The onboard optic flow algorithm uses the temporal filtered Lucas Kanade method. The presented implementation is focused on efficiency and uses integer arithmetic. The following pseudo-code illustrates the procedure:

P, n, pixel, GB, GBt=(0,0,0,0,0)

for x, y in P

gx = pixel[x+1,y] – pixel[x-1,y]

gy = pixel[x, y+1] – pixel[x, y-1]

gt = pixel[x, y] – pixel_old[x, y]

GBt += (gx * gx, gx * gy, gy * gy, gx * gt, gy * gt)

GB -= (GB(0) >> n, GB(1) >> n, GB(2) >> n, GB(3) >> n, GB(4) >> n)

GB += (GBt(0) >> n, GBt(1) >> n, GBt(2) >> n, GBt(3) >> n-1, GBt(4) >> n-1)

det = GB(0) * GB(2) – GB(1) * GB(1)

u = (GB(2)*GB(3)-GB(1)*GB(4))/det;

v = (GB(0)*GB(4)-GB((1)*GB(3))/det;

The sensor data for the current and previous time step is contained in pixel and pixel_old, respectively. P denotes the spatial integration patch and GB contains the integrated values for G and B. Since G is symmetric it is sufficient to store 3 values for G instead of 4. The multiplications required for the temporal filtering are implemented as bitwise shift operations (>>n) which limits the possible α values for the filter but improves performance. Note that GB contains signed valued which requires an arithmetic shift with sign extension instead of a logic shift. A shift value of 4 corresponds to a division by 16 (α = 0.0625). In the computation of the spatial gradients a divisor of 2 is omitted. These factors cancel out in the final solving step up to a factor of 2 for the temporal gradient which is accounted for in the integration step on line 8.

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