ImageDistance

ImageDistance[image₁,image₂]

returns a distance measure between image₁ and image₂.

ImageDistance[image₁,image₂,pos]

places the center of image₂ at position pos in image₁.

ImageDistance[image₁,image₂,pos₁,pos₂]

places the point pos₂ of image₂ at position pos₁ in image₁.

Details and Options

ImageDistance[image₁,image₂] centers image₂ in image₁ and returns the distance between the overlapping regions in the two images.
ImageDistance works with arbitrary 2D and 3D images.
Images should either have the same number of channels or one should be a single-channel image. If either of image₁ or image₂ is a single-channel image, the channel is replicated to match the number of channels in the other image.
Position specification pos can be of the form:

	{x,y} or {x,y,z}	absolute pixel position
	Scaled[{s_x,…}]	scaled position from 0 to 1 across the object
	Center	center alignment
	Left,Right	axis in both 2D and 3D
	Bottom,Top	axis in 2D, axis in 3D
	Front,Back	axis in 3D
	{pos_x,…}	a list of named positions

If alignment along each axis is not given, it is assumed to be Center.
The following options can be given:
DistanceFunction EuclideanDistance distance function to use

Masking All region of interest
Some typical distance function settings include:

	EuclideanDistance	Euclidean distance (default)
	SquaredEuclideanDistance	squared Euclidean distance
	NormalizedSquaredEuclideanDistance	normalized squared Euclidean distance
	ManhattanDistance	Manhattan or "city block" distance
	CosineDistance	angular cosine distance
	CorrelationDistance	correlation coefficient distance
	f	function f that is given the overlapping regions of the two images as arguments

	"MeanEuclideanDistance"	mean Euclidean distance
	"MeanSquaredEuclideanDistance"	mean squared Euclidean distance
	"RootMeanSquare"	mean squared root distance
	{"MeanReciprocalSquaredEuclideanDistance",λ}	one minus the mean of the robust distances , where is the Euclidean distance of corresponding pixels (default )
	{"MutualInformationVariation",n}	joint entropy minus mutual information using n-bin histogram (default )
	{"NormalizedMutualInformationVariation",n}	the mutual information variation divided by the joint entropy using n-bin histogram (default )
	{"DifferenceNormalizedEntropy",n}	entropy of the difference image using n-bin histogram (default )
	"MeanPatternIntensity"	mean local pattern intensity difference
	"GradientCorrelation"	mean of the correlation distances between the spatial derivatives
	"MeanReciprocalGradientDistance"	one minus the mean of the distances , with values and variances of the spatial derivatives along dimension s of image_i
	{"EarthMoverDistance",n}	earth mover distance using n-bin histogram

Using Masking->roi, a region of interest in image₁ is specified. With Masking->{roi₁,roi₂}, the intersection of roi₁ and roi₂ on the overlapped images is used.
Predefined ImageDistance metrics are symmetric and non-negative. However, some distances may not satisfy the triangle inequality. The distance between two images can be 0 with some methods, even if they are not identical. User-defined functions might break these properties.
If there are no overlapping regions or the measure cannot be determined, Indeterminate is returned. »