ENGS 111 - Homework Assignment 2
Due 4/15 Friday before class

Part 1 - Playing with Frequency Domain Filters.

Devise the following 3 filters:
a) One that removes details that are oriented in the vertical direction
b) One that removes details that are oriented in the horizontal direction
c) One that removes details oriented at 45°

Explain your reasoning and show your results in a composite figure. For each filter, include the
following images in your composite figure:
a) the original image provided (H-V-45_test_image.ppm)
b) the FFT of the original image
c) your frequency domain filter
d) the image resulting from applying your filter on the original image

First use it on the H-V-45_test_image.ppm image, then try it on any other image you like, could
be one of your own photographs. It will help to remember what we learned about the FFT of
rotated images. A bit of trial and error may serve as guidance as well.

Part 2 – Experimenting with Everything you Know so Far

You may remember an example image that consisted of an image of a poem printed on a sheet
of paper and photographed with a very bright light source that causes a shading gradient. The
supplied image "handwriting.png" presents a similar problem in that shading precludes easily
thresholding the handwriting.

Part 2.1
The first part of this assignment is to work out a filter that will remove the lighting gradient from
the image and make it possible to threshold it to make the writing readable. At this stage, your
filter is only expected to remove the background gradient, proceeding exclusively in the
frequency domain. I suggest you think of the lighting gradient as a large scale feature in the
spatial domain. Show your "improved" image next to the original, after filtering the lighting
gradient. Are there still features you'd like to be able to remove?

Part 2.2
Let's make the problem slightly more complicated (but not much) by requiring that we remove
the graph paper lines that are still visible. You may design a 2nd filter that will remove the
gridlines using what you know about filter properties. You may use as few or as many stages (i.e.
separate filters) and operations (i.e. rotate something) as you want.