A new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented. For one-dimensional edge patterns an ideal edge is fit to the data by matching moments. It is shown that the edge location is related to the so-called ``Christoffel numbers.'' Also presented is the study of the effect of additive noise on edge location. The method is extended to include two-dimensional edge patterns where a line equation is derived to locate an edge. This in turn is compared with the standard Hueckel edge operator. An application of the new edge operator as an edge detector is also provided and is compared with Sobel and Hueckel edge detectors in presence and absence of noise.