Image Understanding

Figure 5.15: Local structure and region adjacency graph.

This is a nonlinear relaxation problem. Taking eq. (5.20) into eq. (5.21), a global optimization function can be obtained:

$F={\displaystyle \sum _{k=1}^T{\displaystyle \sum _{l=1}^{N}P\left(q_i=w_k\right)}}{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{l=1}^{T}r\left(q_i=w_k,q_j=w_l\right)P\left(q_j=w_l\right)}}\left(5.23\right)$

The constraints for solutions

${\displaystyle \sum _{k=1}^{T}P\left(q_l=w_k\right)}=1\forall iP\left(q_i=w_k\right)\ge 0\forall i,k\left(5.24\right)$

In the concrete use of probabilistic relaxation labeling method, the conditional probabilities of a tag for all objects are first determined, then the iteration repeats and the following ...