ENH: Suppress "Bad Rotation Matrix" warnings

[dzenanz]

This warning show up a lot for me (e.g. from here). Should I be concerned?

Example of occurrence:

Progress  | 0 | 0.01 | 0.0345 | 0.059 | 0.0835 | 0.108 | 0.1325 | 0.157 | 0.1815 | 0.206
 | 0.2305 | 0.255WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (000002581E7CA7F0): Bad Rotation Matrix 1.02555 -0.00607706 0.00711725 1.02636

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581E930950): Bad Rotation Matrix 1.0038 0.000658097 0.0181835 1.0196

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581E8193D0): Bad Rotation Matrix 1.01296 -0.000485504 0.00252202 0.99968

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581F07ABF0): Bad Rotation Matrix 1.00139 -0.0353489 0.014181 0.954691

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581E8F5140): Bad Rotation Matrix 0.94323 0.00672548 -0.0293821 1.00311

 | 0.2795 | 0.304 | 0.3285 | 0.353 | 0.3775 | 0.402 | 0.4265 | 0.451
 | 0.4755 | 0.5WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (000002581EC262E0): Bad Rotation Matrix 1.01756 -0.00261415 0.0241831 1.00784

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581EC265A0): Bad Rotation Matrix 1.05521 -0.0124403 0.0215943 0.991163

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581F29B710): Bad Rotation Matrix 0.943761 -0.00148547 -0.0278611 1.00295

 | 0.5245 | 0.549 | 0.5735 | 0.598 | 0.6225 | 0.647 | 0.6715 | 0.696
 | 0.7205 | 0.745WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (000002581EF693A0): Bad Rotation Matrix 1.02405 -0.00516537 0.0336307 1.01107

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581EF69BE0): Bad Rotation Matrix 1.04952 -0.0166267 0.00826341 0.983876

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581EF69D40): Bad Rotation Matrix 0.946308 -0.0141908 -0.0155272 1.0036

 | 0.7695 | 0.794 | 0.8185 | 0.843 | 0.8675 | 0.892 | 0.9165 | 0.941
 | 0.9655 | 0.99WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (000002581EDCFCE0): Bad Rotation Matrix 1.02332 -0.0042626 0.0304406 1.01458

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581EDD07E0): Bad Rotation Matrix 1.04445 -0.00741455 0.0214106 0.99242

WARNING: In C:\Dev\ANTsWasm\VS22py\_deps\ants_inner-src\ImageRegistration\itkANTSCenteredAffine2DTransform.hxx, line 138 ANTSCenteredAffine2DTransform (000002581EDD0680): Bad Rotation Matrix 0.955261 -0.0237769 -0.00559731 0.994758

 | 1
Filter took 147.606 seconds.

Should we try to retain these warnings in command-line tools?

[dzenanz]

Ping!

[cookpa]

It looks like it's not able to get a pure rotation matrix from the transform, which seems bad but I don't know for sure why this is happening.

If you register the same data with antsRegistration, do you see these errors?

[dzenanz]

I am using Faces example. The warning gets triggered by the original script too:

dzenan@corista:~/ANTsWasm/TemplateBuildingExample/Faces$ ANTSPATH=/home/dzenan/ANTs/Scripts ./templateCommand.sh > run.log
WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c8f7d4ffc0): Bad Rotation Matrix 1.02839 -0.0157299
0.0204534 1.0099


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c8f7d504f0): Bad Rotation Matrix 1.04678 0.00573631
0.00611402 0.981415


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c8f7d509d0): Bad Rotation Matrix 1.03557 -0.01256
0.0241544 1.02507


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c8f7d51120): Bad Rotation Matrix 0.972547 -0.00227736
-0.00214852 0.945171


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c8f7d51390): Bad Rotation Matrix 0.946277 0.00597829
-0.0209535 0.992051


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c3ff2f3fc0): Bad Rotation Matrix 1.02244 -0.0224988
0.0328645 1.02861


