MATLAB: Convex hull in 3D binary matrix

3d matrixbwconvhullconvex hullrgb

I've looked at a few options in Matlab and can't seem to find a way to do what I want it to do. How can I use Matlab to draw a convex hull around specific cells in a 3D binary matrix?
I'm working with RGB image colors in a 256x256x256 binary matrix with the axes representing the R, G, and B color coordinates from 0 to 255. If an image has a specific color, let's call it "x,y,z", then the cell at coordinates x,y,z in the matrix is set to 1, else it's a 0. What I'm doing is adding 1's to the RGB cube, each representing colors from color samples that I want to be able to flag in RGB colorspace (specifically, they represent samples of colors that need to be deleted from a given image, leaving the rest of the colors in the image unchanged). What this results in is basically like a 3D scatterplot of points in RGB space from the samples.
However, the sample colors themselves (represented by the points) are not all I'm interested in. I also want to eliminate closely-related colors whose exact RGB coordinates may not have been represented in the color samples, but those colors are similar enough to some that WERE sampled that they should be flagged along with them. Example: suppose I sample pixel value 120,96,71 in an image. A very similar color is 126,108,75. However, suppose 126,108,75 was not sampled. I still want to be able to eliminate it because it is a very similar shade to another color I want to remove.
What I want to do is to fill in nearby cells in the RGB cube representing those related color values using a 3D convex hull grouping the sampled color values together AND filling in all cells on or within the convex hull with 1's if they have not already been set to 1. I can then use the RGB cube as a lookup table to see if a given pixel value should or should not be eliminated from a given image (if a given pixel's color coordinates fall on or within the hull in RGB colorspace, it gets eliminated, if not, it remains).
Basically what I'm asking is how to do a 3D convex hull like the bwconvhull() function (which as far as I know only works for 2D images). Also note, this is different from PLOTTING a convex hull in a 3D graph. Visualization does me no good for this. I need to use the convex hull itself as a lookup table, which means this needs to be stored as a 3D binary matrix. I am aware of functions like convhull(), convhulln(), and using the Delaunay triangulation convex hull. None of these do me any good for what I'm trying to accomplish.

Best Answer

It is easy enough to do, although I will suggest that a convex hull is often a bad idea when applied to color data. AN alpha shape is often better IMHO. You don't show any data, so I'll need to conjour some up. As it turns out, I had some garbage data hidden away. I saved a .mat file with the variable mat in it.
load mat.mat
rgbind = find(mat);
[r,g,b] = ind2sub(size(mat),rgbind);
So that extracts the elements in mat that were non-zero. We can see them here:
plot3(r,g,b,'o')
grid on
box on
We can easily enough wrap a convex hull around them. I like to use alphaShape, because this allows me to plot it trivially, as well as change the value of alpha.
S = alphaShape(rgbs,inf);
plot(S)
An alpha shape with inf alpha produces the convex hull of your data.
A sometimes problem with a convex hull however, especially when applied to color data is these gamut sets are rarely convex. It is easy enough here to change alpha. But if we stick with the convex hull...
[rall,gall,ball] = ndgrid(1:256,1:256,1:256);
rgball = [rall(:),gall(:),ball(:)];
inlist = inShape(S,rgball);
sum(inlist)
ans =
     1137778
      
256*256*256
ans =
    16777216
      
plot3(rall(inlist),gall(inlist),ball(inlist),'.')
grid on
box on
So out of the 16.7 million possible colors we could encode in that color cube, around 1.1 million lie inside the convex hull of the point set I provided in mat.
Given inlist, it is now easy enough to go back, and stuff them into the original matrix.
Related Question