SIFT (28) | For each character j, we use the normalized SIFT descriptors d→i∈ℝ128 (with ‖d→i‖2=1) and the spatial locators l→i∈[1,aL]2 for at most 40 significant key points ki=(d→i,l→i), according to the original SIFT implementation. The resulting feature is a set fjSIFT={ki}i=140. | The distance between f1SIFT and f2SIFT is determined as follows: |

| *i*) For each key point ki1∈f1SIFT, find a matching key point mi2∈f2SIFT s. t. mi2=argmin(dj2,lj2)∈f2SIFTdist(ki1,kj2); where dist(ki1,kj2)=arccos(〈di1,dj2〉)⋅‖li1−lj2‖22. Thus, our definition augments the original SIFT distance by adding spatial information. |

| | *ii*) The one-sided distance is DSIFT1,2=mediani{dist(ki1,mi2)}. |

| | *iii*) The final distance is DSIFT(1,2)=DSIFT1,2+DSIFT2,12. |

Zernike (29) | An off-the-shelf (39) implementation was used. Zernike moments up to the fifth order were calculated. | DZernike is the *L*_{1} distance between the Zernike feature vectors. |

DCT | MATLAB (R2009a) default implementation was used. | DDCT is the *L*_{1} distance between the DCT feature vectors. |

*K*_{d}-tree (30) | An off-the-shelf (40) implementation was used. Both orders of partitioning are used (first height, then width, and vice versa) | DKd−tree is the *L*_{1} distance between the *K*_{d}-tree feature vectors. |

Image projections (31) | The implementation results in cumulative distribution functions of the histogram on both axes. | DProj is the *L*_{1} distance between the projections’ feature vectors; this is similar to the Cramér–von Mises criterion (which uses *L*_{2} distance). |

L1 | Existing character binarizations. | DL1 is the *L*_{1} distance between the character images. |

CMI (32) | Existing character binarizations, with values in {0,1}. | The CMI computes a difference between the averages of the foreground and the background pixels of ℑ, marked by a binary mask M, CMI(M,ℑ)=μ1−μ0, where μk=mean{ℑ(p,q)|M(p,q)=k}k=0,1 |

| | In our case, given character binarizations B1,B2, the one-sided distance is DCMI1,2=1−CMI(B1,B2). |

| | The final distance is DCMI(1,2)=DCMI1,2+DCMI2,12. |