caffe源码分析---AP与mAP计算

Precision、Recall、P-R曲线

Percision

评估所有检测为positive的结果中，有多少是真的positive。
$$Precision=\frac{TP}{Total\_Predicted\_Positive}=\frac{TP}{TP+FP}$$

Recall

评估所有真的positive中，有多少positive被准确检测出。
$$Recall=\frac{TP}{Total\_Actual\_Positive}=\frac{TP}{TP+FN}$$

P-R曲线

设置不同的score阈值，可以得到不同的Precison和Recall，然后以Precision为纵坐标，Recall为横坐标，即可绘制出P-R曲线。

AP(average precision)

VOC2007的11Point方法

设置一组阈值为[0, 0.1, 0.2, …, 0.9, 1]， 对于recall大于阈值组中的某个阈值（比如0.1），可以得到一个对应的最大precision，这样就可以计算出11个precision，然后对这11个precision取平均值，得到AP值。

	// VOC2007 style for computing AP.
    vector max_precs(11, 0.);
    int start_idx = num - 1; // num = tp.size()
    for (int j = 10; j >= 0; --j) {
      for (int i = start_idx; i >= 0 ; --i) {
        if ((*rec)[i] < j / 10.) {
          start_idx = i;
          if (j > 0) {
            max_precs[j-1] = max_precs[j];
          }
          break;
        } else {
          if (max_precs[j] < (*prec)[i]) {
            max_precs[j] = (*prec)[i];
          }
        }
      }
    }
    for (int j = 10; j >= 0; --j) {
      *ap += max_precs[j] / 11;
    }

Integral方法（Natural Integral方法）

根据积分的定义，计算P-R曲线下的面积。公式如下：
$$\sum _{k=1}^{N}P(k)\ast \Delta r(k)$$

    // Natural integral.
    float prev_rec = 0.;
    for (int i = 0; i < num; ++i) {
      if (fabs((*rec)[i] - prev_rec) > eps) {
        *ap += (*prec)[i] * fabs((*rec)[i] - prev_rec);
      }
      prev_rec = (*rec)[i];
    }

VOC2012以及ILSVRC的MAXIntegral方法

将Integral方法中的$P(k)$改为$ma{x}_{\tilde{k}\ge k}P(\tilde{k})$：
$$\sum _{k=1}^{N}ma{x}_{\tilde{k}\ge k}P(\tilde{k})\ast \Delta r(k)$$

假设N个样本中有M个正样本，则得到M个recall和precision，对于每个recall值r，计算大于r时的最大precision，然后计算${\sum }_{k=1}^{N}ma{x}_{\tilde{k}\ge k}P(\tilde{k})\ast \Delta r(k)$，得到AP值。

	// VOC2012 or ILSVRC style for computing AP.
    float cur_rec = rec->back();
    float cur_prec = prec->back();
    for (int i = num - 2; i >= 0; --i) {
      cur_prec = std::max((*prec)[i], cur_prec);
      if (fabs(cur_rec - (*rec)[i]) > eps) {
        *ap += cur_prec * fabs(cur_rec - (*rec)[i]);
      }
      cur_rec = (*rec)[i];
    }
    *ap += cur_rec * cur_prec;

ComputeAP完整代码

相关文章：https://sanchom.wordpress.com/tag/average-precision/（中文翻译：https://blog.csdn.net/hysteric314/article/details/54093734）

来自caffe.ssd/src/caffe/util/bbox_util.cpp

// Compute average precision given true positive and false positive vectors.
//    tp: contains pairs of scores and true positive. 
//    num_pos: number of positives.
//    fp: contains pairs of scores and false positive.
//    ap_version: different ways of computing Average Precision.
//      Check https://sanchom.wordpress.com/tag/average-precision/ for details.
//      11point: the 11-point interpolated average precision. Used in VOC2007.
//      MaxIntegral: maximally interpolated AP. Used in VOC2012/ILSVRC.
//      Integral: the natural integral of the precision-recall curve.
//    prec: stores the computed precisions.
//    rec: stores the computed recalls.
//    ap: the computed Average Precision.
void ComputeAP(const vector >& tp, const int num_pos,
               const vector >& fp, const string ap_version,
               vector* prec, vector* rec, float* ap) {
  const float eps = 1e-6;
  // tp.size() = fp.size()
  CHECK_EQ(tp.size(), fp.size()) << "tp must have same size as fp.";
  const int num = tp.size(); 
  // Make sure that tp and fp have complement value.
  for (int i = 0; i < num; ++i) {
	// |tp[i].first - fp[i].first| < eps
    CHECK_LE(fabs(tp[i].first - fp[i].first), eps);
    // tp[i].second = 1 - fp[i].second
    CHECK_EQ(tp[i].second, 1 - fp[i].second);
  }
  prec->clear();
  rec->clear();
  *ap = 0;
  if (tp.size() == 0 || num_pos == 0) {
    return;
  }

