[Insight-users] Parameters of the MattesMutualInformationImageToImageMetric

[Michael Kuhn]

Hi,

I'm not quite sure if I correctely understand the meaning of the 'number 
of histogram bins' and the 'number of spatial samples' parameters used 
in the MattesMutualInformationImageToImageMetric. Here what I think they 
mean:

To calculate a mutual information metric, a probability distribution 
function has to be set up. I guess, that this distribution function is 
approximated by choosing a certain amount (number of spatial samples) of 
pixels. For each pixel, a counter belonging to the intensity value of 
this pixel is increased. This gives a distribution function that 
basically represents the histogram (if only one picture is considered). 
To get the joint distribution function, instead of having a counter for 
each intensity value, there is a counter for each pair of intensity 
values. This then gives a function p(x,y) where x is the intensity value 
of one image, and y is the intensity value of the other image. To 
calculate the mutual information, we have to integrate over these 
probablity functions. Therefore, they are better not defined for each 
intensity value, but several intensity values are collected in one bin 
(i.e. if one bin represents the intensity values from 500 to 1000, all 
the counters belonging to the intensities from 500 to 1000 are added, 
and the sum is assigned to that bin). So, I think the number of bins 
defines the range over which we have to integrate. Since for the joint 
entropy, a two dimensional integration takes place, the computing times 
rises approximately by O(m^2) (when m is the number of histogram bins) 
and by O(n) (when n is the number of spatial samples).

Can anybody tell me, if my understanding of these parameters is correct?

Thanks,

Michael