For a given image $\mathbf X$, the equivalence class for pixels $p$ with labels $l$.

Question

$\left[l\right]=\left\{p \in\mathbf X|\,p\sim l\right\}$.

This is taken from this paper on image segmentation, page $2$. I don't know how to interpret this, do they mean "all the pixels on image $\mathbf X$ that share a label $l$ on algorithm step $t$ become equivalent"?

Answer 1

Yes, that's correct. The equivalence classes partition X by grouping together the pixels with the same label. For the purposes of this algorithm, pixels that share the same label are considered equivalent.