**Selective Search** is a region proposal algorithm for object detection tasks. It starts by over-segmenting the image based on intensity of the pixels using a graph-based segmentation method by Felzenszwalb and Huttenlocher. Selective Search then takes these oversegments as initial input and performs the following steps

1. Add all bounding boxes corresponding to segmented parts to the list of regional proposals
2. Group adjacent segments based on similarity
3. Go to step 1

At each iteration, larger segments are formed and added to the list of region proposals. Hence we create region proposals from smaller segments to larger segments in a bottom-up approach. This is what we mean by computing “hierarchical” segmentations using Felzenszwalb and Huttenlocher’s oversegments.

Given a pattern $P,$ that is more complicated than the patterns, we fragment $P$ into simpler patterns such that their exact count is known. In the subgraph GNN proposed earlier, look into the subgraph of the host graph. We have seen that this technique is scalable on large graphs. Also, we have seen that subgraph GNN is more expressive and efficient than traditional GNN. So, we tried to explore the expressibility when the pattern is fragmented into smaller subpatterns.

Fragmentation

Improving Expressivity of Graph Neural Networks using Localization

Selective Search

**Point-wise Spatial Attention (PSA)** is a [semantic segmentation](https://paperswithcode.com/task/semantic-segmentation) module. The goal is capture contextual information, especially in the long range, by aggregating information. Through the PSA module, information aggregation is performed as a kind of information flow where we adaptively learn a pixel-wise global attention map for each position from two perspectives to aggregate contextual information over the entire feature map.

The PSA module takes a spatial feature map $\mathbf{X}$ as input. We denote the spatial size of $\mathbf{X}$ as $H \times W$. Through the two branches as illustrated, we generate pixel-wise global attention maps for each position in feature map $\mathbf{X}$ through several convolutional layers.

We aggregate input feature maps based on attention maps to generate new feature representations with the long-range contextual information incorporated, i.e., $\mathbf{Z}\_{c}$ from the ‘collect’ branch and $\mathbf{Z}\_{d}$ from the ‘distribute’ branch.

We concatenate the new representations $\mathbf{Z}\_{c}$ and $\mathbf{Z}\_{d}$ and apply a convolutional layer with [batch normalization](https://paperswithcode.com/method/batch-normalization) and activation layers for dimension reduction and feature fusion. Then we concatenate the new global contextual feature with the local representation feature $\mathbf{X}$. It is followed by one or several convolutional layers with batch normalization and activation layers to generate the final feature map for following subnetworks.

Year	2000
Data Source	CC BY-SA - https://paperswithcode.com