Re: Could you please consider helping us with this project....

Posted by Mikhail Umorin on
URL: http://imagej.273.s1.nabble.com/Could-you-please-consider-helping-us-with-this-project-tp3699856p3699857.html

Ema --

Identifying fish and estimating their volumes seems to be more a AI
(Artificial Intelligence) problem then IA (Image Analysis) problem.

I think, the problem can be formalized as follows:

you have a 3-D density distribution and you have three 2-D projections of this
3-D volume distribution. You want to recreate the 3-D density from the three
2-D projections.

The problem is not solvable in such general case. The problem is not solvable
even if you had marginal 2-D distributions which carry more information than
projections (I define here that marginal distribution gives you a
cumulative/integrated density along a projection path while projection simply
gives yes/no if there is a non-zero density along a projection path).

The example you give uses very strong assumptions:
1) the shape of objects (rectangular parallelepiped);
2) the number of objects (1);

Firstly, even if the object looks square on projections that does not mean
it's a cube. The three projection images you have simply cannot tell you the
shape. In fact, you know that your fish are not rectangular parallelepipeds
which are defined by 3 numbers. You will have to assume the shape of the
objects and then calculate their volumes based on 1, 2, or 3 measurements for
each object (say max length in each dimension). You may be able to assume the
shapes based, say, on the species of fish which will have to be determined
from the images. This may be a very complicated problem in itself.

Secondly, the number of objects cannot be generally determined from three
projections you have. Consider 8 objects (same shape) placed at the vertices
of a cube whose sides a parallel to the projection axis. You can take out any
one or any two diagonally opposite objects and your projections will not show
the difference. You will have to estimate the number of objects on the images
from some other information or assume that there is no triple-overlap, i.e.
that an object does not overlap with others on all three projections. (I am
not sure about the double-overlap -- it may be solvable but may be very
tough). Assumption of small number of objects (<?) may also help.

So, the bottom line is: you can reconstruct a 3-D picture only if you have an
MRI of a volume, projections won't do. To estimate the number of objects you
will have to make assumptions that may or may not hold true. To estimate the
volume of each object you will have to assume its shape and you may not have
sufficient information to do that. So, the problem may be solvable in
specific instances (which, fortunately, you may just pick from the total set
you have), but not in general.  

Good luck!

Mikhail.