# How is per-class rate defined?

For our pixel labeling, consistent with [20], we report the number of pixels correctly classified (per-pixel rate) and the average of per-class rates. The per-pixel rate indicates how well the system is doing on the large common classes, while the average per-class rate is more affected by the smaller, less common classes.

Source: Scene Parsing with Object Instances and Occlusion Ordering by Joseph Tighe, Marc Niethammerm, Svetlana Lazebnik.

I know per-pixel rate:

$$ppr(image) = \frac{\text{pixels which were assigned the correct class}}{\text{total number of pixels of image}} \cdot 100$$

But I'm not sure how per-class rate is defined. I can imagine two ways. Let $C$ be the set of all classes.

$$pcr_A(image) = \frac{1}{|C|} \sum_{\text{class }c \in C}\frac{\text{pixels of class c classified correctly}}{\text{total number of pixels of class } c} \cdot 100$$

$$pcr_B(image) = \frac{1}{|C|} \sum_{\text{class }c \in C}\frac{\text{Pixels classified as class }c}{|\{\text{Pixels classified as class }c\} \cup \{\text{Pixels of class }c\}|} \cdot 100$$

Which one is the one used in the work I've cited above? Is the other one used? Where? Is there a definition in literature?

• Why do you think the $\text{Pixels classified as class } c$ should be used? That will include erroneously labelled pixels, which can easily be maximized by saying ALL the pixels in the image are of class $c$. Also, shouldn't the numerator always be $\text{pixels of class$c$classified correctly}$ ? – Peter K. Dec 4 '15 at 14:42