LIC (Line Integral Convolution) is a well-known texture synthesis technique proposed by Cabral and Leedom [33] at Lawrence Livermore National Laboratory in ACM SigGraph 93. It employs a low-pass filter to convolve an input noise texture along pixel-centered symmetrically bi-directional streamlines to exploit spatial correlation in the flow direction. LIC provides a global dense representation of the flow, analogous to the resulting pattern of a tract of wind-blown sand (Figure 1). Here is a mini version of the LIC source code.
 
Figure 1. LIC emulates what happens when an area of fine sand is blown by strong wind (© Zhanping Liu).
 
LIC is an image-space or Eulerian-based texture synthesis technique for steady flow visualization (whereas UFLIC - Unsteady Flow LIC [60] used for time-varying flows is an object-space or Lagrangian-based texture synthesis method by which a particle released at a time under investigation leaves its footprint at, i.e., contributes its property / texture to, succeeding positions downstream as the flow evolves). For each pixel of the output LIC image, the contributing or correlated pixels are first located along the bi-directionally advected streamline and then the associated noise texture values are referenced for convolution (Figure 2). A sequence of animated LIC frames can be produced by shifting the phase of a periodic convolution kernel like Hanning kernel (care needs to be taken to handle the abrupt-replay problem with non-periodic kernels, such as a box kernel used in FastLIC [34]).
 
Figure 2. The basic idea of 2D LIC and the image-space based implementation (© Zhanping Liu).
 
Since the introduction of basic LIC, there have been a variety of optimizations or extensions such as Oriented LIC [39], Enhanced LIC [40], Volume LIC [42], [43], FastLIC [34], ProLIC, TexMapLIC (ACM SigGraph 99 Course Note), UFLIC [60], AUFLIC (Accelerated UFLIC) [61], [62], and the application of LIC to image processing. Other variants include parallel LIC [35], LIC on curvilinear grids [36], LIC on triangulated surfaces [37], multi-frequency LIC [38], dyed LIC [41], and HyperLIC [44].
     
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