Precise RoI Pooling
Precise RoI Pooling
**Precise RoI Pooling**, or **PrRoI Pooling**, is a region of interest feature extractor that avoids any quantization of coordinates and has a continuous gradient on bounding box coordinates. Given the feature map $\mathcal{F}$ before RoI/PrRoI Pooling (eg from Conv4 in [ResNet](https://paperswithcode.com/method/resnet)-50), let $w_{i,j}$ be the feature at one discrete location $(i,j)$ on the feature map. Using bilinear interpolation, the discrete feature map can be considered continuous at any continuous coordinates $(x,y)$:

$$
f(x,y) = \sum_{i,j}IC(x,y,i,j) \times w_{i,j},
$$

where $IC(x,y,i,j) = max(0,1-|x-i|)\times max(0,1-|y-j|)$ is the interpolation coefficient. Then denote a bin of a RoI as $bin=\{(x_1,y_1),(x_2,y_2)\}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are the continuous coordinates of the top-left and bottom-right points, respectively. We perform pooling (e.g. [average pooling](https://paperswithcode.com/method/average-pooling)) given $bin$ and feature map $\mathcal{F}$ by computing a two-order integral:
Acquisition of Localization Confidence for Accurate Object Detection
https://paperswithcode.com/paper/acquisition-of-localization-confidence-for
Acquisition of Localization Confidence for Accurate Object Detection