Table 1 Equations for evaluation metrics used
From: Automatic detection of developmental stages of molar teeth with deep learning
Average Precision |
|---|
\({{\varvec{A}}{\varvec{P}}}_{{\varvec{t}}{\varvec{h}}{\varvec{r}}{\varvec{e}}{\varvec{s}}{\varvec{h}}{\varvec{o}}{\varvec{l}}{\varvec{d}}}={\int }_{0}^{1}{\varvec{p}}\left({\varvec{x}}\right){\varvec{d}}{\varvec{x}}\) |
Mean Average Precision for n-classes |
\({\varvec{m}}{{\varvec{A}}{\varvec{P}}}_{{\varvec{t}}{\varvec{h}}{\varvec{r}}{\varvec{e}}{\varvec{s}}{\varvec{h}}{\varvec{o}}{\varvec{l}}{\varvec{d}}}=\frac{1}{{\varvec{n}}}{\sum }_{{\varvec{i}}=1}^{{\varvec{n}}}{{\varvec{A}}{\varvec{P}}}_{{\varvec{i}}}\) |
Accuracy |
\({\varvec{A}}{\varvec{c}}{\varvec{c}}{\varvec{u}}{\varvec{r}}{\varvec{a}}{\varvec{c}}{\varvec{y}}=\boldsymbol{ }\frac{{\varvec{T}}{\varvec{P}}+{\varvec{T}}{\varvec{N}}}{{\varvec{T}}{\varvec{P}}+{\varvec{T}}{\varvec{N}}+{\varvec{F}}{\varvec{P}}+{\varvec{F}}{\varvec{N}}}\) |
Precision |
\({\varvec{P}}{\varvec{r}}{\varvec{e}}{\varvec{c}}{\varvec{i}}{\varvec{s}}{\varvec{i}}{\varvec{o}}{\varvec{n}}=\boldsymbol{ }\frac{{\varvec{T}}{\varvec{P}}}{{\varvec{T}}{\varvec{P}}+{\varvec{F}}{\varvec{P}}}\) |
Recall (Sensitivity) |
\({\varvec{R}}{\varvec{e}}{\varvec{c}}{\varvec{a}}{\varvec{l}}{\varvec{l}}=\boldsymbol{ }\frac{{\varvec{T}}{\varvec{P}}}{{\varvec{T}}{\varvec{P}}+{\varvec{F}}{\varvec{N}}}\) |
F1-score |
\({\varvec{F}}1\boldsymbol{ }{\varvec{S}}{\varvec{c}}{\varvec{o}}{\varvec{r}}{\varvec{e}}=2\boldsymbol{*}\frac{{\varvec{P}}{\varvec{r}}{\varvec{e}}{\varvec{c}}{\varvec{i}}{\varvec{s}}{\varvec{i}}{\varvec{o}}{\varvec{n}}\boldsymbol{*}{\varvec{R}}{\varvec{e}}{\varvec{c}}{\varvec{a}}{\varvec{l}}{\varvec{l}}}{{\varvec{P}}{\varvec{r}}{\varvec{e}}{\varvec{c}}{\varvec{i}}{\varvec{s}}{\varvec{i}}{\varvec{o}}{\varvec{n}}+{\varvec{R}}{\varvec{e}}{\varvec{c}}{\varvec{a}}{\varvec{l}}{\varvec{l}}}=\boldsymbol{ }\frac{2\boldsymbol{*}{\varvec{T}}{\varvec{P}}}{2\boldsymbol{*}{\varvec{T}}{\varvec{P}}+{\varvec{F}}{\varvec{P}}+{\varvec{F}}{\varvec{N}}}\) |
Intersection over Union (IoU) |
\({\varvec{I}}{\varvec{o}}{\varvec{U}}=\boldsymbol{ }\frac{{\varvec{a}}{\varvec{r}}{\varvec{e}}{\varvec{a}}({\varvec{g}}{\varvec{r}}{\varvec{o}}{\varvec{u}}{\varvec{n}}{\varvec{d}}\boldsymbol{ }{\varvec{t}}{\varvec{r}}{\varvec{u}}{\varvec{t}}{\varvec{h}}\boldsymbol{ }\cap {\varvec{p}}{\varvec{r}}{\varvec{e}}{\varvec{d}}{\varvec{i}}{\varvec{c}}{\varvec{t}}{\varvec{e}}{\varvec{d}})}{{\varvec{a}}{\varvec{r}}{\varvec{e}}{\varvec{a}}({\varvec{g}}{\varvec{r}}{\varvec{o}}{\varvec{u}}{\varvec{n}}{\varvec{d}}\boldsymbol{ }{\varvec{t}}{\varvec{r}}{\varvec{u}}{\varvec{t}}{\varvec{h}}\boldsymbol{ }\cup {\varvec{p}}{\varvec{r}}{\varvec{e}}{\varvec{d}}{\varvec{i}}{\varvec{c}}{\varvec{t}}{\varvec{e}}{\varvec{d}})}\) |