The Effect of Motion Blurring on Contrast Edges

    Motion blurring occurs in photographs when the image, or part of it, moves across the film during the exposure.  This could be due to the camera moving while photographing a still scene, the image moving while the camera is still, or some combination of both.  The results are essentially the same.  A contrast edge in a photo is just what it sounds like.  It is a boundary between areas of different brightness or color.  These features are actually where the information, as we see it, lies.  Any measurement in a photograph is necessarily made using contrast edges.  The edges used in the measurements on this site are chosen to have high contrast because they are "preserved" better during motion blurring.  All edges do not maintain the same spatial relationship when blurred, however.  Since distances between edges are being measured, it is important to choose edges which are affected the same way so that the spatial relationship is preserved.  First, some actual images to illustrate blurring effects.

        405                        414                      412                      402

These are late frames from the Zapruder film.  In the horizontal direction the camera is pointed very nearly toward the sun so there is a great deal of contrast between the highly reflective street and the backlighted lamppost.  Frame 405 has the least amount of motion blurring and gives an idea of the actual appearance of the post. In 414 and 412, the post appears narrower.  412 appears to have been reduced on the right while in 414 it has lost width on both sides.  Note that the contrast edges forming the boundaries are still pretty sharp even though they have been "moved".  The edges are not really as sharp as they appear at first glance, however, as a faint "ghost" can be seen to the right of the the post in 412 and on both sides in 414.

      a) blurring                   b) result

    This is a schematic representation of the post against the street in 412.  The arrow indicates the direction the image is moving across the film. The white background represents the street.  The black rectangle in a) represents the position of the post on the film at the beginning of the exposure.  The red outlined rectangle represents the post's position at the end of the exposure.  Regions 1 and 3 are exposed to the bright light from the street during part of the exposure.  Region 2 is covered by the post throughout the exposure.  Due to the nonlinear response of film to light and perhaps in part to the workings of the human visual system, regions 1 and 3 look much more like the bright street rather than the post.  This is true even of the parts of the regions that are only "hit" by the street for a small fraction of the exposure.  Only 2 comes out looking like post.  An important observation is that the left edge of the post as seen in the image represents its position at the beginning of the exposure while the right edge represents its position at the end of the exposure.  The width of the post is decreased by the blur length.
    The post is chopped off on both sides in 414 because the camera reverses direction during the exposure.  I will leave it to the reader to visualize how this happens.  In 402, the blur length is greater than the width of the post so the post is completely obliterated.  What is actually visible is the part of the man standing behind the post as seen in 405.  The dark area is the part of the film that was covered by either the post or the man during the entire exposure.

    The optical density (roughly brightness) of exposed film as function of the amount of light it is exposed to is essentially exponential except at very low and very high exposures.  The following diagram shows a simulation of blurring boundaries of various contrasts where the response is modeled by an exponential function.  The top bar of each pair shows the actual boundary at the beginning of the exposure.  The arrow indicates the blurring direction.  The distance between the vertical lines is the distance that the image moves during the exposure.  The vertical line at the tail of the arrow moves to the line at the head of the arrow.  Each column contains boundaries of equal contrast. The top pair in each column represents blurring to the right.  The bottom pair shows blurring to the left. Note that, when the contrast is high, the boundary is moved  by nearly the entire blurring distance when the bright side is moved over the dark but hardly moves when dark is blurred over bright.