Algorithm 1. Gaussian mixture model-based moving target detection

input: the enhanced image Rx, y and parameters of Gaussian mixture model μx,y,k, σx,y,k and ωx,y,k, where x ∈ [1,Width], y ∈ [1,Height], k ∈ [1,K]

output: the foreground image Fx, y, where x ∈ [1,Width], y ∈ [1,Height]

procedure GaussianMixtureModelDetection(R, μ, σ, w)

Step #1 Initialize the parameters of Gaussian mixture model

μx,y,k←rand(), σx,y,k←σ0, ωx,y,k←1/K

Step #2 Try to match the Gaussian mixture model with the n-th image

for k = 1 to K do

if Rx,y,n $-$ μx,y,k < d·σx,y,k then

matchk = 1

ωx,y,k = (1 − α)·ωx,y,k + α

μx,y,k = (1 − α/ωx,y,k)·μx,y,k + α/ωx,y,k·Rx,y,n

σx,y,k = $\sqrt{(1-\alpha /w_{x,y,k})\cdot {\sigma }_{{}_{x,y,k}}^2+\alpha /w_{x,y,k}\cdot {(R_{x,y,k}-{\mu }_{x,y,k})}^2}$

else

ωx,y,k = (1 − α)·ωx,y,k

end if

end

Step #3 Normalize the weight ωx,y,k and sort the model with ωx,y,k/σx,y,k

Step #4 Reinitialize the model with minimum weight if there is no matched model,

if ${\displaystyle \sum _{k=1}^{\mathrm{K}}matc{h}_k=0}$ then

μx,y,0 = pixelx,y,n

σx,y,k = σ0

end if

Step #5

for k = 1 to K do

if ωx,y,k > T and Rx,y,n $-$ μx,y,k < d·σx,y,k then

Fx, y = 0

break

else

Fx, y = 255

end if

end

Step #6 Execute 3 × 3 erode and dilate operations over R(x, y)

Step #7 Execute connected region analysis and list potential moving target

Step #8 Specify the object larger than AreaThresh as the target

end procedure