# Optimizer's stopping condition is rounding error. Registration framework

**URL:** <https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603>\
**Category:** Algorithms\
**Tags:** simpleitk, registration, python\
**Created:** [November 23, 2021, 5:58pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603 "2021-11-23T17:58:05Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![Luciano\_Rivetti](https://discourse.itk.org/user_avatar/discourse.itk.org/luciano_rivetti/32/2395_2.png) [@Luciano\_Rivetti](https://discourse.itk.org/u/Luciano_Rivetti)\
**Post date:** [November 23, 2021, 5:58pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603/1 "2021-11-23T17:58:05Z")

</div>

Hi everyone,

I’m doing B-Spline registration of CT vs CBCT images.

The Registration method Im using is:

```auto
 registration_method = sitk.ImageRegistrationMethod()
  
 grid_physical_spacing = [15.0]*3 
 image_physical_size = [size*spacing for size,spacing in zip(fixed_image.GetSize(), fixed_image.GetSpacing())]
 mesh_size = [int(image_size/grid_spacing + 0.5) \
              for image_size,grid_spacing in zip(image_physical_size,grid_physical_spacing)]

 initial_transform = sitk.BSplineTransformInitializer(image1 = fixed_image, 
                                                      transformDomainMeshSize = mesh_size, order=3)    

 registration_method.SetInitialTransformAsBSpline(initial_transform,
                                                  inPlace=False)

 registration_method.SetMetricAsMattesMutualInformation(numberOfHistogramBins=150)

 registration_method.SetMetricSamplingStrategy(registration_method.RANDOM)
 registration_method.SetMetricSamplingPercentage(0.001)

 registration_method.SetInterpolator(sitk.sitkLinear)
 registration_method.SetOptimizerAsLBFGS2(solutionAccuracy=1e-10, numberOfIterations=150, deltaConvergenceTolerance=1e-10)

```

The Optimizer’s stopping condition is: A rounding error occurred

I would like to understand why the optimizer always stop for a rounding error and how to stop this to happen.

Thanks in advance,  
Luciano

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<div class="post-metadata">

**Author:** ![dzenanz](https://discourse.itk.org/user_avatar/discourse.itk.org/dzenanz/32/1093_2.png) [@dzenanz](https://discourse.itk.org/u/dzenanz)\
**Post date:** [November 23, 2021, 7:57pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603/2 "2021-11-23T19:57:27Z")

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> [@Luciano\_Rivetti](#):
>
> `solutionAccuracy=1e-10`, …, deltaConvergenceTolerance=1e-10

This is very strict. The usual values are close to the image spacing, .e.g `0.01` or `0.001`. That might be the reason.

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<div class="post-metadata">

**Author:** ![Luciano\_Rivetti](https://discourse.itk.org/user_avatar/discourse.itk.org/luciano_rivetti/32/2395_2.png) [@Luciano\_Rivetti](https://discourse.itk.org/u/Luciano_Rivetti)\
**Post date:** [November 23, 2021, 8:04pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603/3 "2021-11-23T20:04:56Z")

</div>

To the image dimension in which dimension, meters?

For which parameter is the suggestion? solutionAccuracy and deltaConvergenceTolerance?

Thanks,  
Luciano

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<div class="post-metadata">

**Author:** ![dzenanz](https://discourse.itk.org/user_avatar/discourse.itk.org/dzenanz/32/1093_2.png) [@dzenanz](https://discourse.itk.org/u/dzenanz)\
**Post date:** [November 23, 2021, 8:34pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603/4 "2021-11-23T20:34:01Z")

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ITK is unitless. ITK uses whichever unit your image spacing is expressed in. That is usually millimeters in medicine, meters in earth observation satellite images, milli-arc-seconds in astronomy (I think).

Probably both parameters need to be much larger.

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<div class="post-metadata">

**Author:** ![banikr](https://discourse.itk.org/user_avatar/discourse.itk.org/banikr/32/3296_2.png) [@banikr](https://discourse.itk.org/u/banikr)\
**Post date:** [May 3, 2023, 8:19pm UTC](https://discourse.itk.org/t/optimizers-stopping-condition-is-rounding-error-registration-framework/4603/5 "2023-05-03T20:19:11Z")

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I have the similar issue in multiscale mode. Following the instructions here:  
[https://insightsoftwareconsortium.github.io/SimpleITK-Notebooks/Python\_html/65\_Registration\_FFD.html#:~:text=registration\_method.SetOptimizerAsLBFGS2(solutionAccuracy%3D1e-2%2C%20numberOfIterations%3D100%2C%20deltaConvergenceTolerance%3D0.01)](https://insightsoftwareconsortium.github.io/SimpleITK-Notebooks/Python_html/65_Registration_FFD.html#:~:text=registration_method.SetOptimizerAsLBFGS2(solutionAccuracy%3D1e%2D2%2C%20numberOfIterations%3D100%2C%20deltaConvergenceTolerance%3D0.01))

```auto
registration_method.SetOptimizerAsLBFGS2(
            solutionAccuracy=1e-2,
            # hessianApproximateAccuracy=60,
            numberOfIterations=1000,
            deltaConvergenceTolerance=10,
            # lineSearchMaximumEvaluations=40,
            # lineSearchMaximumStep=1e20,
            # lineSearchMinimumStep=1e-20,
            # lineSearchAccuracy=1e-4
        )

```

The fixed and moving image sizeare: `(96, 72) (57, 86)`  
The `metric curve` looks like:  
 ![image](https://discourse.itk.org/uploads/default/original/2X/4/4337a89319b30c8cd3a6390f278c29a308f95f7c.png)