r-cnn学习（五）：SmoothL1LossLayer论文与代码的结合理解

A Loss Function for Learning Region Proposals

训练RPN时，只对两种anchor给予正标签：和gt_box有着最高的IoU && IoU超过0.7。如果对于

所有的gt_box，其IoU都小于0.3，则标记为负。损失函数定义如下：

其中i为一个mini-batch中某anchor的索引，p_i表示其为目标的预测概率,p_i*表示gt_box（正为1，否则为0）。

t_i和t_i*分别表示预测框的位置和gt_box框的位置。L_reg如下：

bound-box regression中各参数的计算方式为：

   （4）

其对应的SmoothL1LossLayer代码如下：

// ------------------------------------------------------------------
// Fast R-CNN
// Copyright (c) 2015 Microsoft
// Licensed under The MIT License [see fast-rcnn/LICENSE for details]
// Written by Ross Girshick
// ------------------------------------------------------------------  

#include "caffe/fast_rcnn_layers.hpp"  

namespace caffe {
 //SmoothL1的前向计算，即（3）式
template <typename Dtype>
__global__ void SmoothL1Forward(const int n, const Dtype* in, Dtype* out,
    Dtype sigma2) {
  // f(x) = 0.5 * (sigma * x)^2          if |x| < 1 / sigma / sigma
  //        |x| - 0.5 / sigma / sigma    otherwise
  CUDA_KERNEL_LOOP(index, n) {
    Dtype val = in[index];
    Dtype abs_val = abs(val);
    if (abs_val < 1.0 / sigma2) {
      out[index] = 0.5 * val * val * sigma2;
    } else {
      out[index] = abs_val - 0.5 / sigma2;
    }
  }
}
 //
template <typename Dtype>
void SmoothL1LossLayer<Dtype>::Forward_gpu(const vector<Blob<Dtype>*>& bottom,
    const vector<Blob<Dtype>*>& top) {
  int count = bottom[0]->count();
  caffe_gpu_sub(
      count,
      bottom[0]->gpu_data(),  //ti
      bottom[1]->gpu_data(),  //ti*
      diff_.mutable_gpu_data());    // d := ti - ti*
  if (has_weights_) {
    // apply "inside" weights  //乘上相关的权重
    caffe_gpu_mul(
        count,
        bottom[2]->gpu_data(),
        diff_.gpu_data(),
        diff_.mutable_gpu_data());  // d := w_in * (b0 - b1)
  }    //

SmoothL1Forward<Dtype><<<CAFFE_GET_BLOCKS(count), CAFFE_CUDA_NUM_THREADS>>>( count, diff_.gpu_data(), errors_.mutable_gpu_data(), sigma2_); CUDA_POST_KERNEL_CHECK; if (has_weights_) { // apply "outside" weights caffe_gpu_mul( count, bottom[3]->gpu_data(), errors_.gpu_data(), errors_.mutable_gpu_data()); // d := w_out * SmoothL1(w_in * (b0 - b1)) } Dtype loss; caffe_gpu_dot(count, ones_.gpu_data(), errors_.gpu_data(), &loss); top[0]->mutable_cpu_data()[0] = loss / bottom[0]->num(); } template <typename Dtype> __global__ void SmoothL1Backward(const int n, const Dtype* in, Dtype* out, Dtype sigma2) { // f‘(x) = sigma * sigma * x if |x| < 1 / sigma / sigma  // = sign(x) otherwise CUDA_KERNEL_LOOP(index, n) { Dtype val = in[index]; Dtype abs_val = abs(val); if (abs_val < 1.0 / sigma2) { out[index] = sigma2 * val; } else { out[index] = (Dtype(0) < val) - (val < Dtype(0)); } } } template <typename Dtype> void SmoothL1LossLayer<Dtype>::Backward_gpu(const vector<Blob<Dtype>*>& top, const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) { // after forwards, diff_ holds w_in * (b0 - b1) int count = diff_.count(); SmoothL1Backward<Dtype><<<CAFFE_GET_BLOCKS(count), CAFFE_CUDA_NUM_THREADS>>>( count, diff_.gpu_data(), diff_.mutable_gpu_data(), sigma2_); CUDA_POST_KERNEL_CHECK; for (int i = 0; i < 2; ++i) { if (propagate_down[i]) { const Dtype sign = (i == 0) ? 1 : -1; const Dtype alpha = sign * top[0]->cpu_diff()[0] / bottom[i]->num(); caffe_gpu_axpby( count, // count alpha, // alpha diff_.gpu_data(), // x Dtype(0), // beta bottom[i]->mutable_gpu_diff()); // y if (has_weights_) { // Scale by "inside" weight caffe_gpu_mul( count, bottom[2]->gpu_data(), bottom[i]->gpu_diff(), bottom[i]->mutable_gpu_diff()); // Scale by "outside" weight caffe_gpu_mul( count, bottom[3]->gpu_data(), bottom[i]->gpu_diff(), bottom[i]->mutable_gpu_diff()); } } } } INSTANTIATE_LAYER_GPU_FUNCS(SmoothL1LossLayer); } // namespace caffe