CSci 6971: Image Registration Lecture 8: Registration Components February 6, 2004

1. CSci 6971: Image Registration Lecture 8: Registration ComponentsFebruary 6, 2004 Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware

2. Image Metrics How similar is image A to image B ? Lecture 8

3. Image Metrics Does Image Bmatches Image A better than Image C ? Lecture 8

4. Image Metrics >< Match( A , B ) Match( A , C ) Image B Image A Image C Lecture 8

5. Image Metrics Match( A , B )Simplest MetricMean Squared Differences Lecture 8

6. Mean Squared Differences For each pixel in A Image A Image B Difference( index ) = A( index ) – B( index ) Sum += Difference( index ) 2 Match( A , B ) = Sum / numberOfPixels Lecture 8

7. j j i i Moving Image Grid Fixed Image Grid y’ y Space Transform x’ x Moving ImagePhysical Coordinates Fixed ImagePhysical Coordinates For each pixel in the Fixed Image Lecture 8

8. Image Metrics FixedImage Metric Value MovingImage Interpolator Transform Parameters Lecture 8

9. Mean Squared Differences #include "itkImage.h" #include "itkMeanSquaresImageToImageMetric.h" #include "itkLinearInterpolateImageFunction.h" #include "itkTranslationTransform.h" typedef itk::Image< char, 2 > ImageType; ImageType::ConstPointerfixedImage = GetFixedImage(); ImageType::ConstPointermovingImage = GetMovingImage(); typedef itk::LinearInterpolateImageFunction<ImageType, double >InterpolatorType; InterpolatorType::Pointerinterpolator = InterpolatorType::New(); typedef itk::TranslationTransform< double, 2 > TransformType; TransformType::Pointertransform = TransformType::New(); Lecture 8

10. Mean Squared Differences typedef itk::MeanSquaresImageToImageMetric< ImageType,ImageType > MetricType; MetricType::Pointermetric = MetricType::New(); metric->SetInterpolator( interpolator ); metric->SetTransform( transform ); metric->SetFixedImage( fixedImage ); metric->SetMovingImage( movingImage ); MetricType::TransformParametersTypetranslation( Dimension ); translation[0] = 12; translation[1] = 27; double value = metric->GetValue( translation ); Lecture 8

11. Mean Squared Differences MetricType::TransformParametersTypetranslation( Dimension ); double value[21][21]; for( int dx = 0; dx <= 20; dx++) { for( int dy = 0; dy <= 20; dy++) { translation[0] = dx; translation[1] = dy; value[dx][dy] = metric->GetValue( translation ); } } Lecture 8

12. Evaluating many matches y y Transform x x Fixed Image Moving Image Lecture 8

13. Plotting the Metric Mean Squared Differences Transform Parametric Space Lecture 8

14. Plotting the Metric Mean Squared Differences Transform Parametric Space Lecture 8

15. Evaluating many matches y y Transform (-15,-25) mm x x Fixed Image Moving Image Lecture 8

16. Plotting the Metric Mean Squared Differences Transform Parametric Space Lecture 8

17. Plotting the Metric Mean Squared Differences Transform Parametric Space Lecture 8

18. The Best Transform Parameters Evaluation of the full parameter spaceis equivalent to performoptimization by exhaustive search Lecture 8

19. The Best Transform Parameters Very SafebutVery Slow Lecture 8

20. The Best Transform Parameters Better Optimization Methodsfor exampleGradient Descent Lecture 8

21. Image Registration Framework FixedImage Metric MovingImage Interpolator Optimizer Transform Parameters Lecture 8

22. G( x , y ) = ∆ f( x , y ) Gradient Descent Optimizer f( x , y ) S = Step L = LearningRate S=L∙ G( x , y ) Lecture 8

23. G( x , y ) = ∆ f( x , y ) Gradient Descent Optimizer f( x , y ) S=L∙ G( x , y ) Lecture 8

24. G( x , y ) = ∆ f( x , y ) Gradient Descent Optimizer f( x , y ) L too large S=L∙G( x , y ) Lecture 8

25. G( x , y ) = ∆ f( x , y ) Gradient Descent Optimizer f( x , y ) L too small S=L∙G( x , y ) Lecture 8

26. Gradient Descent Optimizer What’s wrong with this algorithm ? Lecture 8

27. Gradient Descent Optimizer = millimeters SUnits ? = intensity f(x,y) Units ? = intensity / millimeters G(x,y)Units ? S=L∙G( x , y ) = millimeters2 / intensity LUnits ? Lecture 8

28. Gradient Descent Optimizer f( x ) S=L∙G( x ) 1 1 Lecture 8

29. Gradient Descent Optimizer f( x ) S=L∙G( x ) S=Large in high gradients S=Small in low gradients 1 1 Lecture 8

30. Gradient Descent Optimizer f( x ) S=L∙G( x ) Works great with this function Works badly with this function Lecture 8

31. Gradient Descent Variant Driving Safe ! Lecture 8

32. Regular Step Gradient Descent f( x ) ^ S=D∙G( x ) IfG changes direction Di=Di-1/ 2.0 D1 D1 D2 D1 Lecture 8

33. Regular Step Gradient Descent f( x ) ^ S=D∙G( x ) User Selects D1 User Selects Dstop User Selects Gstop D1 D1 D2 D1 Lecture 8

34. Optimizers are like a car Watch while you are driving ! Lecture 8

35. Watch over your optimizer Example:Optimizer registering an image with itself starting at (-15mm, -25mm) Lecture 8

36. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 1.0 mm Lecture 8

37. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 2.0 mm Lecture 8

38. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 5.0 mm Lecture 8

39. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 10.0 mm Lecture 8

40. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 20.0 mm Lecture 8

41. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 40.0 mm Lecture 8

42. Watch over your optimizer Example:Optimizer registering an image shifted by (-15mm, -25mm)The optimizer starts at (0mm,0mm) Lecture 8

43. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 1.0 mm Lecture 8

44. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 2.0 mm Lecture 8

45. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 5.0 mm Lecture 8

46. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 10.0 mm Lecture 8

47. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 20.0 mm Lecture 8

48. Plotting the Optimizer’s Path Mean Squared Differences Step Length = 40.0 mm Lecture 8

49. Other Image Metrics Normalized Correlation Lecture 8

50. Normalized Correlation For each pixel in A Image A Image B SumAB += A( index ) ∙ B( index ) SumAA += A( index ) ∙ A( index ) SumBB += B( index ) ∙ B( index ) Match( A , B ) = SumAB / √ ( SumAA∙SumBB ) Lecture 8