distance_transform | Distance Transforms of Sampled Functions | Data Manipulation library

I'll give you a vague general answer, and I'm sure others will give you more details. This issue comes up all the time in image processing. There are N ways to solve my problem, which one should I use? The answer is, start with the simplest one that you understand the best. For most people, that's probably 1 or 2 in your example. In most cases, they will be nearly identical and sufficient. If for some reason the techniques don't work on your data, you have now learned for yourself, a case where the techniques fail. Now, you need to start exploring other techniques. This is where the hard work comes in, in being a image processing practitioner. There are no silver bullets, there's a grab bag of techniques that work in specific contexts, which you have to learn and figure out. When you learn this for yourself, you will become god like among your peers.

For this specific example, if your data is roughly ellipsoidal, all these techniques will be similar results. As your data moves away from ellipsoidal, (say spider like) the PCA/Second order moments / contours will start to give poor results. The skeleton approaches become more robust, but mapping a complex skeleton to a single axis / orientation can become a very difficult problem, and may require more apriori knowledge about the blob.