# Estimating the position of vertexes in a 3D model

Introduction to my project:

We are machine learning scientists and working on a biomedical system for tracking tongue for speech pathology using a technology called EMA (Electromagnetic articulography). In EMA a coil is attached to tongue surface using a glue and its 3D pos and orientation (roll and pitch) are read by EMA measurement system. So, you can track the coil and thus a point on the surface of tongue while speech is made. Also let's assume we have a low density 3D model of tongue for the patient is obtained by 3D MRI and we know exactly that which vertex in 3D model corresponds to the point that coil is attached.

It would be very valuable for our research if we can visualize the tongue for the patient. But the issue is that we just track 1 or 2 points on the tongue but our 3D model has more than 100 vertices which are not tracked. Now, we think it might be possible to estimate the position of those point given these two points.

Here are some of the facts that we think it should be possible:

1. Although tongue is not a solid object, it has a degree of rigidity thus the position of these 100 vertexes are correlated by physics For example how much they can be stretched or bent (Something like spring and mass model in physics).
2. by looking at a training set of 3D models for tongue during production of different sounds, we might say that the position of vertexes are not pure random and there is a distribution for them which might be estimated using the training dataset (sequence of MRI 3D models).
3. we might assume that in our presentation the tongue can have just a bent toward the palate to simplify the modeling problem. or a 2D profile of tongue (like the line at the center) is enough for modeling. or any simplification that we can make.

Now my question:

What do you know in computer graphics literature which resembles to our problem (any model, method, tool, software, library,....)? What is your suggestion for us to do this task in more efficient way?

Thanks,

Mike

• This is a difficult, under-determined problem. Perhaps look at minimizing the Willmore energy of a closed surface that approximates the tongue. The literature on this topic might give you ideas. Sep 5 '19 at 12:40
• 2 points are not enough to accurately represent a tongue model, even if you know that they are points on some manifold with rigidity constraint. The closest thing I can think of is Sumner's paper on deformation transfer. Sep 5 '19 at 15:00