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c3ff2f5120): Bad Rotation Matrix 0.963474 0.0117549
-0.0205578 0.954667


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x55c3ff2f5390): Bad Rotation Matrix 0.948863 -0.0052806
-0.00569918 1.00631


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x562b801c4fc0): Bad Rotation Matrix 1.02179 -0.0224462
0.0431247 1.03127


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x562b801c6120): Bad Rotation Matrix 0.964812 0.00868409
-0.0161593 0.94557


WARNING: In /home/dzenan/ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx, line 138
ANTSCenteredAffine2DTransform (0x562b801c6390): Bad Rotation Matrix 0.951257 0.00278727
-0.0111354 1.0092

[cookpa]

@ntustison @stnava do you know if these warnings are harmless?

[stnava]

I dont know - are these matrices stored in .txt? my recollection is that the matrices will get projected to the closest orthogonal .... so potentially low impact if not harmless at least in this context

[dzenanz]

These are intermediate affine matrices which are getting averaged during groupwise registration.

[cookpa]

Here's the function that produces the error

ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx

Lines 96 to 140 in 0ec3fa5

	/** Compute the Angle from the Rotation Matrix */
	template <typename TScalarType>
	void
	ANTSCenteredAffine2DTransform<TScalarType>::ComputeMatrixParameters(void)
	{
	typedef vnl_matrix_fixed<TScalarType, 2U, 2U> TMatrix;
	const TMatrix A{ this->GetMatrix().GetVnlMatrix() };
	vnl_qr<ScalarType> myqr(A.as_matrix());
	TMatrix R = myqr.Q(); // Q() is the rotation
	TMatrix Q = myqr.R(); // R() is the upper triangluar
	TMatrix dq(itk::NumericTraits<TScalarType>::ZeroValue());
	for (unsigned i = 0; i < 2; i++)
	{
	dq(i, i) = (Q(i, i) >= 0) ? 1 : -1;
	}
	R = R * dq;
	Q = dq * Q;
	// std::cout << "A=" << A << std::endl;
	// std::cout << "Q=" << Q << std::endl;
	// std::cout << "R=" << R << std::endl;
	// std::cout << "dq=" << dq << std::endl;
	m_Angle = std::acos(R[0][0]);
	if (this->GetMatrix()[1][0] < itk::NumericTraits<TScalarType>::ZeroValue())
	{
	m_Angle = -m_Angle;
	}
	m_S1 = Q[0][0];
	m_S2 = Q[1][1];
	m_K = Q[0][1] / Q[0][0];
	this->ComputeMatrix();
	if (static_cast<double>(this->GetMatrix()[1][0]) - static_cast<double>(std::sin(m_Angle)) > 0.000001)
	{
	itkWarningMacro("Bad Rotation Matrix " << this->GetMatrix());
	}
	}

It does a QR decomposition on the matrix but then uses R to get m_Angle, which looks backwards to me.

Then it sets the full matrix and checks that matrix[1][0] == sin(m_Angle), but don't you need to do the QR decomposition again to extract the rotation?

[cookpa]

OH!

ANTs/ImageRegistration/itkANTSCenteredAffine2DTransform.hxx

Lines 106 to 107 in 0ec3fa5

	TMatrix R = myqr.Q(); // Q() is the rotation
	TMatrix Q = myqr.R(); // R() is the upper triangluar

OK now it all makes sense. So I think the answer is that the matrix is correct, but the check for "bad rotation" is not, because it's checking the full affine transform directly and not just the rotation part.

[dzenanz]

Feel free to take over this PR if you have an improvement!

[cookpa]

Sure, I will change it to do the sanity check by redoing the decomposition, but only if in debug mode.

[cookpa]

Will merge shortly. I re-ran the template example and don't see the warning now, even in debug mode. The rotations look correct, the warning was being triggered by a test on the composed affine transform, not the rotation component.

[dzenanz]

Looks good to me