Methods and Techniques for Geometric Shape Detection?

I'm currently in high school working on a research project with help from a local computer science professor. I'm aiming towards improving the classification accuracy of landforms on terrestrial surfaces. My knowledge of pattern recognition is extremely limited. We decided to enter a new phase of research by analyzing the geometric shapes and features of the different landforms. The landforms, as you may imagine, resemble different shapes. For example, a ridge is linear, a crater is circular, a crater wall is donut shaped, etc.

Since then, I've been hunting down and reading about established methods and techniques. The two main techniques I've came across are:

Skeletonization

Edge based detection

Because of my limited knowledge, I sometimes have a hard time following the papers. I was wondering if someone here could point me to the right direction or even inform me of some techniques that could directly aid my research.

Thanks.