First of all, it seems they don't want you to download their pictures. Please consider this while acting.
Technically you would be able to download the pictures using custom tags/attributes. You can check their custom attributes downloading the html source. Unfortunately wget (yet) doesn't support arbitrary custom tags. Basically you have two options:
- Extend wget with this feature as suggested at https://unix.stackexchange.com/questions/258835/wget-follow-custom-url-attributes
- Download the source and write your own post processor.
In the second case, you have to download the index file and extract the image url-s. You need to keep in mind they don't want you to use wget, so they forbid it's user agent string. You have to fake something eg. mozilla. If you are on Linux something like this would list you the pictures:
wget -O --user-agent="Mozilla/5.0 (Macintosh; Intel Mac OS X 10.8; rv:21.0) Gecko/20100101 Firefox/21.0" "https://pixabay.com/en/photos/?q=cats&hp=&image_type=&cat=&min_width=&min_height=" | grep -o 'https://cdn.pixabay[^" ]*'
You just have to feed it back into wget and you are done.
..... | xargs wget
edit: @vera's solution is also nice, however it seems to downloading fraction of pictures in case of image search. [sorry not enough points to comment :)]