Consider an illustrative example of a region of interest (RoI) pooling layer computation. Suppose we select the upper-left $$3 	imes 3$$ region of interest on a $$4 	imes 4$$ input matrix and apply a $$2 	imes 2$$ RoI pooling layer. This pooling layer divides the $$3 	imes 3$$ region into a $$2 	imes 2$$ grid of subwindows to obtain a $$2 	imes 2$$ output. Because the subwindow dimensions must be integers, they are rounded up. The four resulting subwindows contain the following elements from the input matrix: $$0, 1, 4,$$ and $$5$$; $$2$$ and $$6$$; $$8$$ and $$9$$; and $$10$$. By extracting the maximum value from each of these subwindows, the RoI pooling layer produces an output matrix containing $$5, 6, 9,$$ and $$10$$.

Claude

The region of interest (RoI) pooling layer is introduced in Fast R-CNN to extract fixed-shape features from regions of interest of varying sizes. Unlike standard pooling layers that indirectly control output shape through window size, padding, and stride, RoI pooling allows the output shape (e.g., $$h_2 \times w_2$$) to be specified directly. For an input region of shape $$h \times w$$, the RoI pooling layer divides the region into an $$h_2 \times w_2$$ grid of subwindows, where each subwindow is approximately of shape $$(h/h_2) \times (w/w_2)$$. The subwindow dimensions are rounded up, and the maximum element in each subwindow is taken as its output.

Region of Interest Pooling Layer

Dive into Deep Learning

The region of interest (RoI) pooling layer can be implemented in deep learning frameworks like PyTorch using `torchvision.ops.roi_pool`. The function takes the CNN-extracted feature map, a tensor of region proposals, the desired output size, and a spatial scale factor. Each region proposal is represented by five elements: the object class index, followed by the $$(x, y)$$-coordinates of its upper-left and lower-right corners. Because the feature map is typically downsampled relative to the original image, the `spatial_scale` argument is used to scale the region proposal coordinates from the original image space to the feature map space before pooling.

```python
import torch
import torchvision

X = torch.arange(16.).reshape(1, 1, 4, 4)
rois = torch.Tensor([[0, 0, 0, 20, 20], [0, 0, 10, 30, 30]])
torchvision.ops.roi_pool(X, rois, output_size=(2, 2), spatial_scale=0.1)
```

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