For an $n\!\times\! n$ random image with independent pixels, black with probability $p(n)$ and white with probability $1\!-\!p(n)$, the probability of satisfying any given first-order sentence tends to $0$ or $1$, provided both $p(n)n^{\frac{2}{k}}$ and $(1-p(n))n^{\frac{2}{k}}$ tend to $0$ or $+\infty$, for any integer $k$. The result is proved by computing the threshold function for basic local sentences, and applying Gaifman's theorem.