How to and how not to usegraph cuts

Karen Liu and Brett Allen

What graph cuts is good for

• Suppose you want to label the nodes in a graph:

• For each node, you have:– a data term: D(p, fp) – the cost of labeling node p with label fp– a neighbor term, V(fp, fq), the cost of labeling connected nodes p and q with labels fp and fq.

• You want to minimize:

The algorithm

• we used an existing min-cut implementation

• for each α-expansion, we build a graph that expresses the desirability of switching each node’s label to α ( ):

Application 1: Stripe labeling

A harder case

Using graph cuts

color labelcolor pixel),( pfpD

otherwise1

1 if0

if0

),( qp

qp

qp ff

ff

ffV

Results

What went wrong?!

True labeling: … 11 12 13 14 15 16 17 18 19 …

Current labeling: … 11 12 13 1 2 3 17 18 19 …

…any α-expansion will not improve the energy!

α-expansion only works if:

Application 2: Stereo

Using graph cuts

)by shiftedcolor pixelright (color pixelleft ),( pp fwfpD

otherwise1

if0

),(qp

qp

ff

ffV

Results

Graph cuts Ground truth

Parameters: 12 labels (12-34 pixel displacement), w = 10

Results

Results (2)

Input

Graph cuts Ground truth

Results (3)