Obtain the cygwin64 installer
https://cygwin.com/install.html > setup-x86_64.exe

Run the installer and do the following
Set the root directory to something like C:\cygwin64
Set the Local Package Directory to something like C:\cygwin64-Local-Pkg-Dir
Leave the rest on default settings, select any mirror when it asks.

Install the c++ development tools using this tutorial
https://www.youtube.com/watch?v=DAlS4hF_PbY&t=4

Double check that the following packages are set to install / are installed:
lynx, wget, ImageMagick

Click next twice to finish the setup. The download will likely take ~10 minutes or so.

(Optional) Manually install cyg-apt
Right click on the link https://raw.githubusercontent.com/transcode-open/apt-cyg/master/apt-cyg
Select "Save link as" and save it to "c:\cygwin64\bin" (or wherever your Cygwin bin folder is)
Rename the downloaded file and remove the .txt extension so that it's just apt-cyg
Open your cygwin64 Terminal and enter the following commands

$ sudo chmod +x apt-cyg 
$ apt-cyg update

Verify apt-cyg is working with the following command

$ apt-cyg install nano

Navigate to your home directory and create a directory for Git

$ cd ~
$ mkdir Git

Clone the Image_Processing Git Repository

$ cd Git
$ git clone https://github.com/jakefoglia/Image_Processing.git
$ cd Image_Processing

Try to build and run the project
Enter the following commands

$ make exe
$ ./a.exe

If it doesn't build, there is a good chance its an issue with the Makefile.
Try the following commands instead.

$ g++ `Magick++-config --cppflags` main.cpp `Magick++-config --ldflags --libs`
$ ./a.exe

If the issue persists, you may be missing necessary components, or our code is bugged.