Hi y'all, for the longest time now... There's been a lot of discussion
about rendering ambisonic soundfields down to binaural of late, and in
the past couple of years. I don't really think this is a problem that
has been solved in any principled fashion as of yet, so I'd like to
invite some discussion. Especially since I once was about to try my hand
at the problem, but found my skills woefully lacking.
AFAICS, the thing here is to have a set of HRTF measurements -- the
well-known and open KEMAR set, but also any other -- and then to derive
from it an LTI coupling from a representation of the soundfield to two
ears perceiving the field. The representation ought to be isotropic, as
per basic ambisonic principles, and it ought to be matched to the order
of the ambisonic field. If you had a neat set of measurements, over the
whole sphere of directions, which was designed to be in perfect
quadrature, this would be easy as cheese.
The trouble is that no set of measurements really behaves this way.
They're not in quadrature at all, and almost *always* you'll have a
sparsity, or even a full gap, towards the direction straight down. If
the directional sampling was statistically uniform over the whole
sphere of directions, and in addition the sample of directions probed
was to be in quadrature, it would be an easy excercise in discrete
summation to gain the transform matrix we need. But now it very much
isn't.
It truly isn't so when you have those gaps of coverage in the HRTF data
to the above, and especially below. It leads to divergent, numerically
touchy problems in *very* high dimension: if even one of your points
in the KEMAR set happens to be out of perfect quadrature, you're led
to an infinite order contribution from that one data point.
It also doesn't help that, directionally speaking, our known HRTF/HRIF's
don't really come in quadrature, so that they actually contribute to
directional aliasing, *statistically*. To negate their individual
error contributions out, to a degree. But then, again, I know of *no*
global, stochastic error metric out there, nor any optimization
strategy, proven to be optimal for this sort of optimization task.
So the best framework I could think of, years past, was to try and
interpolate the incoming directional point cloud from the KEMAR and
other sets, to the whole sphere, and then integrate. Using a priori
knowledge for the edge, singular cases, where a number of the empirical
observations prove to be co-planar, and as such singular in inversion. I
tried stuff such as information theoretical Kullback-Leibner divergence,
and Vapnik-Cervonenkis dimension, in order to pare down the stuff. The
thing I settled on was a kind of mutual recursion between the
directional mutual information between empirical point gained/removed
and Mahalanobis distance to each spherical harmonic added/removed. It
ought to have worked.
But it didn't. My heuristic, even utilizing exhaustive search at points,
didn't cut it even close. It didn't even approach what Gerzon did
analytically in 4.0 or 5.1.
So, any better ideas on how to interpolate and integrate, using ex ante
knowledge? In order to go from arbitrary point clouds to regularized,
isotropic, optimized, ambisonic -> binaural mappings?
--
Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front
+358-40-3751464, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
_______________________________________________
Sursound mailing list
Sursound@music.vt.edu
https://mail.music.vt.edu/mailman/listinfo/sursound - unsubscribe here, edit
account or options, view archives and so on.
