How generate a set of interest points on a surface from some points.

Hello, I have been able to see in some surgical navigation systems (like Mako for example) selecting some points, the system can generate automatically a broader set of points in places of interest.
For example, in this case:

Figure 1. A 3D image of the pelvis and three selected points.

Selecting those 3 points (A, B, C) is enough to generate these other set of points

Figure 2. Points generated automatically.

Does anyone have any idea how to do these things, if there is any recommended methodology or algorithms? I suppose that in this case, it is possible adjust a circle to those 3 points and generate some points, but there would still be more points that cannot be generated from a circle.

Anyone have any ideas or recommendations on how to do these things?

To give some more context, this is a point pattern that the Stryker/Mako surgical navigation system generates to guide the surgeon in surface point collection (page 33 in this online pdf):

This is just a convenience feature to guide surgeons who are not familiar with capabilities and limitations of point based registration. It is not necessary for the registration.

You can of course implement a similar feature. For example you can designate areas of interest on a template that you approximately register to the patient anatomy and then do random uniform sampling in those areas.

Note that convenience features like this are often covered by patents, so before investing significant amount of time into developing this you may want to have a look at Stryker’s patents. There is a lot of prior art and many variations in how to do this registration, so patents rarely have any practical relevance, but it is still useful to be aware.

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The question was first posted on the VTK forum and some discussion is going on there, too:

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@lassoan Thanks for your answer, I just needed to know what is the methodology used to work with these problems and your answer has helped me. Thank you.

To learn more about how exactly the Stryker/Mako software chooses the recommended sampling points, you may have a look at the patents that describe this method. They might have even published some papers about it.

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Is a preop patient CT is being used and loaded in the system before hand?

@drvarunagarwal yes, it is

I suspect that placing the point is not as simple as placing those in a circle.
The system maybe using some algorithms to segment the bone
and using some AI model data to determine an place those points on the bone for registration.

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