BIL 717 Image Processing

• Example: " label smoothing " grid Unary potential 0 1 0 0 K 1 K 0 Pairwise Potential 0:-logP(y i = 0 ; data) 1:-logP(y i = 1 ; data) ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 Main idea: • Construct a graph such that every st-cut corresponds to a joint assignment to the variables y • The cost of the cut should be equal to the energy of the assignment, E(y; data) *. • The minimum-cut then corresponds to the minimum energy assignment, y ⋆ = argmin y E(y; data). Cost to split nodes ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 Cost to split nodes ∑ ∑ ∈ + = edges j i j i i i data y y data y data Energy , 2 1 For all pixels p /* Add a node to the graph */ nodeID(p) = g->add_node(); /* Set cost of terminal edges */ set_weights(nodeID(p),fgCost(p), bgCost(p)); end for all adjacent pixels p,q add_weights(nodeID(p),nodeID(q), cost(p,q)); end g->compute_maxflow(); label_p = g->is_connected_to_source(nodeID(p)); // is the label of pixel p (0 or 1) a 1 a 2 fgCost(a 1) Sink (1) Source (0) fgCost(a 2) bgCost(a 1) bgCost(a 2) Graph *g; For all pixels p /* Add a node to the graph */ nodeID(p) = g->add_node(); /* Set cost of terminal edges */ set_weights(nodeID(p),fgCost(p), bgCost(p)); end for all adjacent pixels p,q add_weights(nodeID(p),nodeID(q), cost(p,q)); end g->compute_maxflow(); label_p = g->is_connected_to_source(nodeID(p)); // is the label of pixel p (0 or 1) a 1 a 2 fgCost(a 1) Sink (1) Source (0) fgCost(a 2) bgCost(a 1) bgCost(a 2) cost(p,q) Graph *g; For all pixels p /* Add a node to the graph */ nodeID(p) = g->add_node(); /* Set cost of terminal edges */ set_weights(nodeID(p),fgCost(p), bgCost(p)); end for all adjacent pixels p,q add_weights(nodeID(p),nodeID(q), cost(p,q)); end g->compute_maxflow(); label_p = g->is_connected_to_source(nodeID(p)); // is the label of pixel p (0 or 1) a 1 a 2 fgCost(a 1) Sink (1) Source (0) fgCost(a 2) bgCost(a 1) bgCost(a 2) cost(p,q) a 1 = bg a 2 = fg Graph *g; For all pixels p /* Add a node to the graph */ nodeID(p) = g->add_node(); /* Set cost of terminal edges */ set_weights(nodeID(p),fgCost(p), bgCost(p)); end for all adjacent pixels p,q add_weights(nodeID(p),nodeID(q), cost(p,q)); end g->compute_maxflow(); label_p = …