Identity matrix when point clouds are planar?

[Makogan]

I am feeding the algorithm 2 point clouds where all the points are contained in the same plane. FOr example these are a subset of both:

Cloud1:

79.9322  -29.1766         0
  79.0491  -29.9871         0
  77.9883  -30.5455         0
  76.8435   -30.901         0
  75.6688  -31.1422         0
   74.497  -31.3972         0
   73.326  -31.6563         0
  72.1549  -31.9149         0
  70.9831  -32.1699         0
  69.8104   -32.421         0
  68.6367  -32.6678         0
  67.4619  -32.9089         0
  66.2842  -33.1353         0
  65.1034  -33.3449         0

Cloud2:

 -53.1773    -46.1855           0
 -52.0631    -46.0045           0
 -50.9379    -45.8592           0
  -49.806    -45.7634           0
 -48.6745    -45.6633           0
 -47.5434    -45.5648           0
 -46.4184    -45.4074           0
 -45.2863      -45.32           0
 -44.1639    -45.1455           0
 -44.1639    -45.1455           0
 -42.9911    -45.0785           0
 -41.8164    -45.0597           0
 -40.6471    -44.9518           0
 -39.4825    -44.7987           0
  -38.313    -44.6947           0

The icp method for this data is returning the identity matrix, i.e.

Estimated transformation matrix H:
[    1.000000     0.000000     0.000000     0.000000]
[    0.000000     1.000000     0.000000     0.000000]
[    0.000000     0.000000     1.000000     0.000000]
[    0.000000     0.000000     0.000000     1.000000]

With iterations:

Iteration | correspondences | mean(residuals) |  std(residuals)
   orig:0 |            1582 |          0.0000 |          0.0000
        1 |            1582 |          0.0000 |          0.0000
        2 |            1582 |          0.0000 |          0.0000
        3 |            1582 |          0.0000 |          0.0000
        4 |            1582 |          0.0000 |          0.0000
        5 |            1582 |          0.0000 |          0.0000
        6 |            1582 |          0.0000 |          0.0000
        7 |            1582 |          0.0000 |          0.0000
        8 |            1582 |          0.0000 |          0.0000
        9 |            1582 |          0.0000 |          0.0000
       10 |            1582 |          0.0000 |          0.0000
       ```

I tried multiple different parameters and I always get the identity despite the point clouds being clearly different. I was wondering if you could help me identify the issue.

[Philipp Glira]

Interesting. Are both planes at z=0?

Maybe simpleICP simply fits two identical planes at z=0 and consequently all residuals are equal to 0.

Can you share point clouds and code?

[MeerssemanBastien]

Hi i'm having the same issues im using two point cloud of 10 points for each but the program give me back identity matrix also, do you have any idea of what could happen ? and if there is a way to help me im a having also for some cloud point an error about an "empty matrix"

[Philipp Glira]

Please keep in mind that simpleICP matches planes, not points. Consequently, rather dense point clouds are needed to estimate the planes from a certain number of points (parameter neighbors). Thus, a point cloud consisting of 10 points only is not suitable for this algorithm.

However, if you have such small point clouds and if these points (or at least a subset of them) are identical in both point clouds, a point-to-point matching algorithm would be the right choice. Is that the case?

Can you share your PCs?

[MeerssemanBastien]

Thanks for your answer , i think you are right , my points are exactly the same in both of the PCs , so i will try to check for an algorithme that use point to point. my PCs are :
the cloud represent a polygone (trapezium)
the fixed one :
1.000 1.000 0.000
2.500 3.000 0.000
3.500 4.500 0.000
7.000 4.500 0.000
10.000 4.500 0.000
10.500 3.500 0.000
12.000 1.000 0.000
7.000 1.000 0.000
4.500 1.000 0.000
2.000 1.000 0.000

the movable one is the same trapezium but rotated by an angle on the Z axis :
2.500 6.500 0.000
4.850 7.600 0.000
6.400 8.390 0.000
9.400 6.590 0.000
12.000 5.000 0.000
12.000 3.870 0.000
12.000 1.000 0.000
7.700 3.500 0.000
5.500 4.750 0.000
3.400 6.000 0.000

thank you