diff toolboxes/FullBNT-1.0.7/bnt/examples/static/fgraph/fg_mrf2.m @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/bnt/examples/static/fgraph/fg_mrf2.m	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,150 @@
+seed = 0;
+rand('state', seed);
+randn('state', seed);
+
+nrows = 5;
+ncols = 5;
+npixels = nrows*ncols;
+
+% we number pixels in transposed raster scan order (top to bottom, left to right)
+
+% H(i,j) is the number of the hidden node at (i,j)
+H = reshape(1:npixels, nrows, ncols);
+% O(i,j) is the number of the obsevred node at (i,j)
+O = reshape(1:npixels, nrows, ncols) + length(H(:));
+
+
+% Make a Bayes net where each hidden pixel generates an observed pixel
+% but there are no connections between the hidden pixels.
+% We use this just to generate noisy versions of known images.
+N = 2*npixels;
+dag = zeros(N);
+for i=1:nrows
+  for j=1:ncols
+    dag(H(i,j), O(i,j)) = 1;
+  end
+end
+
+
+K = 2; % number of discrete values for the hidden vars
+ns = ones(N,1);
+ns(H(:)) = K;
+ns(O(:)) = 1;
+
+
+% make image with vertical stripes
+I = zeros(nrows, ncols);
+for j=1:2:ncols
+  I(:,j) = 1;
+end
+
+% each "hidden" node will be instantiated to the pixel in the known image
+% each observed node has conditional Gaussian distribution
+eclass = ones(1,N);
+%eclass(H(:)) = 1;
+%eclass(O(:)) = 2;
+eclass(H(:)) = 1:npixels;
+eclass(O(:)) = npixels+1;
+bnet = mk_bnet(dag, ns, 'discrete', H(:), 'equiv_class', eclass);
+
+
+%bnet.CPD{1} = tabular_CPD(bnet, H(1), 'CPT', normalise(ones(1,K)));
+for i=1:nrows
+  for j=1:ncols
+    bnet.CPD{H(i,j)} = root_CPD(bnet, H(i,j), I(i,j) + 1);
+  end
+end
+
+% If H(i,j)=1, O(i,j)=+1 plus noise
+% If H(i,j)=2, O(i,j)=-1 plus noise
+sigma = 0.5;
+bnet.CPD{eclass(O(1,1))} = gaussian_CPD(bnet, O(1,1), 'mean', [1 -1], 'cov', reshape(sigma*ones(1,K), [1 1 K]));
+ofactor = bnet.CPD{eclass(O(1,1))};
+%ofactor = gaussian_CPD('self', 2, 'dps', 1, 'cps', [], 'sz', [K O], 'mean', [1 -1], 'cov', reshape(sigma*ones(1,K), [1 1 K)));
+
+
+data = sample_bnet(bnet);
+img = reshape(data(O(:)), nrows, ncols)
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Now create MRF represented as a factor graph to try and recover the scene
+
+% VEF(i,j) is the number of the factor for the vertical edge between HV(i,j) - HV(i+1,j)
+VEF = reshape((1:(nrows-1)*ncols), nrows-1, ncols);
+% HEF(i,j) is the number of the factor for the horizontal edge between HV(i,j) - HV(i,j+1)
+HEF = reshape((1:nrows*(ncols-1)), nrows, ncols-1) + length(VEF(:));
+
+nvars = npixels;
+nfac = length(VEF(:)) + length(HEF(:));
+
+G = zeros(nvars, nfac);
+N = length(ns);
+eclass = zeros(1, nfac); % eclass(i)=j  means factor i gets its params from factors{j}
+vfactor_ndx = 1; % all vertcial edges get their params from factors{1}
+hfactor_ndx = 2; % all vertcial edges get their params from factors{2}
+for i=1:nrows
+  for j=1:ncols
+    if i < nrows
+      G(H(i:i+1,j), VEF(i,j)) = 1;
+      eclass(VEF(i,j)) = vfactor_ndx;
+    end
+    if j < ncols
+      G(H(i,j:j+1), HEF(i,j)) = 1;
+      eclass(HEF(i,j)) = hfactor_ndx;
+    end
+  end
+end
+
+
+% "kitten raised in cage" prior - more likely to see continguous vertical lines
+vfactor = tabular_kernel([K K], softeye(K, 0.9));
+hfactor = tabular_kernel([K K], softeye(K, 0.5));
+factors = cell(1,2);
+factors{vfactor_ndx} = vfactor;
+factors{hfactor_ndx} = hfactor;
+
+ev_eclass = ones(1,N); % every observation factor gets is params from ofactor
+ns = K*ones(1,nvars);
+%fg = mk_fgraph_given_ev(G, ns, factors, {ofactor}, num2cell(img), 'equiv_class', eclass, 'ev_equiv_class', ev_eclass);
+fg = mk_fgraph_given_ev(G, ns, factors, {ofactor}, img, 'equiv_class', eclass, 'ev_equiv_class', ev_eclass);
+
+bnet2 = fgraph_to_bnet(fg);
+
+% inference
+
+
+maximize = 1;
+
+engine = {};
+engine{1} = belprop_fg_inf_engine(fg, 'max_iter', npixels*2);
+engine{2} = jtree_inf_engine(bnet2);
+nengines = length(engine);
+
+% on fg, we have already included the evidence
+evidence = cell(1,npixels);
+tic; [engine{1}, ll(1)] = enter_evidence(engine{1}, evidence, 'maximize', maximize); toc
+
+
+% on bnet2, we must add evidence to the dummy nodes 
+V = fg.nvars;
+dummy = V+1:V+fg.nfactors;
+N = max(dummy);
+evidence = cell(1, N);
+evidence(dummy) = {1};
+tic; [engine{2}, ll(2)] = enter_evidence(engine{2}, evidence); toc
+
+
+Ihat = zeros(nrows, ncols, nengines);
+for e=1:nengines
+  for i=1:nrows
+    for j=1:ncols
+      m = marginal_nodes(engine{e}, H(i,j));
+      Ihat(i,j,e) = argmax(m.T)-1;
+    end
+  end
+end
+Ihat