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Optimizing Graph Cuts: Techniques, Applications, and Challenges in Node Labeling

This document explores the effective use and pitfalls of graph cuts in node labeling, focusing on minimizing costs associated with labeling nodes in a graph. It discusses constructs like data terms and neighbor terms and describes an α-expansion algorithm built on an existing min-cut implementation. Through two applications—stripe labeling and stereo—insights are provided on the outcomes and issues encountered, especially regarding the efficacy of α-expansion in improving labeling results. Analyzing true versus current labeling reveals vital considerations in applying graph cuts effectively.

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Optimizing Graph Cuts: Techniques, Applications, and Challenges in Node Labeling

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  1. How to and how not to usegraph cuts Karen Liu and Brett Allen

  2. You want to minimize: 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.

  3. 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 ( ):

  4. Application 1: Stripe labeling A harder case

  5. Using graph cuts

  6. Results

  7. 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:

  8. Application 2: Stereo

  9. Using graph cuts

  10. Results Ground truth Graph cuts Parameters: 12 labels (12-34 pixel displacement), w = 10

  11. Results

  12. Results (2) Input Ground truth Graph cuts

  13. Results (3)

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