Edges and Gaps in Blurred Photographs

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In a sharp, non-blurred photo, edges consist of a light area adjacent to a darker area, with little to no gray area between them. A measurement from one edge to another is straightforward and can be done by using a ruler on the photo. If the photographer moves the camera during the exposure, as Mary Moorman did tracking the limo as it passed by her, edges and other features become spread out in the photo. There are no well-defined edge lines to measure against.

The information to locate the edge, though, is still available in the photo. One can digitize the photo and perform calculations on the brightness values of the image points (the pixels) around the edge. The following two graphs illustrates these concepts.

Each gap image below is 150 pixels high with a 50-pixel high gap in the middle. The areas surrounding the gap are brighter than the gap area, as it is with the gap of interest in the Moorman photo. The window opening and the pedestal face are brighter than the darker, shadowed wall between them. To the right of each image is a graph of the intensity (brightness) values from a column of pixels running down the middle of the image. The higher the red point in the graph, the brighter the pixel.

The top image at the right contains no blur. The edges in the graph are in the form of two steep, nearly vertical lines separated by 50 units.

The bottom image is the result of applying Photoshop's Motion Blur filter, set to 20 pixels, in the vertical direction. The edges are no longer visibly distinct. The graph shows that the formerly vertical lines are now tilted because the intensity gradually changes from light to dark and back again.

Although the edges are blurred, one can still locate the original edge positions. This information is not necessarily lost. Since the blurring algorithm is linear, one can calculate the intensity value of, say the top edge by averaging the intensity of the bright flat area above the edge (191) and the darker flat area below the edge (64). 191 plus 64 divided by 2 equals 128 (rounded up). The same average applies to the lower edge in this case. The distance between the points at the 128-intensity value is 50 pixels, the size of the original, non-blurred gap.

This demonstrates that the edge location technique Dr. Costella used is generally sound--that is, assuming the image is reasonably linear and that one locates the proper "above" and "below" points (the flat areas in the graph surrounding the edge). However, noise and other photographic defects in the Moorman image complicate this measurement and may lead to errant results. That is what happened with Dr. Costella’s study

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