Computing Mass Displacement for Motion Capture Sequence, fail.

In summary, "Computing Mass Displacement" is a process used in motion capture technology to calculate the change in an object's position over time, which is important for creating realistic and accurate movements in digital characters or objects. A motion capture sequence is a series of frames captured by sensors to track movements and is used to create a digital representation. Failures in "Computing Mass Displacement" can be caused by technical issues, incorrect placement or calibration of sensors, or errors in data collection. To prevent these failures, proper calibration and placement of sensors and careful data collection and review are necessary.
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Hello!

Homework Statement


As the title says I am attempting to calculate the mass displacement of a motion capture sequence, however I am not seeing the results I expect which is why I am posting here to make sure I have understood everything correctly. The data that is known is the transformation hierarchy of the character over time which encodes the position and orientation of each body part.

Homework Equations


Calculating the mass displacement for the whole sequence comes down to calculating the displacement over one frame to another by summing the displacement for each body part.

The displaced mass of body part k is given by;
[tex]E_k=\iiint_{i}\mu_i(\mathbf{p}_i-\mathbf{\bar{p}}_i)^{2}dx dy dz[/tex]
pi is a point in the body part and μi is its infinitesmal mass. Note that all things "bar"-ed relates to "the other frame". Furthermore,
[tex]\mathbf{p'}_i=\mathbf{R}_0\mathbf{R}_1\cdots \mathbf{R}_{j-1}\mathbf{x}_i[/tex]
where xi is a point in the local space of a body part, and R0 contain the global rotation and translation, but since we are interested in the relative mass displacement we define;
[tex]\mathbf{p}_i=\mathbf{R}_1\cdots \mathbf{R}_{j-1}\mathbf{x}_i=\mathbf{W}_j\mathbf{x}_i[/tex]
Ultimately Ek is given by;
[tex]E_k=tr(\mathbf{W}_i\mathbf{M}_i(\mathbf{W}_i-2\mathbf{\overline{W}}_i)^T)[/tex]
Here tr() is the trace operator - the sum of the diagonals of a matrice and Mi is the inertia tensor if the body part i.
The thing that confuses me at the moment is that since R0 contain the global rotation and translation all the matrices R1...j-1 should be 4x4 matrices. However, as far as I have understood it is not possible to use anything but 3x3 matrices with inertia tensors in R3, so what are these Wi really?

The paper I am getting this from is available http://www.cs.washington.edu/homes/zoran/sigg99/preprint.pdf" , and the equations are at page 6. The section they are in should be understandable out of context, so no need to read too much.

The Attempt at a Solution


My attempted solution was to define Wi as the 3x3 rotation matrice that transforms a point by rotation, from its local coordinate frame to its position in a global coordinate frame, pi.
Also, I should say that I use the inertia tensor to compute the angular momentum for the motion and that seems work fine.

Anyhow, I suppose my problem could be anything, but for now I'll stick to my question regarding the 4x4/3x3 matrice mixup. Any help would be beyond awesome :-)

Cheers,

- Miki
 
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  • #2


Hello Miki,

Thank you for reaching out to the forum for help with your calculations. It seems like you have a good understanding of the equations and variables involved, but you are unsure about the use of 4x4 and 3x3 matrices in this context.

Firstly, let me clarify that the Wi matrices are indeed 3x3 rotation matrices. The reason for this is that in this particular scenario, we are only interested in the rotational displacement of the body parts, not the translational displacement. Therefore, we do not need to consider the translation component of the transformation, which is why we only use the rotational component (represented by a 3x3 matrix).

As for the confusion about using 4x4 matrices in R0, this is because R0 contains the global rotation and translation information, which is necessary for calculating the relative mass displacement of each body part. However, when we are calculating the actual displacement of a body part, we only need to consider the rotation component, which is why we use 3x3 matrices for the Wi matrices.

I hope this clarifies your confusion. If you have any further questions or need additional help with your calculations, please don't hesitate to reach out.
 

FAQ: Computing Mass Displacement for Motion Capture Sequence, fail.

What is "Computing Mass Displacement"?

"Computing Mass Displacement" is a process used in motion capture technology to calculate the change in an object's position over time. This is important because it allows for the creation of realistic and accurate movements in digital characters or objects.

What is a "Motion Capture Sequence"?

A motion capture sequence is a series of frames captured by sensors that track the movements of an object or person. These frames are then used to create a digital representation of the object's or person's movements.

Why is "Computing Mass Displacement" important in motion capture?

"Computing Mass Displacement" is important in motion capture because it helps to create more realistic and accurate movements in digital characters or objects. By calculating the change in an object's position over time, it allows for the creation of smooth and natural movements that closely mimic real-life motions.

What can cause a failure in "Computing Mass Displacement" for a motion capture sequence?

There are several factors that can cause a failure in "Computing Mass Displacement" for a motion capture sequence. These can include technical issues with the sensors or software used, incorrect placement or calibration of the sensors, or errors in the data collected during the motion capture process.

How can failures in "Computing Mass Displacement" be prevented in motion capture?

To prevent failures in "Computing Mass Displacement" for a motion capture sequence, it is important to ensure that the sensors used are properly calibrated and placed on the object or person being tracked. It is also important to carefully collect and review the data during the motion capture process to identify and correct any errors that may occur.

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