Why can i not create a rigid3d object from this matrix?

Hi,

i want to use Matlab for SfM. I have have position prior in world coordinates for the views that i read in from a csv file. When i want to create a rigid3d object from my data i get an error as seen in the following example copied from the command window:

posPrior =

1.000000000000000 -0.000113000000000 0.000234000000000 0

0.000114000000000 1.000000000000000 -0.000011000000000 0

-0.000234000000000 0.000011000000000 1.000000000000000 0

0.099970000000000 -0.299979000000000 0.885011000000000 1.000000000000000

Error using rigid3d (line 143)

The transformation matrix is not rigid.

A rigid transformation matrix must only contain a rotation and a translation.

The final column must consist of zeros, except for a one in the last row.

The posPrior matrix is my position i read in from my file. Then when i want to create a rigid3d object with pos = rigid3d(posPrior) i get the error. My matrix has the same structure as the T property so i dont know what im doing wrong here. I tried to separate the Rotation and Translation, but something seems wrong with the Rotation.

Thanks in advance

Answer 1

[Pratyush Roy]

Hi Thomas,

For a transformation to be rigid, it should satisfy the following conditions:

1. Similarity Transform: For homogeneous scale, all singular values of the rotation matrix should approximately be equal (within roughly eps of largest singular value)

2. abs(det(T) - 1) ~= 0

The transformation matrix does not satisfy either of the above conditions. Both of these conditions fail due to small differences of about 1e-4.

'rigid3d' is working as expected. For the issue of using the same Transform matrix which worked before, there is a precision issue of what the older exported transformation was and what the new values you are trying to create rigid3d form. There could also possibly a datatype mismatch.

Using the same values as provided in the question, casting the values to single before creating the rigid3d object works fine. Please take a look at the following for single vs double values:

>>href = rigid3d(priorPos)
Error using rigid3d (line 143)
The transformation matrix is not rigid.
A rigid transformation matrix must only contain a rotation and a translation.
The final column must consist of zeros, except for a one in the last row.

Casting into single datatype resolves the issue. But note that doing this might lead in loss of precision.

>> href =  rigid3d(single (priorPos))
href = 
  rigid3d with properties:
            Rotation: [3x3 single]
        Translation: [0.09997 -0.299979 0.885011]

Hope this helps!