docs(ssd): variance加速

Author: zjZSTU

docs/index.md

@@ -19,4 +19,5 @@
 * 先验框
 * 匹配策略
 * 损失函数
-* Hard Negative Mining
+* Hard Negative Mining
+* variance变量

docs/ssd/data_argumentation.md

@@ -28,4 +28,8 @@
 * 输入图像尺寸为$300\times 300$
 * 数据集为`PASCAL VOC`
 
-最后再进一步扩充到$500\times 500$的场景
+最后再进一步扩充到$500\times 500$的场景
+
+## 相关阅读
+
+* [【SSD算法】史上最全代码解析-核心篇](https://zhuanlan.zhihu.com/p/79854543?from_voters_page=true)

docs/ssd/index.md

@@ -1,2 +1,69 @@
 
-# variance变量
+# variance变量
+
+## 边界框回归
+
+参考：[[R-CNN]边界框回归](https://blog.zhujian.life/posts/dd3aa53a.html)
+
+已知先验框$P=(P_{x}, P_{y}, P_{w}, P_{h})$和标注框坐标$G=(G_{x}, G_{y}, G_{w}, G_{h})$，计算回归目标$t$
+
+$$
+t_{x} = (G_{x} - P_{x}) / P_{w} \\
+t_{y} = (G_{y} - P_{y}) / P_{h} \\
+t_{w} = \log(G_{w} / P_{w}) \\
+t_{h} = \log(G_{h} / P_{h})
+$$
+
+## variance使用
+
+不过在`SSD`算法实现中，额外增加了一个`variance`变量
+
+$$
+t_{x} = (G_{x} - P_{x}) / P_{w} /center\_variance\\
+t_{y} = (G_{y} - P_{y}) / P_{h} /center\_variance\\
+t_{w} = \log(G_{w} / P_{w}) /size\_variance\\
+t_{h} = \log(G_{h} / P_{h}) /size\_variance
+$$
+
+其中
+
+$$
+center\_variance = 0.1 \ \ 
+size\_variance=0.2
+$$
+
+参考：
+
+[[question] What is the purpose of the variances?](https://github.com/rykov8/ssd_keras/issues/53)
+
+[variance in priorbox layer #155](https://github.com/weiliu89/caffe/issues/155)
+
+[Bounding Box Encoding and Decoding in Object Detection](https://leimao.github.io/blog/Bounding-Box-Encoding-Decoding/)
+
+`variance`的作用在于对回归目标$t$进行了一次归一化操作，从而实现更好的训练精度
+
+$$
+{t}' = \frac {t - mean}{variance} = \frac {t - 0}{0.1或者0.2}
+$$
+
+`variance`表示的其实是标准方差（`standard variance`）
+
+当然最后预测时，同样需要使用`variance`变量
+
+$$
+Pred_{x} = {t}'_{x} * center\_variance * P_{w} + P_{x}\\ 
+Pred_{y} = {t}'_{y} * center\_variance * P_{h} + P_{y}\\ 
+Pred_{w} = \exp ({t}'_{w} * size\_variance) * P_{w}\\
+Pred_{h} = \exp ({t}'_{h} * size\_variance) * P_{h}
+$$
+
+## 具体实现
+
+* `py/ssd/utils/box_utils.py`
+
+```
+def convert_locations_to_boxes(locations, priors, center_variance, size_variance):
+。。。
+def convert_boxes_to_locations(center_form_boxes, center_form_priors, center_variance, size_variance):
+。。。
+```

docs/ssd/variance.md

@@ -69,4 +69,5 @@ nav:
         - 先验框: ssd/prior_boxes.md
         - 匹配策略: ssd/matching_strategy.md
         - 损失函数: ssd/loss_function.md
-        - 'Hard Negative Mining': ssd/hard_negative_mining.md
+        - 'Hard Negative Mining': ssd/hard_negative_mining.md
+        - variance变量: ssd/variance.md