Focal Loss for Dense Object Detection

Motivation

• The imbalance of foreground objects and background objects is a key problem in detection model training
• OHEM automatically select hard examples to solve this issue
• This paper proposes the Focal Loss to down-weight the loss assigned to well-classified examples, which is a dynamically scaled cross-entropy loss

Method

Binary CE Loss

Starting from the cross-entropy (CE) loss for binary classification

$$\mathrm{CE}(p,y)=\{\begin{array}{ll}-\log p,& y=1\\ -\log (1-p),& \text{otherwise}\end{array}$$

In the above $y\in \left\{\pm 1\right\}$ specifies the ground-truth class and $p\in [0,1]$ is the model's estimated probability for the class with label $y=1$. For notation convenience, we define $p_t$ as

$$p_t=\{\begin{array}{ll}p& \text{if }y=1\\ 1-p& \text{otherwise}\end{array}$$

and rewrite $\mathrm{CE}(p,y)=-\log (p_t)$

Balanced Cross Entropy

A common method for addressing class imbalance is to introduce a weighting factor $\alpha \in [0,1]$ for class $1$ and $1-\alpha$ for class $1$. In practice $\alpha$ may be set by inverse class frequency or treated as a hyper-parameter to set by cross validation. For notation convenience, we define ${\alpha }_t$ analogously to how we defined $p_t$. We write the $\alpha$-balanced CE loss as:

$$\mathrm{CE}(p_t)=-{\alpha }_t\log (p_t)$$

Focal Loss

While $\alpha$ balances the importance of positive/negative examples, it does not differentiate between easy/hard examples. Therefore, we propose to add a modulating factor $(1-p_t{)}^{\gamma }$ to the cross entropy loss with tunable focusing parameter $\gamma \ge 0$. We define the focal loss as

$$\mathrm{FL}(p_t)=-(1-p_t{)}^{\gamma }\log (p_t)$$

Properties of Focal Loss

• When an example is misclassified and $p_t$ is small, the modulating factor is near $1$ and the loss is unaffected. As $p_t\to 1$, the factor goes to $0$ and the loss for well-classified examples is down-weighted.
• The focusing parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted. When $\gamma =0$, FL is equivalent to CE, and as $\gamma$ is increased the effect of the modulating factor is likewise increased.

RetinaNet

Combine FPN with Focal Loss