Hi,
well, the code in the "filter" view file, that you can edit via the menu Display>Views, will require a big overhaul.
You'll need to add the small images at the top, with custom javascript to hide/display the divs of each filter, and then, if you want to go further, you'll need to add further javascript to display a list of the number of results possible with an ajax request to submit the form and get the results in the javascript, count them, etc.
So it's a big task if you want exactly the same result. But it's possible.