You might try alpha shapes:

https://en.wikipedia.org/wiki/Alpha_shape

It is like a convex hull, but with an additional parameter: the maximum distance allowed between neighboring vertices. If set very large, the alpha shape equals the convex hull. If set sufficiently small, then concavities will appear.

Thank you Prof. Lambert Zijp

I appreciate your attention to this matter. Actually, I have made a new method based on DBSCAN clustering algorithm for this purpose. It is currently under review and I should mention Alpha Shapes as a competing method. I thought that there is not any other approach doing this.

Our new method can be found here:

Preprint A Grid-based Approach for Convexity Analysis of a Density-ba...

Best Regards,

Ahmad

Hi Ahmad,

I read your paper 'diagonally', and it seems to me your method has two advantages: much faster than Delaunay/Voronoi computations, and being able to detect 'hollowness' (i.e. unsampled areas inside the object of interest). Also, by using a grid, you won't run into floating point accuracy problems!

But the method comes with a cost: you need to know the sample density of the object in order to determine the grid size, and the resulting shape will be less accurate. I mean, going from one data-representation to another (grid to vertices or vice versa) always involves losses.

Hi Prof. Zijp,

First, I have to thank you a lot for your generous comments on my humble paper. I am sure that I can use them to improve the content. Furthermore, you made me so happy, for at least for now I am sure that my method could be deemed as useful. In truth, I made it to overcome a weakness in another one of my papers for outlier detection.

But let me tell you that this paper is not published yet and it is currently under review by a journal (which is not an ISI one). In fact, I submitted this paper firstly to the journal of IEEE Trans. on Knowledge and Engineering, and the Editor immediately rejected it because of lack of real data in the experiments, and also because the motivation to the problem was not described correctly, as he told me.

Next, I submitted it to the journal of Information Processing Letters (Elsevier), and again the Editor rejected that because of the way the method was presented. He told me that it should be mostly theoretically proposed, not empirically. But actually, I did not have enough time in that moment to amend the paper in that way they were suggesting. Moreover, my knowledge in the field of Statistics and Computational Geometry is not deep enough yet to support my claims.

Finally, I submitted the paper to the Journal of AI and Data Mining (Shahrood University of Technology), which is published in my home country Iran (not ISI), but it is an open access journal and in English language. I have not got any feedback from the reviewers yet, but I hope that they will understand the problem, and I will be lucky at last.

Now after all this, I just wanted to demand you to guide me through this situation and help me to put better on the paper. As it is obvious that you are a well-known scholar and I am totally a tyro in the field of research.

In fact, about the lack of real data sets in the experiments, I seriously could not find any real data that claims on the convexity of its inherent clusters. And also about the motivation to the problem, it would be great if you just suggest me some relevant references. The other point is that I want to know that if you were about to publish such paper, to where publication you would submit it. I mean that do you know any better and more suitable journal for publishing this method?

That would be an honor if you just help me with this, and I totally appreciate you for bearing me till now.

Gratefully yours,

Ahmad

Email: [email protected]; [email protected]

Homepage: https://ceit.aut.ac.ir/~sann_cv/