillance applications. Current gait analysis and modelling approaches have however severe limitations. For instance, several approaches require a side view of the walks since this viewpoint is optimal for gait analysis and modelling. Most approaches also require the walks to be observed far enough from the camera in order to avoid perspective distortion effects that would badly affect the resulting gait analyses and models. Moreover, current approaches do not allow for changes in walk direction and in walking speed, which greatly constraints the walks that can be analyzed and modelled in medical and surveillance applications. The approach proposed in this thesis aims at performing gait analysis, modelling and comparison from unconstrained walks and viewpoints in medical and surveillance applications. The proposed approach mainly consists in a novel view-rectification method that generates a fronto-parallel viewpoint (side view) of the imaged trajectories of body parts. The view-rectification method is based on a novel walk model that uses projective geometry to provide the spatio-temporal links between the body-part positions in the scene and their corresponding positions in the images. The head and the feet are the only body parts that are relevant for the proposed approach. They are automatically localized and tracked in monocular video sequences using a novel body parts tracking algorithm. Gait analysis is performed by a novel method that extracts standard gait measurements from the view-rectified body-part trajectories. A novel gait model based on body-part trajectories is also proposed in order to perform gait modelling and comparison using the dynamics of the gait. The proposed approach is first validated using synthetic walks comprising different viewpoints and changes in the walk direction. The validation results shows that the proposed view-rectification method works well, that is, valid gait measurements can be extracted from the view-rectified body-part trajectories. Next, gait analysis, modelling, and comparison is performed on real walks acquired as part of this thesis. These walks are challenging since they were performed close to the camera and contain changes in walk direction and in walking speed. The results first show that the obtained gait measurements are realistic and correspond to the gait measurements found in references on clinical gait analysis. The gait comparison results then show that the proposed approach can be used to perform gait modelling and comparison in the context of surveillance applications by recognizing people by their gait. The computed recognition rates are quite good considering the challenging walks used in this thesis.