1. A device for detecting a boundary of a roadway upon which a vehicle travels, the device comprising: camera means for generating electronic signals representing an image of the roadway, the image comprising a view of the roadway extending in a direction of travel of the vehicle; a signal inputting unit for digitizing the signals representing the image of the roadway; an edge detecting unit for processing the digitized signals to produce edged picture element signals differentiated with respect to pixel to pixel brightness variations; a preprocessing unit for receiving the edged picture element signals from the edge detecting unit and storing in a multivalue memory circuit edged picture data corresponding to the edged picture element signals, the edged picture data corresponding to each edged picture element signal comprising an address in an X-Y coordinate system and an edged brightness value; digital differential analysis computing means including a plurality of digital differential analysis computing circuits which are serially connected, each for converting the addresses of the edged picture data from the X-Y coordinate system to an .alpha.-.beta. coordinate system and computing a rotary motion recurrence formula to generate a plurality of approximate HOUGH curves in a .rho.-.theta. coordinate system, the approximate HOUGH curves intersecting at a plurality of points in the .rho.-.theta. coordinate system, and said rotary motion recurrence formula comprising the equation EQU .alpha..sub.i+1 =.alpha..sub.i -2.sup.-m .beta..sub.i ; and EQU .beta..sub.i+1 =2.sup.-m .alpha..sub.i+1 +.beta..sub.i wherein an angle of rotation comprises EQU .epsilon.=2.sup.-m (rad) (m=0, 1, 2,. .. ); a histogram memory circuit for storing address data corresponding to the intersection points between the generated approximate HOUGH curves; and a processor for generating a signal representing the boundary of the roadway based on the stored address data corresponding to the intersection points of the approximate HOUGH curves.