The question
Is there a known benchmark or theoretical substantiation on the optimal (rendering speed wise) image size?
A little background
The problem is as follows: I have a collection of very large images, thousands of pixels wide in each dimension. These should be presented to the user and manipulated somehow. In order to improve performance of my web app, I need to slice them. And here is where my question arises: what should be the dimensions of these slices?
It's hard to give a definitive dimension, but I successfully used 256x256 tiles. This is also the size used by Microsoft Deep Zoom technology.
In absence of any other suggestions, I'd just use whatever Google Maps is using. I'd imagine they would have done such tests.
You can only find out by testing, every browser will have different performance parameters and your user base may have anything from a mobile phone to a 16-core Xeon desktop. The larger determining factor may actually be the network performance in loading new tiles which is completely dependent upon how you are hosting and who your users are.
As the others already said, you can save a lot of research by duplicating the sizes already used by similar projects: Google Maps, Bing Maps, any other mapping system, not forgetting some of the gigapixel projects like gigapan.