Moment-Based parameterization of evolving cyclograms on gradually changing slopes

gradually changing slopes Ambarish Goswami and Emmanuel Cordier INRIA Rhône-Alpes, Grenoble, France e-mail: [email protected] Abstract The problem under study is the parameterization of a series of gradually evolving cyclograms with a small number of feature descriptors. The descriptors we selected are the geometric moments of the cyclograms. The thesis of the work is that the gradual evolution of gait on inclined planes, which is manifested by the progressive shape change of these closed-contour curves, can be tracked by observing the evolution of the moment parameters. Parameterization of cyclograms has several useful applications including the quanti cation of normal gait and the diagnosis of pathological gait. The cyclograms considered in this study were obtained from natural human walk on a variableinclination treadmill with slope varying from 13 to +13 at each 1 interval. Although in this work we limit ourselves to planar cyclograms consisting of hip angle and knee angle, the described method is fairly general in nature and may be used without restriction for any closed curve such as the phase diagrams and the moment-angle diagrams. Moreover, the method can be extended to higher dimensions and thus we can treat cyclograms involving three or more joint angles. Moment-based identi cation of physical objects from their images is a topic of active research in the eld of pattern recognition. We perform the necessary adaptations of these techniques to make them suitable for our purpose. We collected sagittal plane position data of retro-re ective markers attached to the traditionally used bony landmarks of two healthy treadmill-habituated male subjects with a video camera as seen in Fig. 1(a). The treadmill speed was adjusted so that the subjects could walk with their natural gaits. After each run, consisting of several datasets from the same slope, the treadmill inclination was changed without any pre-speci ed order to prevent any anticipatory gait by the subjects. The marker position data were subsequently smoothed using a Butterworth lter and the inter-segmental angles were extracted from them. Fig. 1(b) exhibits the substantial change in the forms of the hip-knee cyclograms. The results are similar to those found by [4].