1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
% function a = afromncut(v,s,d,visimg,no_rep,pixel_loc)
% Input:
% v = eigenvectors of d*a*d, starting from the second.
% (the first is all one over some constant determined by d)
% s = eigenvalues
% d = normalization matrix 1/sqrt(rowsum(abs(a)))
% visimg = 1/0 if each eigenvector is/not 2D (so v is 3D)
% no_rep = 1 (default), affinity has attraction only
% if 1, the first column of v is the second eigenvector
% if 0, the first column of v is the first eigenvector.
% pixel_loc = nx1 matrix, each is a pixel location
% Output:
% a = diag(1/d) * na * diag(1/d);
% If pixel_loc = []; a is returned, if not out of memory
% otherwise, only rows of a at pixel_loc are returned.
%
% This routine is used to estimate the original affinity matrix
% through the first few eigenvectors and its normalization matrix.
% A test sequence includes:
% a = randsym(5);
% [na,d] = normalize(a);
% [v,s] = ncut(a,5);
% v = v(:,2:end); s = s(2:end);
% aa = afromncut(v,s,d);
% max(abs(aa(:) - a(:)))
% Stella X. Yu, 2000.
function a = afromncut(v,s,d,visimg,no_rep,pixel_loc)
[nr,nc,nv] = size(v);
if nargin<4 | isempty(visimg),
visimg = (nv>1);
end
if nargin<5 | isempty(no_rep),
no_rep = 1;
end
if visimg,
nr = nr * nc;
else
nv = nc;
end
if nargin<6 | isempty(pixel_loc),
pixel_loc = 1:nr;
end
% D^(1/2)
d = 1./(d(:)+eps);
% first recover the first eigenvector
if no_rep,
u = (1/norm(d)) + zeros(nr,1);
s = [1;s(:)];
nv = nv + 1;
else
u = [];
end
% the full set of generalized eigenvectors
v = [u, reshape(v,[nr,nv-no_rep])];
% This is the real D, row sum
d = d.^2;
% an equivalent way to compute v = diag(d) * v;
v = v .* d(:,ones(nv,1)); % to avoid using a big matrix diag(d)
% synthesis
a = v(pixel_loc,:)*diag(s)*v';
|
