Use of TransformRigidityPenalty Fails

Beginner Questions
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2

I also tried with parameter settings that Jian et al. (2022) used:

// Main Components
(Registration "MultiMetricMultiResolutionRegistration")
(Interpolator "BSplineInterpolator")
(ResampleInterpolator "FinalBSplineInterpolator")
(Resampler "DefaultResampler")
(FixedImagePyramid "FixedRecursiveImagePyramid")
(MovingImagePyramid "MovingRecursiveImagePyramid")
(NumberOfHistogramBins 64)
(ErodeMask "false")
(FixedInternalImagePixelType "float")
(MovingInternalImagePixelType "float")
(FixedImageDimension 3)
(MovingImageDimension 3)
(UseDirectionCosines "true")
// Transformation
(Transform "BSplineTransform")
(HowToCombineTransforms "Compose")
// Similarity measure
(Metric "AdvancedMattesMutualInformation" "TransformRigidityPenalty")
(Metric0Weight 0.1)
(Metric1Weight 0.5)
(LinearityConditionWeight 1.0)
(OrthonormalityConditionWeight 0.1)
(PropernessConditionWeight 0.1)
(UseLinearityCondition "false")
(UseOrthonormalityCondition "true")
(UsePropernessCondition "true")
(CalculateLinearityCondition "true")
(CalculateOrthonormalityCondition "true")
(CalculatePropernessCondition "true")
(DilateRigidityImages "false" "false" "false" "true")
(DilationRadiusMultiplier 1.0)
(UseFixedRigidityImage "false")
(UseMovingRigidityImage "true")
// Multiresolution
(NumberOfResolutions 4)
(FinalGridSpacing 8.0)
(UpsampleGridOption "true")
// Optimizer
(Optimizer "StandardGradientDescent")
(MaximumNumberOfIterations 500)
(SP_a 150000.0 120000.0 70000.0 20000.0)
(SP_alpha 0.602 0.602 0.602 0.602)
(SP_A 100.0 100.0 100.0 100.0)
// Image sampling
(NumberOfSpatialSamples 5000)
(NewSamplesEveryIteration "true")
(ImageSampler "Random")
// Interpolation and Resampling
(BSplineInterpolationOrder 3)
(FinalBSplineInterpolationOrder 3)
(DefaultPixelValue -1024)

It works without any distortion!

However, if I use the parameters that are used by Luu et al. (2015) and Staring et al. (2007) as below:

//  Main Components 
(Registration "MultiMetricMultiResolutionRegistration")
(Interpolator "BSplineInterpolator")
(ResampleInterpolator "FinalBSplineInterpolator")
(Resampler "DefaultResampler")
(FixedImagePyramid "FixedRecursiveImagePyramid")
(MovingImagePyramid "MovingRecursiveImagePyramid")
(FixedInternalImagePixelType "float")
(MovingInternalImagePixelType "float")
(FixedImageDimension 3)
(MovingImageDimension 3)
(UseDirectionCosines "true")
//  Transformation 
(Transform "BSplineTransform")
(HowToCombineTransforms "Compose")
//  Similarity measure 
(Metric "AdvancedMattesMutualInformation" "TransformRigidityPenalty")
(Metric0Weight 1)
(Metric1Weight 0.1 0.1 0.1 4.0)
(LinearityConditionWeight 100.0)
(OrthonormalityConditionWeight 1.0)
(PropernessConditionWeight 2.0)
(UseLinearityCondition "true")
(UseOrthonormalityCondition "true")
(UsePropernessCondition "true")
(CalculateLinearityCondition "true")
(CalculateOrthonormalityCondition "true")
(CalculatePropernessCondition "true")
(DilateRigidityImages "false" "false" "false" "true")
(DilationRadiusMultiplier 1.0 1.0 1.0 2.0)
(UseFixedRigidityImage "false")
(UseMovingRigidityImage "true")
(NumberOfHistogramBins 32)
(ErodeMask "false")
//  Multiresolution 
(NumberOfResolutions 4)
(FinalGridSpacing 8.0)
(UpsampleGridOption "true")
//  Optimizer 
(Optimizer "AdaptiveStochasticGradientDescent")
(UseAdaptiveStepSizes "true")
(MaximumNumberOfIterations 300 300 300 1200)
(SP_a 150000.0 120000.0 70000.0 20000.0)
(SP_alpha 0.602 0.602 0.602 0.602)
(SP_A 100.0 100.0 100.0 100.0)
//  Image sampling 
(NumberOfSpatialSamples 5000)
(NewSamplesEveryIteration "true")
(ImageSampler "Random")
//  Interpolation and Resampling 
(BSplineInterpolationOrder 3)
(FinalBSplineInterpolationOrder 3)
(DefaultPixelValue -1024)

The registered images seems to be working fine till the 4th resolution (final resolution) in B-Spline.
Below you can see registered image after 3rd resolution without and distorted region and the one after final resolution with distorted regions, respectively:

Registered image after 3rd resolution
Registered image after 3rd resolution2619×724 194 KB

Registered image after 4th resolution
Registered image after 4th resolution1920×550 55.8 KB

Is there any hints about what might be causing such a problem?

Thank you!
References:

  1. Jian, B., Azampour, M.F., De Benetti, F., Oberreuter, J., Bukas, C., Gersing, A.S., Foreman, S.C., Dietrich, A.S., Rischewski, J., Kirschke, J.S. and Navab, N., 2022, September. Weakly-supervised Biomechanically-constrained CT/MRI Registration of the Spine. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 227-236). Cham: Springer Nature Switzerland.
  2. Luu, H.M., Niessen, W., Van Walsum, T., Klink, C. and Moelker, A., 2015. An automatic registration method for pre‐and post‐interventional CT images for assessing treatment success in liver RFA treatment. Medical physics, 42(9), pp.5559-5567.
  3. Staring, M., Klein, S. and Pluim, J.P., 2007. A rigidity penalty term for nonrigid registration. Medical physics, 34(11), pp.4098-4108.