Hello SPHARM-PDM experts, 

In the hypothetical situation in which I have hippocampi from two subjects: one hippocampus from "subject A" is very short/fat with almost no tail at all, and the other, from "subject B" is almost identical in shape but has a very, very long tail.

Does spharm-pdm align these two hippocampi with respect to the centroid of each structure?

If this were the case then it would seem to follow that the centroid of subject B would be shifted more posteriorly (in the tail of the hippocampus) whereas the centroid of subject A would be positioned in the head of the hippocampus. This variation in centroid location would in turn then influence what the results, showing in essence, differences in shape of both the head and tail, when in actuality,
the 3d shape differences are localized to the tail only.

I hope this question is sufficiently clear. It's a bit hard to explain without pictures!

Thanks very much in advance,
Lara

Hi Lara,

I believe SPHARM-PDM suggests using Procrustes alignment (the *_procalign.vtk outputs), which doesn't rely on centroids. Rather, it minimizes the distance between all points.

In your example, there would ideally be more points in the head and body to drive the alignment, with the tail having a smaller influence.

That said, this is a substantial problem, especially for curved shapes like the caudate. Your example is illustrated almost exactly in Figure 12 in Gao 2014 (http://onlinelibrary.wiley.com/doi/10.10...). Unfortunately, I don't know of a solution to this as-yet.

Hope this helps,
David.

David correctly identifies the issue. Given that SPHARM employs a (area based) uniform sampling of the surface, Procrustes alignment is actually not much different from a centroid alignment. If you want to specifically align a certain part of the surface, e.g an alignment only based on the head section of the hippocampus, then you need to do such alignment separately.

This could be done, by identifying manually the regions that you want to use for the alignment (i.e. introducing a-priori expert knowledge into the alignment process), e.g. by cutting the surfaces to leave only the head & anterior body sections, then perform a Procrustes alignment & store the rotation/translation information, and finally apply those rotation/translation to the full surfaces. The tools for all this exist, but they are non trivial to use and likely need also adaptation.

Alternatively, and much easier to do, you could identify landmarks on the surfaces and align the surfaces based on those landmarks. For that purpose, simply select a set of landmarks/fiducials on the template surface (using Slicer), select the same ones on each other surfaces. Then the transform can be computed using the fiducial registration in Slicer (very quick) and apply it to the full surface in Slicer.

The one thing you have to do is to use a good enough coverage for the landmarks (or regions) such that the rotation component is still stable.

Martin

Thank you both for your helpful feedback. 

In reading the Gao et al (2014) paper, I see that two important steps in shape analysis that can influence your results are: registration and construction of the correspondence.

Regarding registration: I plan to experiment a bit with a test dataset of my own making to learn more about how results vary according to registration approach using the two registration options provided by spharm-pdm (normalization of the first order ellipsoid vs rigid-body Procrustes alignment).

My questions regarding registration are:

1. Does either approach require that I run a whole brain rigid registration of my data first?
2. What are the major differences between these two approaches? and
3. Why does your group generally recommend that the Procrustes registration be used over the ellipsoid?

Regarding correspondence, I see that in Paniagua,, et al. ("Combined SPHARM-PDM and entropy-based particle systems shape analysis framework." SPIE Medical Imaging. International Society for Optics and Photonics, 2012), improvements to the correspondence methods used by SPHARM-PDM were improved by incorporating an entropy-based particle system. Is this improvement included in the current release of SPHARM-PDM?

Many thanks in advance for your reply!
Lara

Hi Lara
Yes, that's correct, registration and correspondence both influence shape analysis, at least when you are doing vertex-based shape analysis. Most shape correspondence methods even depend on registration (not SPHARM-PDM) and thus a different registration establishes a different correspondence.

Now your questions:
1. Neither procrustes nor first order ellipsoid alignment requires the data to pre-aligned in any fashion, so whole brain registration is not necessary and does not influence your results.
2. difference: ellipsoid alignment only uses the first order ellipsoid, i.e. it is template free, as it simply rotates the axes of the first order ellispoid to the coordinate axes, and sets the zeroth order/center of gravity to (0,0,0). Procrustes alignment aligns the data relative to a template minimizing the least square distance to that template.
3. procrustes alignment is preferred as it a) well known, b) establishes a Kendall shape space and c) the data can be kept in anatomical coordinate frame (e.g. by aligning to an average template in MIN space). The main reason is likely (a), i.e. everyone has been doing it like this... (even non-SPHARM frameworks)

Martin

Hi Martin, 

Thanks for your quick and clear response. Does Figure 3 of your 2006 publication (Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM) represent the basic processes of ellipsoid alignment?

So in this alignment type, there is no nonlinear registration. Just a simple landmarking of the center of the object, and identification and alignment of the meridian and equator to the coordinate axes (which I assume are generic but consistent)?

Regarding my last post, can you also tell me whether the entropy-based particle system outlined in Paniagua et al. (2012) is incorporated the current release of SPHARM-PDM?

Thanks again,
Lara

Figure 3 more represents the correspondence establishment, which employs also the first order ellipsoid.

A bit more information is here (I added it to the paper section in the Documentation menu):
Gerig G, Styner M, Jones D, Weinberger DR, Lieberman J. Shape analysis of brain ventricles using SPHARM. Mathematical Methods in Biomedical Image Analysis, 2001. MMBIA 2001. IEEE Workshop on. 2001. p. 171–8.
http://www.nitrc.org/docman/view.php/308...

And alignment for shape analysis commonly refers to linear (usually rigid or similarity) alignment. The non-linear part is incorporated in the correspondence establishment.

And first order ellipsoid alignment is indeed simple and works great for SPHARM.

Re the particle based correspondence: it is part of the source code and can be compiled if you download the source, but we have not been able to make it work well in the general case, i.e. it needs significant twiddling and adjustments of parameters and sometimes does not work at all. Which is why we don't disseminate it right now.

But, we are in the process to incorporate an alternative method by Lyu et al:
Lyu I, Kim SH, Seong J-K, Yoo SW, Evans A, Shi Y, et al. Robust estimation of group-wise cortical correspondence with an application to macaque and human neuroimaging studies. Frontiers in Neuroscience. 2015;9:210. PMCID: PMC4462677 (open access)

This would allow users to improve the SPHARM correspondence, as well as optionally define manual landmarks that are incorporated in the correspondence evaluation as well, particularly useful when datasets have rotational symmetry when SPHARM has significant issues

Martin