An image-based measurement technique that directly measures the orientation of fibers in a moving web that comprises nonwoven material measures the orientation angles of the individual fibers so that a more robust estimate of the statistical distribution of fibers is obtained. The technique includes the steps of: (a) illuminating an area on at least one side of the web with radiation; (b) obtaining at least one digital image of the illuminated area; and (c) calculating the fiber orientation of the web by processing the at least one digital image with a gradient operator thereby analyzing the distribution of observed fiber orientation angles within the image. The gradient operator is preferably of a non-integer order between 1/3 and 2/3 and particularly between 1/4 and 3/4. The use of fractional-gradient operators yields more reliable results than when integer order gradients are employed.