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Given two matrices $A$ and $B$ with random dimensions, I want to find the largest common sub-matrix, in the sense of the dimension(e.g. $M_{p,q}$ has larger dimension than $N_{s,t}$ iff $p\geq s$ and $q\geq t$). How could I understand this problem in math, or are there some models based on such a problem.

PS: The above problem comes from the image processing, i.e. finding the common area of the two pictures. And, I just knew the brute-force method.

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    How do you rank submatrices by dimension? There is no obvious way to tell whether a $6\times 2$ is larger or smaller than a $3\times 4$. – 2017-01-12
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    I see your edit and stand by my previous comment. How would you rank a $6\times 2$ vs a $3\times 4$? – 2017-01-12
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    @Arthur In your case, no. Maybe, we could suppose that there exists just one largest common sub-matrix in the above rule. – 2017-01-12

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