Detailed Description
This module provides functions to evaluate the similarity between two images. The main usage may be to validate algorithms when comparing results of some algorithm against what is expected (the Ground Truth)
The following conventions are used in the definition of some indices for binary images :
- Positives :
![\[ P(imGt) = |\{p \in imGt \;|\; imGt(p) = True \}| = TP(imGt, imIn)
+ FN(imGt, imIn) \]](form_8.png)
- Negatives :
![\[ N(imGt) = |\{p \in imGt \;|\; imGt(p) = False \}| = TN(imGt, imIn)
+ FP(imGt, imIn) \]](form_9.png)
- True positives :
![\[ TP(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = True \}| \]](form_10.png)
- False positives :
![\[ FP(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = False \}| \]](form_11.png)
- True negatives :
![\[ TN(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = False \}| \]](form_12.png)
- False negatives :
![\[ FN(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = True \}| \]](form_13.png)
![\[ P(imGt) = |\{p \in imGt \;|\; imGt(p) = True \}| = TP(imGt, imIn)
+ FN(imGt, imIn) \]](form_8_dark.png)
![\[ N(imGt) = |\{p \in imGt \;|\; imGt(p) = False \}| = TN(imGt, imIn)
+ FP(imGt, imIn) \]](form_9_dark.png)
![\[ TP(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = True \}| \]](form_10_dark.png)
![\[ FP(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = False \}| \]](form_11_dark.png)
![\[ TN(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = False \}| \]](form_12_dark.png)
![\[ FN(imGt, imIn) =
|\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = True \}| \]](form_13_dark.png)
- See also
- Wikipedia : Confusion matrix
- isBinary()
Collaboration diagram for Images Similarity:
Functions | |
| template<typename T > | |
| double | indexJaccard (const Image< T > &imGt, const Image< T > &imIn) |
| indexJaccard() | |
| template<typename T > | |
| double | indexRuzicka (const Image< T > &imGt, const Image< T > &imIn) |
| indexRuzicka() | |
| template<typename T > | |
| double | indexAccuracy (const Image< T > &imGt, const Image< T > &imIn, const T threshold=0) |
| indexAccuracy() | |
| template<typename T > | |
| double | indexPrecision (const Image< T > &imGt, const Image< T > &imIn) |
| indexPrecision() | |
| template<typename T > | |
| double | indexRecall (const Image< T > &imGt, const Image< T > &imIn) |
| indexRecall() | |
| template<typename T > | |
| double | indexFScore (const Image< T > &imGt, const Image< T > &imIn, const double beta=1.) |
| indexFScore() | |
| template<typename T > | |
| double | indexSensitivity (const Image< T > &imGt, const Image< T > &imIn) |
| indexSensitivity() | |
| template<typename T > | |
| double | indexSpecificity (const Image< T > &imGt, const Image< T > &imIn) |
| indexSpecificity() | |
| template<typename T > | |
| double | indexFallOut (const Image< T > &imGt, const Image< T > &imIn) |
| indexFallOut() | |
| template<typename T > | |
| double | indexMissRate (const Image< T > &imGt, const Image< T > &imIn) |
| indexMissRate() | |
| template<typename T > | |
| double | indexOverlap (const Image< T > &imGt, const Image< T > &imIn) |
| indexOverlap() | |
| template<typename T > | |
| size_t | distanceHamming (const Image< T > &imGt, const Image< T > &imIn) |
| distanceHamming() | |
| template<typename T > | |
| double | distanceHausdorff (const Image< T > &imGt, const Image< T > &imIn) |
| distanceHausdorff() - | |
Function Documentation
◆ indexJaccard()
- for binary images, this function returns the Jaccard similarity coefficient defined by :
![\[
Jaccard(imGt, imIn) = \dfrac{|imGt \cap imIn|}{\vert imGt \cup imIn \vert}
= \dfrac{area(logicAnd(imGt, \; imIn))}{area(logicOr(imGt, \; imIn))}
\]](form_14.png)
- for non binary images, this function returns the Weighted Jaccard similarity coefficient, also known as Ruzicka coefficient - see indexRuzicka()
![\[
Jaccard(imGt, imIn) = \dfrac{|imGt \cap imIn|}{\vert imGt \cup imIn \vert}
= \dfrac{area(logicAnd(imGt, \; imIn))}{area(logicOr(imGt, \; imIn))}
\]](form_14_dark.png)
- See also
- Wikipedia : Jaccard Index
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Jaccard similarity index between two images
◆ indexRuzicka()
Returns the Weighted Jaccard similarity coefficient, also known as Ruzicka coefficient - see indexJaccard()
![\[
Ruzicka(imGt, imIn) = \dfrac{\sum_{p} min(imGt(p), \; imIn(p))}
{\sum_{p} max(imGt(p), \; imIn(p))}
= \dfrac{volume(inf(imGt, \; imIn))}
{volume(sup(imGt, \; imIn))}
\]](form_15_dark.png)
- See also
- Wikipedia : Jaccard Index
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Ruzicka similarity index between two images
◆ indexAccuracy()
| double indexAccuracy | ( | const Image< T > & | imGt, |
| const Image< T > & | imIn, | ||
| const T | threshold = 0 |
||
| ) |
Returns the Rand Index, also called Accuracy or Simple matching coefficient
- For binary images (see isBinary()) this value is evaluated as :
![\[
Accuracy(imGt, imIn) = \dfrac{TP + TN}{TP + FP + TN + FN}
\]](form_16.png)
- for non binary images, pixels values are considered to be equal if their difference is not greater than
threshold
![\[
Accuracy(imGt, imIn) = \dfrac{TP + TN}{TP + FP + TN + FN}
\]](form_16_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Accuracy and precision
- Wikipedia : Rand Index
- Wikipedia : Simple matching coefficient
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify [in] threshold : difference between pixels accepted as equality.
