Weighted L1-norm based Contextual Regularization

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I am Japanese. I'm not good at English, but thank you.

I am currently reading the following treatise.

"Efficient Image Dehazing with Boundary Constraint and Contextual Regularization",Gaofeng MENG,et al 2013, IEEE

I don't understand the Weighted L1-norm based Contextual Regularization formula that appears there.

The equation $W(x,y) = e^{-\Vert I(x)-I(y)\Vert^2 / 2 σ^2} $ is weighting function.

$W(x,y) $ is weighting function. $ I(x) $ and $ I(y) $ is Image. Why $ I(x) $ and $ I(y) $ are 1 -dimentional?

In the paper,$ x$ and $ y $ are called two neighboring pixels. Is this means 4(8)-neighbors of pixel ?