generating pyramid representation of an image

generating pyramid representation of an image

I have a homework problem that I am having a lot of difficulty
conceptualizing. I think the implementation will be fairly straightforward
once I understand my task, which is what I need help doing. The problem is
as follows:
Given an input image, generate its pyramid representation by smoothing and
downsampling with a scaling ratio of 2. For example, for a level 3
pyramid, level 0 image of I^0 is the original input image, level 1 image
I^1 is the smoothed and downsized image of I^0 with m' = m/2, n'=n/2, and
level 2 image I^2 is the smoothed and downsized image of I^1 with m" =
m'/2, n" = n'/2. You can use 3x3 Gaussian filter to smooth an image, and
resample the smoothed image for every other pixel column- and row-wise.
Develop a program that takes input arguments of an image file name, the
number of pyramid levels, and a switch to turn the Gaussian smooth on or
off, then generates the pyramid levels in a series of images with the
level numbers appended in the filename accordingly. Apply your program to
compare the pyramid generation with and without the Gaussian smooth.
Honestly, It's not even clear to me what I am being asked to do, so I
don't know how to approach the problem. Any guidance would be much
appreciated. Also, if there is a more appropriate forum, please point me
in the right direction. I plan on using Java to write my program, but I
could also use Python or C++ if one of those languages is more fitting for
the task.