# Partial Order Rank Features in Colour Space
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l l r r r r r r r r r r} \hline \hline \multirow{2}{*}{**Descriptor**} & \multirow{2}{*}{**Inv.**} & \multicolumn{6}{c}{**Dataset**} \\ \cline{3-13}  & & & & & & & & & & & & & \\ \hline LBP\({}_{\text{grey}}\) & \(C_{a}\) & 91.3-91.7 & 93.2-93.8 & 92.6-92.8 & 93.4-94.6 & 79.5-79.9 & 82.5-82.7 & 97.4-97.7 & 81.5-82.2 & 72.9-73.5 & 94.3-94.5 \\ LBP\({}_{\text{grey}}\) & \(D_{a}\) & 91.5-91.9 & 93.3-93.9 & 92.5-92.7 & 93.4-94.6 & 79.7-80.1 & 82.4-82.7 & 97.3-97.6 & 81.1-81.9 & 73.0-73.6 & 94.3-94.5 \\ \hline TS\({}_{\text{grey}}\) & \(C_{a}\) & 91.3-91.8 & 92.4-93.0 & 94.3-94.6 & 95.2-96.2 & 79.5-79.9 & 97.7-98.1 & 83.5-84.3 & 74.5-75.1 & 86.1-80.2 \\ TS\({}_{\text{grey}}\) & \(D_{a}\) & 91.8-92.2 & 92.3-92.9 & 94.2-94.3 & 95.3-94.3 & 92.8-94.2 & 82.4-82.6 & 97.8-94.2 & 83.0-84.4 & 94.5-75.4 & 86.1-80.2 \\ \hline TS\({}_{\text{c}}\) & \(C_{a}\) & 91.6-92.0 & 92.7-93.3 & 93.7-93.9 & 92.8-94.2 & 79.2-79.6 & 79.5-79.7 & 97.1-97.5 & 83.1-83.8 & 73.9-74.4 & 95.9-86.0 \\ TS\({}_{\text{b}}\) & \(D_{a}\) & 91.8-93.4 & 93.5-97.9 & 92.8-94.2 & 78.8-93.3 & 79.5-97.7 & 97.9-97.4 & 83.7-84.5 & 75.3-74.8 & 95.9-96.0 \\ \hline TS\({}_{\text{c}4}\) & \(C_{a}\) & 91.3-91.6 & 92.9-93.4 & 93.0-93.2 & 94.4-95.6 & 78.6-79.0 & 80.0-80.2 & 96.8-97.3 & 80.6-81.4 & 73.2-73.8 & 95.1-95.2 \\ TS\({}_{\text{d}1}\) & \(D_{a}\) & 91.5-91.8 & 92.8-93.0 & 94.6-95.8 & 78.4-78.9 & 80.0-80.3 & 96.8-97.3 & 80.9-81.7 & 73.0-73.6 & 95.1-95.3 \\ \hline POTTS\({}_{\text{d}n}^{\text{c}}\) & \(C_{a}\) & 86.9-87.3 & 89.3-89.8 & 94.7-94.9 & 93.3-94.4 & 92.3-82.7 & 82.0-82.2 & 97.6-98.0 & 77.6-78.6 & 69.3-69.9 & 94.5-94.6 \\ POTTS\({}_{\text{d}n}^{\text{c}}\) & \(D_{a}\) & 87.0-87.3 & 89.4-89.9 & 94.9-95.1 & 93.3-94.4 & 82.4-82.8 & 82.7-98.1 & 72.0-82.0 & 78.3-79.3 & 63.-69.9 & 94.5-94.6 \\ \hline POTTS\({}_{\text{grey}}^{\text{c}}\) & \(C_{a}\) & 93.0-93.06 & 89.9-90.5 & 95.1-95.3 & 95.8-98.0 & 80.1-80.5 & 78.9-92.3 & 97.5-97.9 & 73.7-74.7 & 64.1-64.7 & 93.1-93.3 \\ POTTS\({}_{\text{grey}}^{\text{c}}\) & \(D_{a}\) & 92.0-90.6 & 89.7-93.0 & 95.2-95.3 & 94.9-96.0 & 80.4-80.9 & 79.0-92.2 & 97.5-97.9 & 74.6-75.6 & 64.4-65.0 & 93.2-93.4 \\ \hline POTTS\({}_{\text{red}}^{\text{c}}\) & \(C_{a}\) & 91.4-91.8 & 93.6-94.1 & 93.4-94.5 & 90.7-92.5 & 73.8-74.3 & 73.4-73.7 & 96.1-96.7 & 82.9-83.7 & 67.7-68.3 & 95.3-95.5 \\ POTTS\({}_{\text{red}}^{\text{c}}\) & \(D_{a}\) & 92.0-92.0 & 93.5-94.0 & 95.2-95.4 & 90.7-92.5 & 73.4-74.7 & 74.0-74.3 & 96.2-96.7 & 83.9-84.7 & 68.1-68.6 & 95.4-95.5 \\ \hline POTTS\({}_{\text{red}}^{\text{c}}\) & \(C_{a}\) & 90.4-90.8 & 94.4-95.4 & 94.9-95.1 & 87.9-90.0 & 72.6-73.0 & 74.5-74.7 & 96.0-96.6 & 82.6-83.4 & 75.2-75.8 & 94.4-95.5 \\ POTTS\({}_{\text{red}}^{\text{c}}\) & \(D_{a}\) & 91.3-91.7 & 94.0-94.5 & 94.8-95.0 & 87.9-90.0 & 73.0-73.5 & 74.8-75.0 & 96.2-96.8 & 83.0-84.5 & 75.2-75.8 & 96.3-96.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overall classification accuracy: confidence intervals for the cross-validated accuracy \(\hat{a}\). Best results highlighted for grey-level (orange) and colour space features (blue). Boldface figures indicate statistically significant differences. even the traditional TS requires a grey-scale conversion, the choice of which can be seen as an integral part of the descriptor. In Table 3 we compare our results to published results obtained using rank-based descriptors in conjunction with other ordering methods in colour spaces. As can be seen, in most cases our partial-order based approach improves significantly over previous results. We should here emphasise that the computational requirements of our partial-order descriptors are not higher than those of the other ordering methods cited.