Prof. Lakaemper,

I'm attaching assignment 7. To simply compress the image using
a constant frequency threshold, run compressImg(source,
threshold). I used the histogram distance we developed in the
second assignment to perform thresholding in the spatial
domain, but I normalized the measure to fall between 0 and 1
(though almost everything seems to fall between .2 and .3).
The function determineThreshold(source, histogramThreshold)
will automatically determine a Fourier threshold to match the
spatial one.

In the second part of the assignment, rather than increasing
the amplitude of the higher coefficients, I created a
two-dimensional linear thresholding function (a plane). An
interesting observation that I made is while the image appears
very different to me with the linear thresholding function,
the histogram distance does not significantly change with
inclusion of more of the high frequency components
(determineThreshold has an optional third argument for the
slope of the plane in both dimensions, but it rarely alters
the results).

The createHighpass(source, slope, intercept) function will
create a linear thresholding function to be used on the
Fourier coefficients, which can be used as an argument to
compressImg. The slope argument should be negative, since we
want a lower threshold for higher frequencies.

It didn't seem to make sense to allow different slopes in
different dimensions, since the desired detail is probably the
same for horizontal and vertical edges.

Thanks,
Michael