Scale and Rotation invariant feature descriptors
As far as alternatives to SIFT/SURF go, the question you linked provides very good answers.

There were two more questions I could read out:


"how could I build a useful (e.g. rotation invariant) feature descriptor"?
"regarding the statement from the linked question, how does he accomplish free rotational invariance?"


Building feature descriptors

This is a valid research topic. Good feature descriptors are not something just anyone can build in an afternoon. People publish articles when they successfully model feature descriptors with desirable properties. This is a reason that currently only a handful of state-of-the-art descriptors are used, and that is also what I advise you to do: find a feature descriptors that's good for your needs.

Achieving rotational invariance "for free"

You can determine the dominant gradient, or orientation at an image patch (your feature area). Then, rotate the image patch so that the gradient is always looking in the same direction, e.g $0$ (upwards). E.g. if you had a |black-&gt;gray-&gt;white| and a |white-&gt;gray-&gt;black| image, their dominant gradients would be pointing left ($-90$) and right ($90$) respectively, and when you rotate them by this amount, you get the same images.

This way you will always calculate the descriptor on an image patch with the same dominant orientation (the rotated patch), and thus you achieve rotational invariance.