Integrate Density over a 3d Vector

Hello,

I want to be able to do a projected density integration for a 3d image (SNR Intensity lin or dB), vector size(x,y,z) = ( 1000, 1000, 1024) over the entire length of y. I've been told imagej can do something of this nature but honestly I can't work it out and would prefer to demonstrate that working with matlab would be the better option. Can anyone advise if there is a function available that can perhaps perform such an integration to obtain a resultant vector size (1000, 1, 1024)?

Very much appreciated for any help forthcoming!

[David Goodmanson]

Hi Jason,

If delta_y is the spacing between the xz planes (assumed to be constant), then by a very simple integral approximation the projection of image A would be:

o If the units of A are intensity then

Aprojy = squeeze(sum(A,2))*delta_y

o If the units of A are dB (now call the matrix A_dB) relative to an reference intensity Int0 :

A = Int0*10.^(A_dB/10)
Aprojy = squeeze(sum(A,2))*delta_y

( Since intensity is a squared quantity (electric field squared for example) the dB calculatons use 10 instead of 20 ).

Then if you wanted it back in dB,

Aprojy_dB = 10*log10(Aprojy/Int0)

If this works out and later I need a couple of guys pushed over a guard rail at 100 mph, I will look you up.

[Jason Bourne]

Hi David, I've updated my response below with an attachment to demonstrate what I would like to achieve by way of integrating over those y-layers those point spreading sources. Can you possibly advise further?

Answer 1

[Jason Bourne]

Hi David,

Unfortunately, it didn't produced the result as hoped. Effectively each y layer (uniformly) spaced presents the Intensity distribution of a number of random point speaders and their distribution in the x-z plane of the sample. So effectively I need the sum of the pixel depth (i.e. pixel intensity over specified depth, y). The idea is then this overall distribution of pixel intensities (due to an iilluminating source of a particular focal point, in z ) produces a guassian profile over the x-z plane.

Any further thoughts?