  // Compute cumsum of tp.
  vector tp_cumsum;
  CumSum(tp, &tp_cumsum); // 按分数从高到底进行排序，然后对数量进行按行/列累加。比如，[1, 2, 1]，执行cumsum操作后，结果为[1, 3, 4]
  CHECK_EQ(tp_cumsum.size(), num);

  // Compute cumsum of fp.
  vector fp_cumsum;
  CumSum(fp, &fp_cumsum);
  CHECK_EQ(fp_cumsum.size(), num);

  // Compute precision. // prec和tp的size相等
  for (int i = 0; i < num; ++i) {
    prec->push_back(static_cast(tp_cumsum[i]) /
                    (tp_cumsum[i] + fp_cumsum[i]));
  }

  // Compute recall. // rec和tp的size相等
  for (int i = 0; i < num; ++i) {
    CHECK_LE(tp_cumsum[i], num_pos);
    rec->push_back(static_cast(tp_cumsum[i]) / num_pos);  // num_pos为label类别的实际pos数量
  }

  if (ap_version == "11point") {
    // VOC2007 style for computing AP.
    vector max_precs(11, 0.);
    int start_idx = num - 1; // num = tp.size()
    for (int j = 10; j >= 0; --j) {
      for (int i = start_idx; i >= 0 ; --i) {
        if ((*rec)[i] < j / 10.) {
          start_idx = i;
          if (j > 0) {
            max_precs[j-1] = max_precs[j];
          }
          break;
        } else {
          if (max_precs[j] < (*prec)[i]) {
            max_precs[j] = (*prec)[i];
          }
        }
      }
    }
    for (int j = 10; j >= 0; --j) {
      *ap += max_precs[j] / 11;
    }
  } else if (ap_version == "MaxIntegral") {
    // VOC2012 or ILSVRC style for computing AP.
    float cur_rec = rec->back();
    float cur_prec = prec->back();
    for (int i = num - 2; i >= 0; --i) {
      cur_prec = std::max((*prec)[i], cur_prec);
      if (fabs(cur_rec - (*rec)[i]) > eps) {
        *ap += cur_prec * fabs(cur_rec - (*rec)[i]);
      }
      cur_rec = (*rec)[i];
    }
    *ap += cur_rec * cur_prec;
  } else if (ap_version == "Integral") {
    // Natural integral.
    float prev_rec = 0.;
    for (int i = 0; i < num; ++i) {
      if (fabs((*rec)[i] - prev_rec) > eps) {
        *ap += (*prec)[i] * fabs((*rec)[i] - prev_rec);
      }
      prev_rec = (*rec)[i];
    }
  } else {
    LOG(FATAL) << "Unknown ap_version: " << ap_version;
  }
}

CumSum

cumsum是matlab中一个函数，通常用于计算一个数组各行的累加值，函数用法是B = cumsum(A,dim)，或B = cumsum(A)。—百度百科

在这里，CumSum先对pairs的第一个值（分数）按降序排序，然后计算向量的pairs的第二个值的累加值，并保存到cumsum向量中。eg: A = [1, 3, 5], cumsum(A) = [1, 1 + 3, 1 + 3 + 5]

template 
bool SortScorePairDescend(const pair& pair1,
                          const pair& pair2) {
  return pair1.first > pair2.first;
}

void CumSum(const vector >& pairs, vector* cumsum) {
  // Sort the pairs based on first item of the pair.
  vector > sort_pairs = pairs;
  std::stable_sort(sort_pairs.begin(), sort_pairs.end(),
                   SortScorePairDescend);

  cumsum->clear();
  for (int i = 0; i < sort_pairs.size(); ++i) {
    if (i == 0) {
      cumsum->push_back(sort_pairs[i].second);
    } else {
      cumsum->push_back(cumsum->back() + sort_pairs[i].second);
    }
  }
}

mAP(mean average precision)

对所有类别的APs求和取平均值，得到mAP。

map APs;
float mAP = 0.;
for label in labels:
	ComputeAP(label_true_pos, label_num_pos, label_false_pos,
                param_.ap_version(), &prec, &rec, &(APs[label]));      
	mAP += APs[label];
mAP /= num_pos.size();

