  This paper extends the problem of 2-dimensional palindrome search into the
area of approximate matching. Using the Hamming distance as the measure, we
search for 2D palindromes that allow up to $k$ mismatches. We consider two
different definitions of 2D palindromes and describe efficient algorithms for
both of them. The first definition implies a square, while the second
definition (also known as a \emph{centrosymmetric factor}), can be any
rectangular shape. Given a text of size $n \times m$, the time complexity of
the first algorithm is $O(nm (\log m + \log n + k))$ and for the second
algorithm it is $O(nm(\log m + k) + occ)$ where $occ$ is the size of the
output.
