Algorithm to minimize distance variance between coordinates

Question

I've been looking around for an algorithm that would optimize the distance between 2 list of coordinates and choose which coordinate should go together.

Say I have List 1:

205|200
220|210
200|220
200|180

List 2:

210|200
207|190
230|200
234|190

Calculated Distance between Coords:

205|200 to 210|200 == 5.00
205|200 to 207|190 == 10.20
205|200 to 230|200 == 25.00
205|200 to 234|190 == 30.68

220|210 to 210|200 == 14.14
220|210 to 207|190 == 23.85
220|210 to 230|200 == 14.14
220|210 to 234|190 == 24.41

200|220 to 210|200 == 22.36
200|220 to 207|190 == 30.81
200|220 to 230|200 == 36.06
200|220 to 234|190 == 45.34

200|180 to 210|200 == 22.36
200|180 to 207|190 == 12.21
200|180 to 230|200 == 36.06
200|180 to 234|190 == 35.44

This Algorithm would pick:

205|200 to 230|200 == 25.00
220|210 to 207|190 == 23.85
200|220 to 210|200 == 22.36
200|180 to 234|190 == 35.44

The Algorithm would pick these numbers as they would be the group that would have the littlest variance between the distance. Conditions:

1. A Coordinate may only be used ones from each list
2. If List 1 or List2 is larger than it still only uses each coordinate once, but it tries to get the smallest distance variance and does nothing with the unused coordinates.

If you need more clarification please ask.

P.S. I've looked at the Hungarian algorithm and it seems like it will sort of do the job, but not exactly how I was expecting. The Hungarian algorithm will only try and make the least distance from all the coordinates, which can mean the smallest variance, but not every time as variance is more important here then least distance optimization.

Answer 1

It is worth to look at ICP algorithm. It is intended to solve similar problems