I guess I was still in my wintersleep in Februari when this was released, but there is a new webservice available in SharePoint Online for rendering optimal-sized images for any device/screen resolution (image renditions don't work well for this )
You can use this in order to minimize the amount of bits sent to your users, especially for mobile users. Or you could use it to minimize the risk of terrible performance when a content editor adds a 6MB image to your site.
The location is https://yourtenantname.sharepoint.com/_layouts/15/getpreview.ashx.
This location is virtual so the service exists in any site collection (NB. so also at https://yourtenantname.sharepoint.com/sites/yoursite/_layouts/15/getpreview.ashx )
If you read the following posts you can learn how to use it with a Path query variable pointing to the URL of the image or with three guids that identify the image file.
Image renditions available - this article also contains the available resolution codes.
Generate thrumbnail from URL in SharePoint
This is an example URL: https://MYTENANT.sharepoint.com/_layouts/15/getpreview.ashx?path=https%3A%2F%2FMYTENANT.sharepoint.com%2Fsites%2FJurgenCommSiteTest%2FSiteAssets%2FSitePages%2FTest-nieuws%2F627-large_9051a70d15cd9b67ba2097efb9e6c74c488d7267.jpg&resolution=6
Note the Path query variable that holds a URL encoded locator of the file and the Resolution which should be a value from 0 to 6.
So you can easily use this new webservice in your display templates or other (JavaScript) code to allow a user a fast download of an optimal size image.