  Given a random binary picture $P_n$ of size $n$, i.e., an $n\times n$ grid
filled with zeros and ones uniformly at random, when is it possible to
reconstruct $P_n$ from its $k$-deck, i.e., the multiset of all its $k\times k$
subgrids? We demonstrate ``two-point concentration'' for the reconstruction
threshold by showing that there is an integer $k_c(n) \sim (2 \log n)^{1/2}$
such that if $k > k_c$, then $P_n$ is reconstructible from its $k$-deck with
high probability, and if $k < k_c$, then with high probability, it is
impossible to reconstruct $P_n$ from its $k$-deck. The proof of this result
uses a combination of interface-exploration arguments and entropic arguments.
