This paper proposed feature pyramid network to find scale invariant object detection, i.e., a model that can detect objects of different scales. One way to tackle scale invariant problem is to form an image pyramid of different scale and process each with the same model. This is a brute-force approach. Another is to form feature hierarchy from same image and scan the feature hierarchy level by level. This paper says that ConvNet inherently generating the feature pyramid, hence we can build a FPN to leverage the features obtained.

It is found that with FPN, the bounding box proposal has 8.0 point increase on average recall (AR), and object detection has 2.3 point improvement on average precision (AP) on COCO and 3.8 point on PASCAL.

FPN is created with the bottom-up pathway, top-down pathway, and lateral connections (see Fig.3 in the paper). The bottom-up pathway is the feed-forward computation of the ConvNet. Often in the ConvNet, multiple consecutive layers produces output feature maps of the same size and they are grouped in the same stage. The bottom-up pathway takes the last map from each stage as usually it contains the strongest features.

ResNet, for example, the bottom-up pathway takes feature maps from C2, C3, C4, and C5 which have strides 4, 8, 16, and 32 pixels respectively w.r.t. input image.

The top-down pathway hallucinates higher resolution features by upsampling spatially coarser but semantically stronger feature maps from higher pyramid levels. The upsampling is using nearest neighbor for simplicity.

Lateral connection enhances the feature map from top-down pathway with that from bottom-up pathway. The bottom-up map goes through a 1×1 conv to match the channel dimension, then elementwise-add with the top-down map. The result are called P2, P3, P4, and P5 to match C2 to C5 of the same spatial size.

All the outputs P2 to P5 are processed by the same classifier and regressor, hence they should be in the same shape. The paper set their depth to $$d=256$$ channels, by adding extra convolution layers without non-linearities to normalize the depth.

There are several applications proposed by the paper:

• RPN: Instead of a single feature map, RPN head (3×3 conv then two sibling 1×1 convs) can be attached to the each level of FPN. This way, the anchors on each level has only one size, namely, pixel area of $$32^2, 64^2, 128^2, 256^2, 512^2$$ for P2, P3, P4, P5, and P6 respectively (but multiple aspect ratio is allowed). The anchors are labeled according to the same rule with the ground-truth, e.g., based on IoU over 0.7 to be positive and below 0.3 to be negative. The size of ground-truth bounding box is not related to the level in FPN, but rather, the size of inferred anchor is easier to match a particular size of ground-truth due to the labelling rule. The RPN heads are shared to all level of FPN output.
• Fast R-CNN: object detection is performed on single-scale feature map. With FPN, the RoI pooling is performed on one particular output $$P_k$$, which $$k=\lfloor k_0 + \log_2(\sqrt{wh}/224)\rfloor$$ for the RoI proposal of size $$w\times h$$ and $$k_0=4$$ to match the ResNet-based Faster R-CNN system that uses C4 as feature map. If the RoI is small, a finer-resolution level will be used.

## Bibliographic data

@inproceedings{
title = "Feature Pyramid Networks for Object Detection",
author = "Tsung-Yi Lin and Piotr Dollár and Ross Girshick and Kaiming He and Bharath Hariharan and Serge Belongie",
booktitle = "Proc CVPR",
pages = "2117--2125",
year = "2017",
note = "arXiv:1612.03144",
}