Using a joint center as tracking marker

[Bhrigu Kumar Lahkar]

This query came to my mind while going through Visual3D (C-motion) guidelines (https://www.c-motion.com/v3dwiki/ind...e_note-Serge-1).

The wiki reports about considering a joint center e.g., Femur Head Center to track the Thigh segment along with other skin-mounted markers. I am not sure if its a good practice to use a joint center as a tracking marker.

Can anyone shed some lights on using the above idea and what may be the consequences on the resultant kinematics?

Regards,
Bhrigu K Lahkar, PhD

[Edmund Cramp]

The joint center is a result of the model calculations which assume that the markers were placed accurately to match the model. And the model basically describes what we think the subject looked like but may not be 100% accurate for a subject - the model leg lengths are usually seen as identical but when I was working with clinical gait analysis I was always told that human leg lengths can vary and that there was an error if they were both entered into the calculations at the same length.
I think that the C-motion link is very helpful but I agree that while joint centers may be accurate, they are estimated as a result of the calculations and marker placements, not measured so any marker placement errors can have an effect that might be hard to detect.

[Dustin Bruening]

I use joint centers for tracking some times. One example would be a sparse marker set where the joint center is needed as a third tracking marker out of necessity. Another would be if you are using a marker cluster on the distal thigh to track the thigh segment, but you are getting quite a bit of translation at the hip (meaning the cluster is not capturing the bone motion well). In this case, adding the hip center (and maybe knee center or lateral knee marker in addition) can control the thigh motion better. The alternative is to constrain the joint using global optimization (but adding the joint center is much simpler). Overall, it depends on which markers are the most well behaved for your model.

[Chris Kirtley]

You've hit on the fundamental problem with biomechanics research over the past 30 years. Anybody who has ever put a marker on a joint centre/axis knows that it simply can't be done. The body is not a set of hinges or even gimbals. The centre of rotation changes as the joint moves. The early models (Helen Hayes/VCM/Vicon) were designed to approximate things and get away with as few markers as possible. More modern thinking is to track each bone individually in 3D. But this does have the problem that the bones can separate at the joints - obviously not true anatomically, but at least you know the data is bullsh*t - with a Vicon model it's all covered up.

http://www.clinicalgaitanalysis.com/faq/hayes/

[John J Davis IV]

Tracking the joint center would function like a “soft” way to reduce joint dislocation. In the limiting case of having two real markers on the segment, and also the joint center of the parent joint, I think this would be nearly identical to modeling the joint as a ball-in-socket that cannot dislocate, since one marker is always pinned at the joint center.

If you have three or more real markers on the segment, and you additionally track one its joint centers as a tracking marker, this would be akin to “pulling” the segment towards, but not completely to, its presumed anatomical connection at the joint, since Visual3D uses (un-weighted) least squares to determine 6DoF orientation if you have more than three tracking markers.

Two disadvantages of this approach versus explicitly enforcing joint constraints via global optimization / inverse kinematics that I can think of:

(1) You are assuming the joint center is defined correctly in the parent segment (e.g. pelvis), and the markers on the child segment (e.g. femur) cannot contribute any information to determining where the joint center is located. In IK, marker locations contribute information in both directions across a joint (thigh markers can “pull” the pelvis, and vice versa).

(2) In cases with more than three markers (including the joint center) I suspect you are inducing something akin to L2 regularization in regression, where you are implicitly putting a maximum value on how much joint translation you are allowing to happen. But instead of having direct control over this value, like in IK, you are relying on the number of real markers to determine how strong of a “pull” towards the joint center you’re getting. The more real markers you have, the further from the joint center your segment can stray (or in other words, the less influence tracking the joint center will have on the kinematics).

