How Logical expression can be dividend?

Question

I work with image processing and I face this equation and I can't understand how logical expression can be dividend here??

I need clarification for this part: $δ(y_1 \ne y_2)$

The full equation: $Ψ^{2D}(y_1,y_2,x_1,x_2) = \frac{δ(y_1 \ne y_2)} { 1+a||RGB_{x1} −RGB_{x2}||_1}$

Update

This equation from A multi-modal graphical model for scene analysis paper to re-evaluate class similarity using RGB (color value) for adjacent superpixels.

• $Ψ^{2D}$: potential function.
• a: constant, weight of the RGB contrast.
• x, y: adjacent superpixels.

Answer 1

The numerator equals one, if and only if $y_1 \neq y_2$.

This formula assigns a zero potential to two superpixels that have identical class labels. Note that in this equation, $x_1$ and $x_2$ represent the superpixels 1 and 2, and $y_1$ and $y_2$ are their class labels respectively.

Answer 2

That might be something like the Iverson bracket. It would be an indicator function: $1$ when the logical expression is true and $0$ otherwise. Assuming this interpretation, it could also be rewritten with the Kronecker delta by $\delta(y_1\neq y_2)=1-\delta_{y_1y_2}$.

Without more context, though, it can be hard to say exactly what a given notation means.