Image Understanding

To match Rl and Rr, a corresponding transform, which yields the minimum error (counted by number of errors) between Rl and Rr, needs to be searched. Note that E is a function of p, so the transform p looked for should satisfy

${\text{dis}}^c\left(R_{\text{1}},R_{\text{r}}\right)=\underset{p}{\inf }\left\{{\displaystyle \sum _i{W}_{i}C}\left[E_i\left(p\right)\right]\right\}\left(4.30\right)$

Referring back to eqs. (4.21) and (4.22), to match two relations sets X, and Xr, a set of transforms pj should be found, which make the following equation valid

${\text{dis}}^c\left(X_1,X_r\right)=\underset{p}{\inf }\left\{{\displaystyle \sum _j^m{V}_j{\displaystyle \sum _i^{}{W}_{ij}c\left[E_{ij}\left(p_j\right)\right]}}\right\}\left(4.31\right)$

In eq. (4.31), it is assumed that n > m, where Vj are the weights for counting the different importance of relations. ...