How do I return pixels associated with a particular topological feature (for example, a ring)

[HeChengBeiDou]

The persistent homology feature is specific to the pixel point, but I haven't found a way to match the pixel point to the barcode, can you help me?

[HuXiaoling]

I would suggest you refer to Fig.4(d) of our NeurIPS'19 paper and the related texts. Let me know if there are more questions.

[HeChengBeiDou]

Thank you for your reply! I have read your paper 'Topology-preserving deep image segmentation', and I think it is really a good study which guided me in the right direction.  In fact, there are some points I don't understand. 1. In Fig.4(b) of the [[NeurIPS'19 paper]](https://proceedings.neurips.cc/paper_files/paper/2019/file/2d95666e2649fcfc6e3af75e09f5adb9-Paper.pdf), the Dgm(g) should only have points whose coordinate are (0, 1), which means the three different color points in Dgm(g) should be overlap in the same place. The reason I can think of is to make the three points displayed correspond to the barcode in Fig.4(a), is that the real reason for it? 2. In my understanding, if there are only three points with the same coordinate, different matching methods for Dgm(f) and Dgm(g)  will have no difference, is that true? 3. I really think the critical points are important, but the Gudhi library and the topolayer(https://github.com/bruel-gabrielsson/TopologyLayer) just return the persistent diagrams, without the coorsponding critical points. It really confused me. Fortunately, the "PersistencePython" library you provided can meet this need. But since the code is writed by using c++, it is really hard for me to learn. So, I have a request, can you provide me a engineering realization flow chart for "PersistencePython", there is a gap between paper and realization, and it really useful for me to understand your c++ code. Looking forward for your reply.   

…

------------------ Original ------------------ From: "Xiaoling ***@***.***>; Date: 2023年3月30日(星期四) 凌晨1:17 To: ***@***.***>; Cc: ***@***.***>; ***@***.***>; Subject: Re: [HuXiaoling/TopoLoss] How do I return pixels associated with a particular topological feature (for example, a ring) (Issue #23) I would suggest you refer to Fig.4(d) of our NeurIPS'19 paper and the related texts. Let me know if there are more questions. — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you authored the thread.Message ID: ***@***.***>