[Insight-users] quasi-3D data, non-spatial dimensions, and orientation

[Michael Halle]

Hello,

As part of a Harvard project, we've been working on getting astronomy data into ITK. The current hangup is ITK coordinate systems, which of course weren't designed with astronomy in mind.  I'm confused about how to represent some of the data, and I hope people more experienced with ITK can help me.

The data we're working with is quasi-3D: it is spatial in two dimensions (right ascension and declination in degrees) and more arbitrary in the other dimension (where the parameter may be a wavelength or velocity distribution).  

Of course, there might be higher dimensions as well (observation time, etc), but for right now three is complex enough.  Also for right now, we're approximating that the spatial dimensions as linear, so we don't need to get into a spherical coordinate nightmare.

I've read through most of the discussion over the past year about orientation in ITK, and I have some questions about the best way to represent this data, especially in LPS space.  It seems like the best representation is to consider the spatial dimensions of the sky as lying in the "L" and "S" plane of LPS space, since that plane is always perpendicular to the eye vector when you look into the sky.   

Now, the big question is what to do about the other axis.  It's not spatial (it represents a distribution or maybe a histogram of some kind).  It has units (say, km/sec or intensity per nanometer) that are important for measurement and display in the user interface.  

I could just dump this other dimension of data into the "P" axis of LPS. Is my direction cosine in that dimension just the a unit vector, and my spacing and origin set up to match the limits of the distribution? 

Or I could say that the physical coordinate vector are strictly spatial LPS, and that "P" isn't related to my non-spatial coordinate, so P should always be 0.  Then my direction cosine matrix deals strictly with spatial orientation: it maps (RA, DEC, velocity_distribution) to (RA, 0, DEC), and the non-spatial dimensions use just spacing and origin to convert from "physical" to index. But the origin is in LPS space now, right? That complicates things.  

Or I could make 2D sample be a vector of samples representing the distribution, but then I lose much of the machinery in ITK for manipulating that data (especially maintaining the physical coordinates for the non-spatial dimensions).

So,  should higher dimensional data, and non-spatial data, interact with ITK's direction cosines?  Say I have a four-dimensional dataset with three spatial dimensions.  What does the direction cosine matrix, origin, and spacing look like for this case?  

Thanks.

Michael Halle