This paper distinct from previous work in the sense that the older approach of object detection first hypothesize bounding boxes, resample features for each box, then apply a classifier. This paper proposed a network that does not resample for bounding box hypotheses but equally accurate. It can do high speed detection, at 59 fps with mAP 74.3% on VOC2007 test set while Faster R-CNN can do only 7 fps with mAP 73.2%. The reasons for the speed up and accuracy improvement are (1) eliminated bbox proposal and feature resampling stage, (2) small conv filter to predict object categories and offsets, (3) separate predictors for different aspect ratio detection.

## Model

SSD is a feed-forward conv net that produces a fixed-size collection of bboxes and scores. Then non-maximum suppression can produce the final detection. The paper suggested an backbone network of VGG-16 truncated before the classifier, which takes an input of 300×300 image and outputs a 38×38 feature map of channel depth 512 at its “conv5_3” layer. Then multiple conv layers are appended to it, with progressively decreased sizes to generate feature maps of different scales.

A feature map of size $m\times n$ produces several detections at each position using a 3×3 small kernel. The output of each convolution position is a $(c+4)k$ results, for $k$ “default boxes” of different size and aspect ratios, each box has $c$ classification scores and 4 regressed bounding box parameters (the bounding box is agnostic to the classification result). Thus, there are $(c+4)kmn$ outputs from a feature map, regardless the channel depth $p$.

The network proposed in the paper (Fig.2) is as follows:

- Backbone: VGG-16, through “Conv5_3” layer, output feature map of 38×38×512 to a classifier of 4×(c+4) output values (4 default boxes per location)
- the previous feature map filtered with Conv 6 (3×3×1024 with 6×6 dilation) than Conv 7 (1×1×1024), producing a feature map of 19×19×1024 to a classifier of 6 default boxes, output 6×(c+4) values
- then filter with Conv 8 (1×1×256 then 3×3×512 stride 2) producing a feature map of 10×10×512 to a classifier of 6 default boxes (output 6×(c+4) values)
- then filter with Conv 9 (1×1×128 then 3×3×256 stride 2) producing a feature map of 5×5×256 to a classifier of 6 default boxes (output 6×(c+4) values)
- then filter with Conv 10 (1×1×128 then 3×3×256 stride 1) producing a feature map of 3×3×256 to a classifier of 4 default boxes (output 4×(c+4) values)
- then filter with Conv 11 (1×1×128 then 3×3×256 stride 1) producing a feature map of 1×1×256 to a classifier of 4 default boxes (output 4×(c+4) values)

The total number of output is \(38^2 \times 4 + 19^2 \times 6 + 10^2 \times 6 + 5^2 \times 6 + 3^2 \times 4 + 1^2 \times 4 = 8732\) boxes, each to classify to \(c\) classes (PASCAL VOC 20 classes + 1 background).

This is commonly called SSD300 model. Another model is SSD512 which takes 512×512 image as input.

## Training: Loss function

In training, SSD only needs an input image and groundtruth boxes for each object. As the output of various resolution and different default box are known, the groundtruth box is matched to the default box whenever >0.5 IoU (a.k.a. Jaccard overlap). Groundtruth is not associate with the single best default box so the network allows to predict high score for multiple boxes rather than requiring it to pick only one.

The loss function at each location is the weighted sum of localization loss $L_\text{loc}$ and confidence loss $L_\text{conf}$:

\[L(x,c,l,g) = \frac{1}{N} (L_\text{conf}(x,c) + \alpha L_\text{loc}(x,l,g))\]where $N$ the number of matched default boxes, $L_\text{loc}$ is the smooth L1 loss between predicted box $l$ and the groundtruth box $g$, and $L_\text{conf}$ the softmax loss over multiple class confidences $c$, and $x\in{0,1}$ the indicator of whether the predicted box match with groundtruth box. Precisely,

\[L_\text{loc}(x,l,g) = \sum_{i=1}^N \sum_{m\in\{cx,cy,w,h\}} x_{ij}^k L1(l_i^m - g_j^m)\]which $m$ is the 4 tuples of a bounding box, (cx, cy, w, h), and $i$ iterates over the $N$ default boxes that matched with groundtruth $j$ (such that $x_{ij}=1$). The groundtruth bbox is in the form of that in R-CNN.

The confidence loss is

\[L_\text{conf}(x,c) = -\sum_i \log c_i^p\]where $c_i^p$ is the softmax output for the correct class $p$ (background class if not matched with any groundtruth bbox) and $i$ iterates over all default boxes.

## Training: Default boxes

The SSD network produced feature maps of different resolutions. The lower layer in higher resolution is believed to have better semantic segmentation quality, and pooling over a global context can also improve the result.

For a SSD network with $m$ feature maps, the scale of the default boxes at feature map $k\in{1,\dots,m}$ is computed as

\[s_k = s_{\min} + \frac{s_{\max} - s_{\min}}{m-1}(k-1)\]with $s_{\min}=0.2$ meaning the lowest layer has a scale of 0.2 and $s_{\max}=0.9$ meaning the highest layer has a scale of 0.9, and all layers in between are evenly scaled. The default boxes are with aspect ratios $a_r\in{\frac13,\frac12,1,2,3}$ which the width and height are $w_k=s_k\sqrt{a_r}, h_k=s_k/\sqrt{a_r}$. An additional square default box of scale $s_k’ = \sqrt{s_k s_{k+1}}$ is added to make up 6 boxes per location.

The center of each box is set to $(\frac{i+0.5}{f_k}, \frac{j+0.5}{f_k})$ (center of a pixel) where $f_k$ is the dimension of the square feature map $k$, and $i,j\in[0,f_k)$.

This way, there are large amount of negative default boxes. In training, those negative boxes with highest confidence loss is picked such that the ratio between positive and negative boxes is maintained at 1:3 or less.

## Training: Augmentation

The input data is randomly augmented by extracting a patch of size 0.1 to 1 of the original image, with aspect ratio between 0.5 and 2. The sampled patch is then resized and randomly flipped horizontally before other photo-metric distortions. A patch is selected only if the IoU with the target object is high enough (e.g., 0.9) to provide enough positive samples.

## Bibliographic data

```
@inproceedings{
title = "SSD: Single Shot MultiBox Detector",
author = "Wei Liu and Dragomir Anguelov and Dumitru Erhan and Christian Szegedy and Scott Reed and Cheng-Yang Fu and Alexander C. Berg",
booktitle = "Proc. European Conference on Computer Vision",
pages = "21--37",
series = "Lecture Notes in Computer Science vol 9905",
editor = "B. Leibe and J. Matas and N. Sebe and M. Welling",
publisher = "Springer",
year = "2016",
doi = "10.1007/978-3-319-46448-0_2",
arxiv = "1512.02325",
}
```