How to get the largest zero region(rectangle) in a 3D matrix/ 2D matrix?

My origin thoughts is that calculating the min and the max in every collum and row, I'm working on it.

I wonder there is more convenient method to realize it.

The RED rectangle is I want to obtain.

Answer 1

[Xuechu Xu]

I recommend region growing algorithm. Find all zero elements as seeds, and begin from one of it. Add one collum or row each time to make a growth, meanwhile delete those grown regions from the seeds. Keep this progress until all seeds are grown to region, find the largest one.

[Xuechu Xu]

Ah, something wrong. Those grown dots can't be deleted from seeds, I didn't consider the different shape. (But this will cost much much more resources and time, just for reference only)