In this paper we consider an non-parametric analytical model of the intensity for a non-rectilinear edge, and derive the relations between the image data and the edge local characteristics, in the discrete case. In order to identify this model we also study how to develop high order non-biased spatial derivative operators, with subpixel accuracy. In fact, this discrete approach corresponds to the notion of spatio-temporal surfaces in the continuous case, and provides a way to obtain some of the spatio-temporal parameters from an image sequence. An implementation proposed, and experimental data are provided.