In computer vision, the Lucas–Kanade method is a widely used differential method for optical flow estimation developed by Bruce D. Lucas and Takeo Kanade. It assumes that the flow is essentially constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion. By combining information from several nearby pixels, the Lucas–Kanade method can often resolve the inherent ambiguity of the optical flow equation. It is also less sensitive to image noise than point-wise methods. On the other hand, since it is a purely local method, it cannot provide flow information in the interior of uniform regions of the image.
Concept The Lucas–Kanade method assumes that the displacement of the image contents between two nearby instants (frames) is small and approximately constant within a neighborhood of the point p {\displaystyle p} under consideration. Thus the optical flow equation can be assumed to hold for all pixels within a window centered at p {\displaystyle p} . Namely, the local image flow (velocity) vector ( V x , V y ) {\displaystyle (V_{x},V_{y})} must satisfy
I x ( q 1 ) V x + I y ( q 1 ) V y = − I t ( q 1 ) I x ( q 2 ) V x + I y ( q 2 ) V y = − I t ( q 2 ) ⋮ I x ( q n ) V x + I y ( q n ) V y = − I t ( q n ) {\displaystyle {\begin{aligned}I_{x}(q_{1})V_{x}+I_{y}(q_{1})V_{y}&=-I_{t}(q_{1})\\I_{x}(q_{2})V_{x}+I_{y}(q_{2})V_{y}&=-I_{t}(q_{2})\\&\;\ \vdots \\I_{x}(q_{n})V_{x}+I_{y}(q_{n})V_{y}&=-I_{t}(q_{n})\end{aligned}}}
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