Hello
you might change something in your process with piwigo, of hoster, or gallery script...
You can generate offline, on local, the resized pictures and upload it : but be sure the resized pics are more recent [Forum, post 131906 by deserteagle in topic 18582] "local" directory versus "_data" directory

You can also generate via the Batch Manager ; it will generate once a lot of pictures and not per view... maybe it's better for your host
What's your host plz ??

So.. all I have to do now is to generate thumbnails in all sizes, upload them to /_data/i/galleries/ and there will be no converting processes again? Piwigo will read images directly from this directory?

If your provider doesn't like convert, you can try to use GD library instead.
In your local config, insert:

$conf['graphics_library'] = 'gd';