完整代码：
caffe.ssd/src/caffe/solver.cpp

template 
void Solver::TestDetection(const int test_net_id) {
  CHECK(Caffe::root_solver());
  LOG(INFO) << "Iteration " << iter_
            << ", Testing net (#" << test_net_id << ")";
  CHECK_NOTNULL(test_nets_[test_net_id].get())->
      ShareTrainedLayersWith(net_.get());
  map > > > all_true_pos;
  map > > > all_false_pos;
  map > all_num_pos;
  const shared_ptr >& test_net = test_nets_[test_net_id];
  Dtype loss = 0;
  for (int i = 0; i < param_.test_iter(test_net_id); ++i) {
    SolverAction::Enum request = GetRequestedAction();
    // Check to see if stoppage of testing/training has been requested.
    while (request != SolverAction::NONE) {
        if (SolverAction::SNAPSHOT == request) {
          Snapshot();
        } else if (SolverAction::STOP == request) {
          requested_early_exit_ = true;
        }
        request = GetRequestedAction();
    }
    if (requested_early_exit_) {
      // break out of test loop.
      break;
    }

    Dtype iter_loss;
    const vector*>& result = test_net->Forward(&iter_loss);
    if (param_.test_compute_loss()) {
      loss += iter_loss;
    }
    for (int j = 0; j < result.size(); ++j) {
      CHECK_EQ(result[j]->width(), 5);
      const Dtype* result_vec = result[j]->cpu_data();
      int num_det = result[j]->height();
      for (int k = 0; k < num_det; ++k) {
        int item_id = static_cast(result_vec[k * 5]);
        int label = static_cast(result_vec[k * 5 + 1]);
        if (item_id == -1) {
          // Special row of storing number of positives for a label.
          if (all_num_pos[j].find(label) == all_num_pos[j].end()) {
            all_num_pos[j][label] = static_cast(result_vec[k * 5 + 2]);
          } else {
            all_num_pos[j][label] += static_cast(result_vec[k * 5 + 2]);
          }
        } else {
          // Normal row storing detection status.
          float score = result_vec[k * 5 + 2];
          int tp = static_cast(result_vec[k * 5 + 3]);
          int fp = static_cast(result_vec[k * 5 + 4]);
          if (tp == 0 && fp == 0) {
            // Ignore such case. It happens when a detection bbox is matched to
            // a difficult gt bbox and we don't evaluate on difficult gt bbox.
            continue;
          }
          all_true_pos[j][label].push_back(std::make_pair(score, tp));
          all_false_pos[j][label].push_back(std::make_pair(score, fp));
        }
      }
    }
  }
  if (requested_early_exit_) {
    LOG(INFO)     << "Test interrupted.";
    return;
  }
  if (param_.test_compute_loss()) {
    loss /= param_.test_iter(test_net_id);
    LOG(INFO) << "Test loss: " << loss;
  }
  for (int i = 0; i < all_true_pos.size(); ++i) {
    if (all_true_pos.find(i) == all_true_pos.end()) {
      LOG(FATAL) << "Missing output_blob true_pos: " << i;
    }
    const map > >& true_pos =
        all_true_pos.find(i)->second;
    if (all_false_pos.find(i) == all_false_pos.end()) {
      LOG(FATAL) << "Missing output_blob false_pos: " << i;
    }
    const map > >& false_pos =
        all_false_pos.find(i)->second;
    if (all_num_pos.find(i) == all_num_pos.end()) {
      LOG(FATAL) << "Missing output_blob num_pos: " << i;
    }
    // mAP计算
    // num_pos包含某个label和某个label_num_pos
    const map& num_pos = all_num_pos.find(i)->second;
    map APs;
    float mAP = 0.;
    // Sort true_pos and false_pos with descend scores.
    for (map::const_iterator it = num_pos.begin();
         it != num_pos.end(); ++it) {
      int label = it->first;
      int label_num_pos = it->second;
      if (true_pos.find(label) == true_pos.end()) {
        LOG(WARNING) << "Missing true_pos for label: " << label;
        continue;
      }
      const vector >& label_true_pos =
          true_pos.find(label)->second;
      if (false_pos.find(label) == false_pos.end()) {
        LOG(WARNING) << "Missing false_pos for label: " << label;
        continue;
      }
      const vector >& label_false_pos =
          false_pos.find(label)->second;
      vector prec, rec;
      ComputeAP(label_true_pos, label_num_pos, label_false_pos,
                param_.ap_version(), &prec, &rec, &(APs[label]));
      mAP += APs[label];
      if (param_.show_per_class_result()) {
        LOG(INFO) << "class" << label << ": " << APs[label];
      }
    }
    mAP /= num_pos.size();
    const int output_blob_index = test_net->output_blob_indices()[i];
    const string& output_name = test_net->blob_names()[output_blob_index];
    LOG(INFO) << "    Test net output #" << i << ": " << output_name << " = "
              << mAP;
  }
}

参考：
https://blog.csdn.net/qq_41994006/article/details/81051150