find boundaries in a binary n-dimensions

Hi, I have n-dimension matrix (with n=7) of ones and zeros. There should be a clear cut between the region of ones and region of zeros, and I want to find approximate equation for it (with 7 variables). In other words, I want to find the boundaries of the region with zeros. There are functions for 2D and 3D. Is there anything I can do with nD?

Many thanks

[Walter Roberson]

What are the input variables to the equations? What form of equation are you hoping for? For example are you looking for something like

(I >= 2 & I <= 5} & J = I*4 + 3 & K = mod(J, 2) + mod(J,5) & ...

[Aviad]

You are right, I was unclear. each dimension of my matrix represents a parameter, and each parameter is sampled at some values. I.e., I have seven additional vectors with the values at which each parameter has samples. I want to find the volume of the allowed parameters (where the matrix' values are 1).

Thanks!

[Aviad]

I want to represent this allowed volume (or the border between the allowed and not allowed volumes) with some equation, like p1=a*p2^2+b*p3+c*p4+..., where p? are the parameters.

[Walter Roberson]

If you are looking for volumes, then you can calculate the volume of each matrix entry. This is much easier if the vectors are sampled uniformly; if they are sampled non-uniformly you can do things like saying that the volume runs half way to the next center in that direction -- but if you do that then you run into problems with boundary cells (unless you know that there are no occupied cells on the outside boundary.) Anyhow, calculate the individual volumes through marginal distances, do an element-wise multiplication by the occupation matrix, sum to get total volume.

[Walter Roberson]

equations like p1=a*p2^2+b*p3+c*p4+... cannot express boundaries unless you use piecewise(), or you use heaviside() and dirac(), or other discrete functions such as mod() or floor() and ceil()