How to estimate moving body deformation?

[Maryam Hajizadeh]

Hello,
I am recently trying to estimate the deformation of a body which moves in space. In fact, I have the 3D coordinate of several points in my body during different time frames. My body is like 17*7 cm, and I have 55 points on it. The body is moving in space (rotation+translation), and it also deforms as an effect of force on it.

The solution that I have now is to project all the points in a single reference frame in each time frame, and calculate how each point has been displaced in this reference frame. However, the problem is that the displacement of the points are a function of the locatioon of my reference frame. I want to calculate the real deformation (displacement) of each point, which is independent of the reference frame.


Does anyone have a suggestion/solutiuon for that?


Thanks,
Maryam Hajizadeh

[Raphael Dumas]

Re: How to estimate moving body deformation?

Hi Maryam,

Several methods have been proposed to assess the so-called soft tissue artefact in terms of deformation:

https://www.ncbi.nlm.nih.gov/pubmed/24287399

In all of these methods you have to start from a reference configuration of the points.
A local coordiante system of the body can be defined but this not mandatory.

1) Individual point displacements
This is what you have described.
You can use the local coordinate system or the registration described below to superimposed all the time frames before computing the displacements.

2) Point-cluster geometrical transformations
The idea is to register the cloud of points of each time frame onto the reference configuration (e.g. first time frame)
This registration can be interpreted as rotation, translation, homothety ans stretch, independent from the the local coordinate system.

3) Skin envelope shape variations
This is almost like the previous method but the interpretation is a series of geometrical modes (similarly to a PCA analysis).

Thus, from a practical point of view, you need to define the reference configuration, compute the registration (least squares matching) and use polar decomposition or proper orthogonal decomposition (or PCA) for the interpretation.


Regards,
Raphaël Dumas

[Maryam Hajizadeh]

Re: How to estimate moving body deformation?

Hi Raphael,

Great thanks for your reply. However, the issue is that I do not want my deformations to be regarded as the soft tissue artifact, and I do not intend to optimize the position of the points using least square method or singular value decomposition. In fact, the deformation of my points are the effect of force on the object, not a consequence of artifact.

If I want to make it simple, a f(t) is the force which is changing over time (its point of effect and its value). This force applies different deformations on each point in the object and this deformation should be a combination of (rotation of the object+translation of the object+deformation of the point). I am interested to depart the rotation+translation of the object from each point at each frame, and to estimate its deformation.

Until now I have tried:
(1) Ordinary Procrustes Analysis (OPA). However, this method diminish a big part of real deformation of the object. It is good for removing artifacts, but not for estimating deformation.

(2) iterative contact points (ICP), this method works better that OPA, but still eliminate a big proportion of real deformation.

I will appreciate if somebody could suggest a robust approach to reach the real deformation.

Thanks
Maryam