Feature extraction

The extracted feature vector ${\bf X_{\cal S}} = (\tilde{\bf x}_{{\cal S}_1},\cdots,\tilde{\bf x}_{{\cal S}_d})^t$, where $d$ is the dimensionality of the feature space, is expressed in the general form as:

$$\tilde{\bf x}_{{\cal S}_i} = \frac {\sum_j \chi_{\omega_{{\cal S}_i}}(l_j)} {\sum_k \chi_{\omega_{\Theta_l}}(l_k)}$$ (1)

where $\chi$ denotes the characteristic (indicator) function, $l$ is a longer linear line, $\omega_{\Theta_l}$ is the set of all longer linear lines, $\omega_{{\cal S}_i}$ is a higher-level structure extracted, and $\tilde{\bf x}_{{\cal S}_i} \in [0,1]$ ( $i \in [1,\cdots,d]$), i.e., the feature space is represented by a unit hypercube.

For generating results for retrieval by both image query and image classification, we set $d = 3$, and ${\omega}_{{\cal S}_i}$ represents ``L'' junctions, ``U'' junctions, and ``significant parallel groups and polygons'' for $i \in \{1,2,3\}$, respectively, i.e., ${\bf\tilde{x}}_{{\cal S}_i}$ represents the corresponding normalized number of lines.