- Returns
- the Accuracy index between two images
◆ indexPrecision()
Returns, for binary images (see isBinary()), the Precision index, also called Positive prediction value
![\[
Precision(imGt, imIn) = \dfrac{TP}{TP + FP}
\]](form_17_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Precision and Recall
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Precision index between two images
◆ indexRecall()
Returns, for binary images (see isBinary()), the Recall index, also called Sensitivity or Hit rate or True Positive Rate
![\[
Recall(imGt, imIn) = \dfrac{TP}{TP + FN}
\]](form_18_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Precision and Recall
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Recall index between two images
◆ indexFScore()
| double indexFScore | ( | const Image< T > & | imGt, |
| const Image< T > & | imIn, | ||
| const double | beta = 1. |
||
| ) |
Returns, for binary images (see isBinary()), the F-Score between two images.
![\[
F_\beta(imGt, imIn) = (1 + \beta^2) . \dfrac{Precision \; . \; Recall}
{\beta^2 \; . \; Precision + Recall}
\]](form_19_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : F-Score
- indexPrecision() and indexRecall()
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify [in] beta : 
1.)
- Returns
- returns F-Score index between two images
◆ indexSensitivity()
Returns, for binary images (see isBinary()), the Sensitivity, also called Recall, Hit rate or True Positive Rate
![\[
Sensitivity(imGt, imIn) = \dfrac{TP}{TP+FN}
\]](form_21_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Sensitivity and Specificity
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Sensitivity index between two images
◆ indexSpecificity()
Returns, for binary images (see isBinary()), the Specificity index, also called Selectivity or True negative rate
![\[
Specificity(imGt, imIn) = \dfrac{TN}{TN+FP}
\]](form_22_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Sensitivity and Specificity
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Specificity index between two images
◆ indexFallOut()
Returns, for binary images (see isBinary()), the Fall Out index, also called False positive rate or False alarm rate
![\[
Fallout(imGt, imIn) = \dfrac{FP}{TN+FP}
\]](form_23_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Sensitivity and specificity
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns FallOut index between two images
◆ indexMissRate()
Returns, for binary images (see isBinary()), the Miss Rate index, also called False negative rate
![\[
MissRate(imGt, imIn) = \dfrac{FN}{TP+FN}
\]](form_24_dark.png)
- See also
- Wikipedia : Confusion matrix
- Wikipedia : Sensitivity and Specificity
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns MissRate index between two images
◆ indexOverlap()
Returns, for binary images (see isBinary()), the Overlap coefficient
![\[
Overlap(imGt, imIn) = \dfrac{|imGt \cap imIn|}{min(|imGt|, |imIn|)} =
\dfrac{area(inf(imGt, imIn))}
{min(area(imGt), area(imIn))}
\]](form_25_dark.png)
- See also
- Wikipedia : Overlap coefficient
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Overlap index between two images
◆ distanceHamming()
Returns the number of pixels with different values in the two images.
- See also
- Wikipedia : Hamming distance
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Hamming distance between two images
◆ distanceHausdorff()
- See also
- Wikipedia : Hausdorff distance
- Note
- only binary images (two classes)
- Parameters
-
[in] imGt : Ground Truth image [in] imIn : image to verify
- Returns
- returns Hausdorff distance between two images
