faster rcnn的源碼理解（一）SmoothL1LossLayer論文與代碼的結合理解

源碼：

// ------------------------------------------------------------------
// 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 {

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(),
      bottom[1]->gpu_data(),
      diff_.mutable_gpu_data());    // d := b0 - b1
  if (has_weights_) {
    // apply "inside" weights
    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

SmoothL1LossLayer 計算一張圖片的損失函數，對應於下圖的加號右邊部分

i是mini-batch的anchor的索引。

Pi是目標的預測概率。

有物體時pi*爲1，否則爲0

ti是一個向量，預測座標

ti*是一個向量，是gt包圍盒的座標

bottom[0]預測座標，對應於下圖的ti

bottom[1]target座標，對應於下圖的ti*

bottom[2]inside，有物體(fg)時爲1，否則爲0，對應於下圖的pi*

bottom[3]outside，沒有前景（fg）也沒有後景（bg）的爲0，其他爲1/（bg+fg），對應於加號右邊的係數部分（但其實這個地方我本人還是不懂，因爲論文上說的係數都是一些固定的值，如入=10。初始代碼一直在更新，估計又換了別的方法。不論如何，在現在的代碼中outside是乘以了後面的結果）