Video Motion Field and Divergence Analysis

Compute and visualize the divergence of a motion field extracted from a video sequence

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This example analyzes motion in a short video clip by computing frame-to-frame image displacements. The displacement field is interpreted as a velocity field, and its divergence is evaluated to detect local expansion and contraction in the scene. The divergence is visualized as a color overlay on the original frames.

Load a short video clip that will be used for motion analysis:

In[1]:=

video=Video["https://cdn.pixabay.com/video/2022/09/04/130231-746395333_tiny.mp4"]

Out[1]=

Compute frame-to-frame displacement vectors using optical flow estimation:

In[2]:=

flow=ImageDisplacements[video];

The result is a time-indexed array of 2D displacement vectors representing horizontal and vertical motion between consecutive frames. See the dimensions of one frame:

In[3]:=

flow〚100〛//Dimensions

Out[3]=

{720,1280,2}

Define a function that computes the divergence of a 2D displacement field using finite differences. This applies centered finite differences to approximate the spatial derivatives of the horizontal and vertical displacement components:

In[4]:=

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"]];

Compute and overlay the divergence field on each frame of the video:

In[5]:=

VideoMapWith{div=(Image@listDivergence@flow〚Min[#FrameIndex,Length[flow]]〛+5)/10},ImageCompose#Image,Colorizediv,

cfun

,.5&,video

Out[5]=

Visualize the displacement field of a selected frame as a vector field to display the local direction and relative magnitude of motion:

In[6]:=

frameIndex=100

Out[6]=

100

In[7]:=

ListVectorPlot[flow〚frameIndex〛,VectorPoints20,VectorScale{Small,Automatic,None}]

Out[7]=

Related Symbols

ImageDisplacements
VideoMap
ImageData

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Contributed by: Wolfram Staff

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Video Motion Field and Divergence Analysis

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