Some poeple claim their background subtraction algorithms use Gaussian Mixture Model, but when I read the code, I find they actually use only one component, and as a result EM algorithm (or its approximated version) is not taken to fit the model. An example can be found here. This configuration is commonly adopted when the background is strictly static, e.g. the scenes without swaying tree branches.

More specifically, their methods use some simple criterion: a pixel is classified as foreground if it satisfies

$$ \sum_{c \in C} w_c\frac{|I_c(x,y)-\mu_c(x,y)|}{\sigma_c(x,y)} > \text{Threshold} $$

where $C$ is the set of channels (RGB, HSV, etc.) and $w_c$ is the weight of channel $c$. Technically there is no mixture distribution any more. Do you think it's still appropriate to call this model GMM?

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