This is the paper to propose YOLOv1 network, which reframed object detection as a regression problem. It is a single convolutional network that simultaneously predicts multiple bounding boxes and class probabilities for those boxes. It is to compare against R-CNN but faster and can see the entire image at once.

## Network Design

The input image is divided into $S\times S$ grid, which the center of an object in a grid cell, that grid cell should detect it. Each grid cell detects $B$ bboxes with confidence score, which is defined as the probability of object times the IoU (i.e., score should be zero for no object). A bbox prediction is 5-tuple, $(x,y,w,h,o)$ which $(x,y)$ is the box center relative to the bounds of the grid cell, $w,h$ are relative to the whole image, and $o$ the IoU between predicted box and groundtruth (class-agnostic).

Each grid cell predicts $C$ classes simultaneously, regardless of the number of bbox predicted. The class-specific confidence score for a box is therefore $P(C_i)\times \text{IoU}$.

In summary, the $S\times S$ grid produces a tensor of $S\times S\times (5B+C)$. For PASCAL VOC, the paper suggested $S=7$, $B=2$ with $C=20$.

The network architecture is depicted in Fig.3 in the paper, with 24 conv layers followed by 2 fully connected layers. A fast YOLO would use 9 conv layers and fewer filters in them. The 24-conv layer version for 20-class PASCAL VOC is as follows, all sequential:

- Conv 7×7×64 stride 2, for input of 448×448
- Max pooling 2×2 stride 2, outputs 112×112
- Conv 3×3×192
- Max pooling 2×2 stride 2, outputs 56×56
- Conv 1×1×128
- Conv 3×3×256
- Conv 1×1×256
- Conv 3×3×512
- Max pooling 2×2 stride 2, outputs 28×28
- Conv 1×1×256 (repetition 1 of 4)
- Conv 3×3×512
- Conv 1×1×256 (repetition 2 of 4)
- Conv 3×3×512
- Conv 1×1×256 (repetition 3 of 4)
- Conv 3×3×512
- Conv 1×1×256 (repetition 4 of 4)
- Conv 3×3×512
- Conv 1×1×512
- Conv 3×3×1024
- Max pooling 2×2 stride 2, outputs 14×14
- Conv 1×1×512 (repetition 1 of 2)
- Conv 3×3×1024
- Conv 1×1×512 (repetition 2 of 2)
- Conv 3×3×1024
- Conv 3×3×1024
- Conv 3×3×1024 stride 2, outputs 7×7
- Conv 3×3×1024
- Conv 3×3×1024
- Fully connected layer, outputs 4096 units
- Dropout at rate 0.5
- Fully connected layer, outputs 7×7×30 units after reshape

The final output of 7×7×30 is for 7×7 grids, each grid cell has 20 class probabilities and 2 bounding boxes, each box represented by a 5-tuple of $(x,y,w,h,o)$.

According to sec 2.2, the final layer uses linear activation, and the rest are using leaky ReLU,

\[\phi(x) = \begin{cases} x & \text{if }x>0 \\ 0.1x & \text{otherwise} \end{cases}\]For PASCAL VOC, the network outputs 7×7×2=98 bounding boxes. At inference, they run through non-maximal suppression to produce 2-3% higher mAP output.

## Training

The YOLO network would pretrained with ImageNet dataset by taking the first 20 conv layers followed by an average pooling layer and a fully connected layer. The paper reported that this classification network can achieve 88% top-5 accuracy.

After the pretraining, the remaining 4 conv layers and 2 FC layers are added, with random weight, and modified the input from 224×224 to 448×448 to provide more fine-grained visual information.

The network output is interpreted as follows:

- width and height on image are normalized by image dimension to between 0 and 1, and network output is the square root of such
- bounding box coordinates $(x,y)$ are offset to grid cell location, which are also between 0 and 1

The network is trained using sum-squared error as loss function, but weighted the loss between positive and negative boxes with $\lambda_\text{pos} = 5$ and $\lambda_\text{neg} = 0.5$ to mitigate the imbalanced sample sizes. The overall loss function:

\[\begin{aligned} L &= \lambda_\text{pos} \sum_{i=0}^{S^2} \sum_{j=0}^B \mathbb{I}_{ij} [(x_i-\hat{x}_i)^2 + (y_i-\hat{y}_i)^2 + (\sqrt{w_i} - \sqrt{\hat{w}_i})^2 + (\sqrt{h_i} - \sqrt{\hat{h}_i})^2] \\ & \quad + \sum_{i=0}^{S^2} \sum_{j=0}^B \mathbb{I}_{ij} (C_i - \hat{C}_i)^2 \\ & \quad + \lambda_\text{neg} \sum_{i=0}^{S^2} \sum_{j=0}^B (1-\mathbb{I}_{ij}) (C_i - \hat{C}_i)^2 \\ & \quad + \sum_{i=0}^{S^2} \mathbb{I}_i \sum_c (P_i(c) - \hat{P}_i(c))^2 \end{aligned}\]where

- Index $i$ iterates over all grid cells, index $j$ iterates over all bounding boxes in a grid cell
- Index $c$ iterates over all classes
- $\mathbb{I}_{i}$ is indicator function for cell $i$ contains an object
- $\mathbb{I}_{ij}$ is indicator function for cell $i$ contains an object in bounding box $j$
- $p_i(c)$ is the classification probability of class $c$ (groundtruth is either 0 or 1)

At training only the predictor with the highest IoU with the groundtruth is considered positive. The paper claimed this can lead to better overall recall as the predictors are trained for certain size and aspect ratios.

The training runs for 135 epochs on datasets of PASCAL VOC 2007 and 2012. Batch size is 64, with momentum 0.9 and weight decay 5e-4. The learning rate started at 1e-3 and gradually increase to 1e-2 in the first epoch. Then trained at 1e-2 for 75 epochs, followed by 1e-3 for 30 epochs, and finally 1e-4 for 30 epochs. Images are augmented with random scaling and translation up to 20% of the original image size, then randomly adjust the exposure and saturation of the image by up to a factor of 1.5 on the HSV space.

## Bibliographic data

```
@inproceedings{
title = "You Only Look Once: Unified, Real-time Object Detection",
author = "Joseph Redmon and Santosh Divvala and Ross Girshick and Ali Farhadi",
booktitle = "Proc. CVPR",
year = "2016",
arxiv = "1506.0264",
}
```