[Allan Carman]

Bhrighu,

I would suggest it is not just a good idea but essential to include virtual joint centers in a 6df, least squares, marker cluster approach. However, you need to consider the adjacent segments before doing so. For the pelvis and lower limbs, the shank has the lowest RMS errors between known local and global marker coordinates in the least square’s reconstruction of segment location (acts most like a rigid body) while the thigh is the worst. In addition, for segments like the thigh and forearm there is a need to avoid placing skin markers on the proximal 1/3 due to large skin movements. While at the same time needing to maintain a well distributed set of markers along at least two axes. The inclusion of virtual hip and knee joint centers greatly improves the validity and reliability of the thigh segment. Whereas for the shank it may not and can be detrimental to the shank to include a virtual knee joint center from the thigh segment.

For the thigh I use 5 markers (anterior, two lateral, posterior and lateral knee) with a virtual hip joint center (Pelvis) and virtual knee joint center (Shank). Similarly, the foot uses four markers pus a virtual ankle joint center (Shank). The shank however is reconstructed from 6 markers with no virtual joint centers.

There is little we know with any degree of certainty in 3D human movement analysis. This Includes errors in 3D marker reconstruction and tracking, skin movement, joint center locations, joint rotational axes, joint translations, anthropometrical measures and segment lengths. Additionally, there are errors introduced by the model used and data processing, including poor marker placement, inappropriate filtering of marker data and imposing joint constraints when reconstructing segments.

The IK model with constrained joints (3df, rotation only at hip, knee and ankle) and global optimization is one such model.
https://www.c-motion.com/v3dwiki/ind...ng_an_IK_Model
By explicitly forcing adjacent segments to coincide at fixed joint centers with fixed segment lengths the model is unable to accommodate the errors present in 3D motion analysis. Joint centers and segments are pulled and pushed producing distorted segment locations as a result of maintaining unrealistic joint constraints in an inexact problem. The IK model is made worse by placing rigid clusters on the thigh, which accentuate skin movement artefacts. If foot strikes are present, then the default 6Hz low pass filter will also introduce errors in the form of oscillations to foot marker locations immediately prior to and following foot impact.

Cheers
Allan

[Bhrigu Kumar Lahkar]

I am thankful to all who provided insights on the issue. Here are my few thoughts and additional queries from the above discussions and other literatures

I find, there are at least two schools of thoughts, one advocates on using Global Optimization Method (GOM) with joint constraints such as spherical, hinge etc., to approximate the nature of a joint by considering the dominant/important DoFs for the joint. The other one is a strong proponent of not considering any artificial joint constraint what so ever. Both methods have its own hypotheses, pros and cons. But, can we strictly say what is right and what not? At least What is recommended and When? I don't think we have a clear-cut answer and I am happy about that. As we say "no model is right and no model is wrong" unless one defines the purpose of the model with sets of hypotheses.

Anatomically, assuming a knee joint as hinge or even spherical joint would be a stupid idea. Perhaps so as the case of Shoulder joint complex. E.g., if the purpose of the model is to quantify joint kinematics (e.g., knee joint) for clinical decision making, considering all 6Dof at the knee would be essential. By the way, who doesn't love about improving accuracy! But, is that enough? What about the hypotheses like rigid-body? Does geometry of the articular structure not have any impact on joint kinematics, what about material properties of the articular and connective tissues, such as ligaments? Anatomically, all play their part in deciding the kinematics. But, should we incorporate all of these in to a model? Again, the purpose of the model will decide.

Approximatively, at the cost of anatomical over-simplifications if the result can be acceptable within its error-limits, can we not consider it? E.g., the purpose of the model is to observe all 6 Dof kinematics of the knee joint, and the model consists of all upper and lower extremity body segments and joints. Now, can we impose relevant joint constraints to other joints except the knee? Again, if we are to study overall joint kinematics at all the joints or all segments-coordination during gait or running can we not consider joint constraints? Well, I am not sure if we have a proper Do's and Don'ts. This is also evident from the above sets of answers.

I would love if anyone can share his/her thoughts on it.

"Happy Modeling"
Bhrigu