I have gotten something similar working in WordPress by incorporating the Masonry script (or isotope if you want filtering)
Here they are:
masonry -> http://masonry.desandro.com/
isotope -> http://isotope.metafizzy.co/
I am assuming you are comfortable with javascript and jQuery so I won’t tell you how to use it (the site has tutorials if you get stuck) – but getting it to work in wordpress is just a matter of enqueueing and targeting correctly – though to get it to work with featured images for posts would take a little bit more work.
Hope this is helpful.