Keywords: PR curve, ROC curve, Machine Learning, image processing

為了幫助大家理解，比如我們需要檢測一個影象中的人，分類器將影象上的每個畫素劃分為人和非人畫素，目標是人，所以檢測為人的畫素用Positives表示，檢測為非人的畫素用Negatives來表示，檢測到了需要報告，檢測到不是需要拒絕，檢測到了實際不是則為誤報（錯誤地報告）或錯檢（非目標當成目標了），該檢測到的沒有檢測到則為漏報或漏檢

• True/False = 正確地/錯誤地

• Positives/Negatives = 識別為目標/識別為非目標
  這樣就容易理解了：

• True positives (TP) = 正確地被識別為目標 的畫素 （正確檢出）
• False positives (FP) = 錯誤地被識別為目標 的畫素（錯檢，報多了）
• True negatives (TN) = 正確地被識別為非目標 的畫素 （正確拒絕）
• False negatives (FN) = 錯誤地被識別為非目標 的畫素 （漏檢，報少了）

這些引數是常用的評估方法的基礎。通過這些引數的值我們可以計算出ROC空間和PR空間的一個點，多個影象就可以得到多個點，連成曲線就是所謂的ROC曲線和PR曲線。

1. ROC空間（面向真實結果Gound Truth）
   橫軸 False Positive Rate (FPR) = 非目標畫素中錯檢為目標的比例（越小越好）
   縱軸 True Positive Rate (TPR) = 目標畫素中正確檢出的比例（越大越好）

2. PR空間（面向檢測結果的正確性）
   橫軸 Recall = TPR 實際目標畫素中正確檢出的比例（越大越好）
   縱軸 Precision = 檢測出的目標畫素中正確的比例，檢測精度（越大越好）

總結圖

來自論文The Relationship Between Precision-Recall and ROC Curves

詳細討論可以看論文，下面引出關鍵段落

2. Review of ROC and Precision-Recall

In a binary decision problem, a classifier labels ex-
amples as either positive or negative.The decision
made by the classifier can be represented in a struc-
ture known as a confusion matrix or contingency ta-
ble. The confusion matrix has four categories: True
positives (TP) are examples correctly labeled as posi-
tives. False positives (FP) refer to negative examples
incorrectly labeled as positive. True negatives (TN)
correspond to negatives correctly labeled as negative.
Finally, false negatives (FN) refer to positive examples
incorrectly labeled as negative.
A confusion matrix is shown in Figure 2(a). The con-
fusion matrix can be used to construct a point in either
ROC space or PR space. Given the confusion matrix,
we are able to define the metrics used in each space
as in Figure 2(b). In ROC space, one plots the False
Positive Rate (FPR) on the x-axis and the True Pos-
itive Rate (TPR) on the y-axis. The FPR measures
the fraction of negative examples that are misclassi-
fied as positive.The TPR measures the fraction of
positive examples that are correctly labeled. In PR
space, one plots Recall on the x-axis and Precision on
the y-axis. Recall is the same as TPR, whereas Pre-
cision measures that fraction of examples classified as
positive that are truly positive. Figure 2(b) gives the
definitions for each metric. We will treat the metrics
as functions that act on the underlying confusion ma-
trix which defines a point in either ROC space or PR
space. Thus, given a confusion matrix A, RECALL(A)
returns the Recall associated with A.