[Insight-users] itkMattesMutualInformationImageToImageMetric: A question about the implementation

[Anja Ende]

Hello everyone,

I was looking at the implementation of this filter and I was wondering
if I could ask a couple of questions about it:

One section of the comment says the following:

// Since a zero-order BSpline (box car) kernel is used for
// the fixed image marginal pdf, we need only increment the
// fixedImageParzenWindowIndex by value of 1.0.

So is a 0th order B-spline kernel just a delta function since we
increment the histogram bin count by 1? I am not sure if the boxcar
kernel is the same as a delta function on that bin. However, if that
is the case than it is not differentiable. I thought the point of
using the Parzen Window kernel was to make the similarity measure
differentiable....

Also, I am a bit confused about this 0 oder B-spline kernel. From some
documents on the internet (ex here: http://tiny.cc/rme88) it seems
they only show this boxcar type B-spline kernel but it is of degree 1.
So what exactly is a B-spline of zero degree?

I would be really grateful if someone could help me understand this...

Many thanks everyone,

Anja