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 :
$P(imGt) = |\{p \in imGt \;|\; imGt(p) = True \}| = TP(imGt, imIn) + FN(imGt, imIn)$
Negatives :
$N(imGt) = |\{p \in imGt \;|\; imGt(p) = False \}| = TN(imGt, imIn) + FP(imGt, imIn)$
True positives :
$TP(imGt, imIn) = |\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = True \}|$
False positives :
$FP(imGt, imIn) = |\{p \in imIn \:|\: imIn(p) = True \land imGt(p) = False \}|$
True negatives :
$TN(imGt, imIn) = |\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = False \}|$
False negatives :
$FN(imGt, imIn) = |\{p \in imIn \:|\: imIn(p) = False \land imGt(p) = True \}|$

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() More...

template<typename T >
double	indexRuzicka (const Image< T > &imGt, const Image< T > &imIn)
	indexRuzicka() More...

template<typename T >
double	indexAccuracy (const Image< T > &imGt, const Image< T > &imIn, const T threshold=0)
	indexAccuracy() More...

template<typename T >
double	indexPrecision (const Image< T > &imGt, const Image< T > &imIn)
	indexPrecision() More...

template<typename T >
double	indexRecall (const Image< T > &imGt, const Image< T > &imIn)
	indexRecall() More...

template<typename T >
double	indexFScore (const Image< T > &imGt, const Image< T > &imIn, const double beta=1.)
	indexFScore() More...

template<typename T >
double	indexSensitivity (const Image< T > &imGt, const Image< T > &imIn)
	indexSensitivity() More...

template<typename T >
double	indexSpecificity (const Image< T > &imGt, const Image< T > &imIn)
	indexSpecificity() More...

template<typename T >
double	indexFallOut (const Image< T > &imGt, const Image< T > &imIn)
	indexFallOut() More...

template<typename T >
double	indexMissRate (const Image< T > &imGt, const Image< T > &imIn)
	indexMissRate() More...

template<typename T >
double	indexOverlap (const Image< T > &imGt, const Image< T > &imIn)
	indexOverlap() More...

template<typename T >
size_t	distanceHamming (const Image< T > &imGt, const Image< T > &imIn)
	distanceHamming() More...

template<typename T >
double	distanceHausdorff (const Image< T > &imGt, const Image< T > &imIn)
	distanceHausdorff() - More...

Function Documentation

◆ indexJaccard()

double smil::indexJaccard	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexJaccard()

for binary images, this function returns the Jaccard similarity coefficient defined by :
$Jaccard(imGt, imIn) = \dfrac{|imGt \cap imIn|}{\vert imGt \cup imIn \vert} = \dfrac{area(logicAnd(imGt, \; imIn))}{area(logicOr(imGt, \; imIn))}$
for non binary images, this function returns the Weighted Jaccard similarity coefficient, also known as Ruzicka coefficient - see indexRuzicka()

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()

double smil::indexRuzicka	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexRuzicka()

Returns the Weighted Jaccard similarity coefficient, also known as Ruzicka coefficient - see indexJaccard()

$Ruzicka(imGt, imIn) = \dfrac{\sum_{p} min(imGt(p), \; imIn(p))} {\sum_{p} max(imGt(p), \; imIn(p))} = \dfrac{volume(inf(imGt, \; imIn))} {volume(sup(imGt, \; imIn))}$

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 smil::indexAccuracy	(	const Image< T > &	imGt,
		const Image< T > &	imIn,
		const T	threshold = `0`
	)

indexAccuracy()

Returns the Rand Index, also called Accuracy or Simple matching coefficient

For binary images (see isBinary()) this value is evaluated as :
$Accuracy(imGt, imIn) = \dfrac{TP + TN}{TP + FP + TN + FN}$
for non binary images, pixels values are considered to be equal if their difference is not greater than threshold

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()

double smil::indexPrecision	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexPrecision()

Returns, for binary images (see isBinary()), the Precision index, also called Positive prediction value

$Precision(imGt, imIn) = \dfrac{TP}{TP + FP}$

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()

double smil::indexRecall	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexRecall()

Returns, for binary images (see isBinary()), the Recall index, also called Sensitivity or Hit rate or True Positive Rate

$Recall(imGt, imIn) = \dfrac{TP}{TP + FN}$

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 smil::indexFScore	(	const Image< T > &	imGt,
		const Image< T > &	imIn,
		const double	beta = `1.`
	)

indexFScore()

Returns, for binary images (see isBinary()), the F-Score between two images.

$F_\beta(imGt, imIn) = (1 + \beta^2) . \dfrac{Precision \; . \; Recall} {\beta^2 \; . \; Precision + Recall}$

See also

Note

only binary images (two classes)

Parameters

[in]	imGt	: Ground Truth image
[in]	imIn	: image to verify
[in]	beta	: $\beta$ coefficient (default value : `1.`)

Returns: returns F-Score index between two images

◆ indexSensitivity()

double smil::indexSensitivity	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexSensitivity()

Returns, for binary images (see isBinary()), the Sensitivity, also called Recall, Hit rate or True Positive Rate

$Sensitivity(imGt, imIn) = \dfrac{TP}{TP+FN}$

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()

double smil::indexSpecificity	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexSpecificity()

Returns, for binary images (see isBinary()), the Specificity index, also called Selectivity or True negative rate

$Specificity(imGt, imIn) = \dfrac{TN}{TN+FP}$

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()

double smil::indexFallOut	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexFallOut()

Returns, for binary images (see isBinary()), the Fall Out index, also called False positive rate or False alarm rate

$Fallout(imGt, imIn) = \dfrac{FP}{TN+FP}$

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()

double smil::indexMissRate	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexMissRate()

Returns, for binary images (see isBinary()), the Miss Rate index, also called False negative rate

$MissRate(imGt, imIn) = \dfrac{FN}{TP+FN}$

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()

double smil::indexOverlap	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

indexOverlap()

Returns, for binary images (see isBinary()), the Overlap coefficient

$Overlap(imGt, imIn) = \dfrac{|imGt \cap imIn|}{min(|imGt|, |imIn|)} = \dfrac{area(inf(imGt, imIn))} {min(area(imGt), area(imIn))}$

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()

size_t smil::distanceHamming	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

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()

double smil::distanceHausdorff	(	const Image< T > &	imGt,
		const Image< T > &	imIn
	)

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

Detailed Description

Functions

Function Documentation

◆ indexJaccard()

◆ indexRuzicka()

◆ indexAccuracy()

◆ indexPrecision()

◆ indexRecall()

◆ indexFScore()

◆ indexSensitivity()

◆ indexSpecificity()

◆ indexFallOut()

◆ indexMissRate()

◆ indexOverlap()

◆ distanceHamming()

◆ distanceHausdorff()