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ImageDisplacements[{image1,image2,…,imagen}]

gives estimated horizontal and vertical displacements between consecutive images.

ImageDisplacements[video]

gives displacements between consecutive video frames.

ImageDisplacements[input,flow]

uses flow as an initial estimate for displacement between first two images or video frames.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Applications  
Interactive Examples  
See Also
Related Guides
History
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ImageDisplacements

ImageDisplacements[{image1,image2,…,imagen}]

gives estimated horizontal and vertical displacements between consecutive images.

ImageDisplacements[video]

gives displacements between consecutive video frames.

ImageDisplacements[input,flow]

uses flow as an initial estimate for displacement between first two images or video frames.

Details and Options

  • ImageDisplacements, also known as dense optical flow, compares consecutive images or video frames and returns a list of displacement matrices.
  • For a pair of consecutive images imagei and imagei+1, the displacement matrix returns a {δx,δy} for every pixel of imagei.
  • ImageDisplacements works with an AnimatedImage, a Video object or a sequence of images of the same dimensions.
  • The following options are supported:
  • MaxIterations10number of iterations to run
    MethodAutomaticthe method to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
  • By default, the more suitable method is used. Possible method settings are "Farneback" and "DenseInverseSearch".

Examples

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Basic Examples  (2)

Compute the displacement between two images:

Wolfram Language code: flow = ImageDisplacements[{[image], [image]}]

Plot the displacements:

Wolfram Language code: Image[Rescale[flow[[1]]]]

Compute the displacements between consecutive images of a list:

Wolfram Language code: list = {[image], [image], [image], [image], [image]};
Wolfram Language code: flows = ImageDisplacements[list];
Wolfram Language code: Image /@ Rescale /@ flows

Applications  (2)

Detect rotating objects in a wind farm:

Wolfram Language code: seq = DynamicModule[«4»]["ImageList"];
Wolfram Language code: flow = Mean@ImageDisplacements[Append[seq, seq[[1]]]];

Extract the rotation component of the flow by computing its curl:

Wolfram Language code: listCurl = flow  ListConvolve[{{0.5, 0, -0.5}}, flow[[All, All, 2]], {{1, 2}, {1, 2}}, "Fixed"] - ListConvolve[{{-0.5}, {0}, {0.5}}, flow[[All, All, 1]], {{1, 2}, {1, 2}}, "Fixed"]; curl = ImageAdjust@Image@GaussianFilter[listCurl@flow, 8{3, 1}]

Colorize the rotation map and superimpose it on top of the original image:

Wolfram Language code: ImageCompose[seq[[1]], SetAlphaChannel[Colorize[curl, ColorFunction -> ColorData[{"TemperatureMap", "Reverse"}]], ColorNegate[curl]]]

Compute and visualize divergence of a velocity field:

Wolfram Language code: video = \!\(\*VideoBox["![Embedded Video Player](video://content-1efui)"]\);

Compute the displacements:

Wolfram Language code: flow = ImageDisplacements[video];

Compute divergence of displacements:

Wolfram Language code: listDivergence = Function[flow, ListConvolve[{{-0.5, 0, 0.5}}, flow[[All, All, 1]], {{1, 2}, {1, 2}}, "Fixed"] + ListConvolve[{{-0.5}, {0}, {0.5}}, flow[[All, All, 2]], {{1, 2}, {1, 2}}, "Fixed"] ];

Visualize the divergence on each frame:

Wolfram Language code: VideoMap[ With[{div = (Image@listDivergence@flow[[Min[#FrameIndex, Length[flow]]]] + 2) / 4}, ImageCompose[#Image, {Colorize[div, IconizedObject[«cfun»]], .5}]]&, video]

Interactive Examples  (1)

Slow motion video effect:

Wolfram Language code: original = {[image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image]};
Wolfram Language code: ListAnimate[original, DefaultDuration -> 2]

Compute the optical flow:

Wolfram Language code: flows = Map[vecField  Transpose@Reverse[vecField], ImageDisplacements[original, MaxIterations -> 1] / 2];

Construct the interpolated frames and insert them into the final sequence:

Wolfram Language code: vecTrafo[xy_, motion_] := xy + Extract[motion, Ceiling[xy]];
Wolfram Language code: oflow = Table[ ImageForwardTransformation[original[[i]], vecTrafo[#, flows[[i]]]&, DataRange -> Full, Background -> White], {i, Length@original - 1}]; slowmo = Riffle[original, oflow];
Wolfram Language code: ListAnimate[slowmo, DefaultDuration -> 4]
Wolfram Research (2016), ImageDisplacements, Wolfram Language function, https://reference.wolfram.com/language/ref/ImageDisplacements.html (updated 2025).

Text

Wolfram Research (2016), ImageDisplacements, Wolfram Language function, https://reference.wolfram.com/language/ref/ImageDisplacements.html (updated 2025).

CMS

Wolfram Language. 2016. "ImageDisplacements." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ImageDisplacements.html.

APA

Wolfram Language. (2016). ImageDisplacements. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ImageDisplacements.html

BibTeX

@misc{reference.wolfram_2026_imagedisplacements, author="Wolfram Research", title="{ImageDisplacements}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ImageDisplacements.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_imagedisplacements, organization={Wolfram Research}, title={ImageDisplacements}, year={2025}, url={https://reference.wolfram.com/language/ref/ImageDisplacements.html}, note=[Accessed: 13-June-2026]}