Line Integral Convolution

Line integral convolution, sometimes called line interval convolution, (LIC) is a flow-visualization method for steady-state flows.

Details

LIC Image of a Vector Field, Field Strength indicated by color (From Fast and Resolution Independent Line Integral Convolution (1995)
LIC Image of a Vector Field, Field Strength indicated by color (From Fast and Resolution Independent Line Integral Convolution (1995)

The LIC algorithm combines a vector field sampled on a uniform Rectilinear Grid (or a structured Curvilinear Grid) with a texture map image (e.g., a random noise field) of the same dimension as the grid to produce an image in which the texture has been "locally blurred" by the vector field. The pixels in the output image are produced by the one-dimensional convolution of the texture pixels along a streamline with a filter kernel.

Therefore each pixel in the output image is a weighted average of all the pixels corresponding to the grid cells along any streamline that passes through the grid cell associated with that pixel. Streamlines are initiated from every grid cell. The output image is a smeared version of the input texture map, where the direction of smearing is determined by the vector field. The figure to the right is an example of an LIC image; unfortunately, it needs to be viewed as part of an animation for full appreciation of the value of the LIC technique. An obvious signal processing issue is determining the best filter or convolution kernel.

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