How can I assign a unique label to all points lying inside a single sub-region of divided 3D space?

Suppose I have a 3D space. I have divided it using grids with X = 0:2:6, Y = 0:1:6 and Z = 0:3:9. So that now I have 54 small 3D regions. Few points are scattered in the entire 3D region. I have to find how many points are lying inside individual small region. Also I have to assign a label for all points in each region, e.g. All points in region 1 will have label 1, all in region 2 will be label 2, so on. I have added the picture for the reference.

Is there any direct function in matlab to find a solution for this problem ? Using if else conditions would be complex if the number of grids and dimensions increases. Is there any idea or hint ?

[Walter Roberson]

Please recheck Z=0:2:10 . Your image is Z=0:3:9 . With 0:2:10 you would have 90 bins.

[Varun Pai]

Thank u for the observation. It is Z =0:3:9 actually.

Answer 1

[KSSV]

Go for logical indexing......If (X,y,z) are you points. To get the points lying between (x1,y1,z1) and (x2,y2,z2) ;

idx = (x>x1 & x<=x2) & (y>y1 & y<=y2) & (z>z1 & z<=z2) ;

Initilize your label matrix and fill the value you want for the above idx.

[Varun Pai]

Logical indexing would be difficult if the dimension and grid size gets increased. The more number of grids, the more conditions we may have to write

[KSSV]

Generally logical indexing would be fast.

Answer 2

[Walter Roberson]

Let the coordinates of the points be stored in x, y, z

nx = 3; ny = 6; nz = 3;
xb = floor(x/2)+1;
yb = floor(y)+1;
zb = floor(z/3)+1;
counts = accumarray([xb(:), yb(:), zb(:)], 1, [nx, ny, nz]);
labels = sub2ind([nx, ny, nz], xb, yb, zb);