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I'm implementing a system, that is receiving on the input imprecise (due to various external influences) coordinates in 2D. My goal is to assign to each coordinate position in regular rectangular mesh. I don't have knowledge on how many rows and columns are there. I know what is the typical distance between rows and columns.

Our current approach is strictly procedural - meaning that we're isolating points which we think belong to the same columns/rows and then merging them together.

I'm wondering whether there exists some suitable numerical method, we could use to fit imperfect data to a perfect rectangular mesh.

EDIT: I will try to elaborate. There are no serious real life consequences of a bad positioning. See image bellow. I receive feedback from my real-life system (step motor feedback). f(x,y), I need to assign to each box discrete position [m,n].

enter image description here

So in this case I would somehow expect that potential transformation to create a mesh with ~6 rows and ~5 columns and assign to each block position in that block.

In practice there may be some slight rotation factor +-10 degrees.

Biggles
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  • Suppose you have $x$ and $y$ coordinates for the input. Do you assume that the rows and columns are parallel to the $x$ and $y$ axes? – Andrei Mar 12 '19 at 13:04
  • Also, is the typical distance a constraint, or can be fitted? – Andrei Mar 12 '19 at 13:06
  • This is too vague. Can you provide a small tiny example showing which input you receive and what output you wish to generate. Please elaborate on you second to last paragraph. Also, what are the real life consequences (if any) of an error? – Carl Christian Mar 12 '19 at 13:08
  • I do not understand your last sentence. Your input consists of points. It does not matter if you rotate a point. Does your input consist of, say, the coordinates of the upper left corner of each rectangle, the length and width of each rectangle and its rotation around some axis? – Carl Christian Mar 12 '19 at 18:08
  • Sorry if I was unclear. You are right, there is no rotation of a point. Imagine the whole image is rotated ~5 degrees. But let's ignore that. I'm just wondering if there is some fitting algorithm, that would work at least for this simpler perpendicular situation. – Biggles Mar 12 '19 at 18:38

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