We propose an edge filter for road white-line detection. Many methods for white-line detection have been proposed for standardized roads. These methods are composed of two stages of processing, i.e., edge detection on an image taken with a camera and then extraction of edge clusters of white-line contours by model fitting. It is difficult to apply these methods to non-standardized roads of for which modeling are difficult. To expand the scope of white-line detection to common roads in the future, it is necessary to achieve processing through clustering without models. However, while clustering can apply to diverse contour lines, there is concern about degrading noise reduction that has so far been done by model fitting. In this study, for the first-stage processing, we developed an edge filter that utilizes the characteristics of white-line contours and detects noise correctly. This filter uses brightness-gradient approximation by discrete values, for which we obtained an idea for a non-linear filter that approximates a low-pass filter plus differential calculus. By applying the method to the images taken by on-board camera, we demonstrate that white-line detection that can apply to diverse road environments but is hardly affected by noise can be realized through combination with model-less clustering.