Algorithm for grid interpolation/regression given points with holes

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I have an image containg a set of identical objects which are disposed into a regular grid fashon. The number of these objects is unknown.

I need to find in a really accurate way the bounding rect of that set of objects and then generate the grid given by them. I can find a lot - but often not all - of these objects in the image using pattern match techiques so i also have the corners coordinates with a good precision.

So, given a number (say, 95%) of the corners coordinates where the missing ones are randomly distributed, i need to "interpolate" the grid.

I'm thinking about linear regression by rows and columns but it seems able to become quite sophisticated if the grid is rotated.

Is there some specific/more general grid-find algorithm which can be suitable for my problem?

Thank you for your attention.

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