Convex Hull in MATLAB.

My objective is 3D image segmentation, I am using 3D active snakes for the same. In order to find the initial segments, I am performing some operations and in the last steps finding the convexhull. Here is the code for the same:

% img is the input 3D image given as 3D stack
szey = size(img,1);
szex = size(img,2);
szez = size(img,3);

thres = adaptthresh(img);
b=imbinarize(img,thres);
Gbw=imdilate(b,strel('disk',4));

Gfl = reshape(imfill(reshape(Gbw,szey,szex*szez),'holes'),szey,szex,szez);
Gfl = bwareaopen(Gfl,5,4);

bwsml = imdilate(imerode(Gfl,strel('disk',4)),strel('disk',4));


%getting the boundary pixels
GX = circshift(bwsml,[1 0 0]);
GY = circshift(bwsml,[0 1 0]);
GZ = circshift(bwsml,[0 0 1]);

Xbound = abs(GX-bwsml); Ybound = abs(GY-bwsml); Zbound = abs(GZ-bwsml);
bnd = or(or(Xbound,Ybound),Zbound);

cmp = bwconncomp(bnd,18);
labeled = labelmatrix(cmp);
mx=1;

% Merging all the different components as one component
for nobj=2:cmp.NumObjects
    labeled(labeled == nobj) = mx;
end
S = regionprops(labeled ,'PixelIdxList');
bnd = false(szey,szex,szez); bnd(S.PixelIdxList)=true;
[bndx,bndy,bndz]=ind2sub([szey szex szez],find(bnd));

% %starting surface: intial surface
conv = convhull(bndx,bndy,bndz);

For a small image stack of 170 x190x 17, I get size of bndx, bndy and bndz as 110500 x 1,

and conv of size 58192 x 3

Attached here is an image of the patch funtion of conv and [bndx, bndy, bndz]

We see that there is a lot of redundance, how do I decrease the size of convex hull?

I used simplify parameter, but it does not give desired results, it gives me conv hull of (32 x 3) size. Is there someway to reduce the redundancy but not this much?

[Matt J]

How many facets is the hull supposed to have?

[Anusha Devulapally]

It should be around 10% of existing, around 5000 or so.