Stephan Paukner :: syslog

Besides the fact that it was a pain to find out how ImageMagick’s -average option is to be used, it turned out to operate wrongly. The switch calculates the mean of an image sequence, i.e. the mean color values for every pixel. Say, if you have a bunch of images with file names like img*.jpg and want the average saved into avg.jpg, the command line is:

Pretty intuitive. The problem is that you define the mean image Ī[n] of n images I[k] as

while ImageMagick does it recursively as

(with Ĩ[1]=I[1]),

giving you wrong weights ¹⁄_2^n−k+1 like e.g. for n=8

instead of the intended weights ¹⁄_n like

.

This misbehaviour can be proven e.g. by taking this sequence of a plain blue, green and red image:

and averaging it with the above command. The result is too reddish:

The solution I found was to call convert recursively like this:

By this, the average of the above example images correctly becomes gray:

There might be similar problems with the other image sequence operators, but I haven’t examined them. Maybe I should file a bug.

Eric Brasseur explained a “bug” in the scaling algorithm of current image processing software. It’s not really a bug, technically, or mathematically. Calculating the numerical average of the surroundings of a pixel as the new color value is a pretty correct approach to scale an image down—if it’s seen as a data matrix. Rather, it’s visually not the thing you’d expect.

Technically speaking, the problem is that “the computations are performed as if the scale of brightnesses was linear while in fact it is an exponential scale.” In mathematical terms: “a gamma of 1.0 is assumed while it is 2.2.”

Here’s an example of what might occur:

The wrong way:

1. Take this image as a start:
   
2. Simply scale it down to 50%:
   

Obviously, this might not be what you intended.

The right way: