csci 6971: image registration lecture 8: registration components february 6, 2004 prof. chuck...
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CSci 6971: Image Registration Lecture 8: Registration Components
February 6, 2004
CSci 6971: Image Registration Lecture 8: Registration Components
February 6, 2004
Prof. Chuck Stewart, RPIDr. Luis Ibanez, KitwareProf. Chuck Stewart, RPIDr. Luis Ibanez, Kitware
Image Registration Lecture 8 2
Image MetricsImage Metrics
How similar is
image A to image B ?
Image Registration Lecture 8 3
Image MetricsImage Metrics
Does Image B
matches Image A better
than Image C ?
Image Registration Lecture 8 4
Image MetricsImage Metrics
Image A Image CImage B
Match( A , B ) Match( A , C )><
Image Registration Lecture 8 5
Image MetricsImage Metrics
Match( A , B )
Simplest Metric
Mean Squared Differences
Image Registration Lecture 8 6
Mean Squared DifferencesMean Squared Differences
Image A Image B
For each pixel in A
Difference( index ) = A( index ) – B( index )
Sum += Difference( index ) 2
Match( A , B ) = Sum / numberOfPixels
Image Registration Lecture 8 7
For each pixel in the Fixed ImageFor each pixel in the Fixed Image
Fixed Image Grid
j
i
y
x
Fixed ImagePhysical Coordinates
y’
x’
Moving ImagePhysical Coordinates
Moving Image Grid
j
i
Space Transform
Image Registration Lecture 8 8
Image MetricsImage Metrics
FixedImage
MovingImage
Metric
Transform
Interpolator
Value
Parameters
Image Registration Lecture 8 9
Mean Squared DifferencesMean Squared Differences
#include "itkImage.h"#include "itkMeanSquaresImageToImageMetric.h"#include "itkLinearInterpolateImageFunction.h"#include "itkTranslationTransform.h"
typedef itk::Image< char, 2 > ImageType;
ImageType::ConstPointer fixedImage = GetFixedImage(); ImageType::ConstPointer movingImage = GetMovingImage();
typedef itk::LinearInterpolateImageFunction< ImageType, double > InterpolatorType;
InterpolatorType::Pointer interpolator = InterpolatorType::New();
typedef itk::TranslationTransform< double, 2 > TransformType;
TransformType::Pointer transform = TransformType::New();
Image Registration Lecture 8 10
Mean Squared DifferencesMean Squared Differences
typedef itk::MeanSquaresImageToImageMetric< ImageType, ImageType > MetricType;
MetricType::Pointer metric = MetricType::New();
metric->SetInterpolator( interpolator );metric->SetTransform( transform );
metric->SetFixedImage( fixedImage );metric->SetMovingImage( movingImage );
MetricType::TransformParametersType translation( Dimension );
translation[0] = 12;translation[1] = 27;
double value = metric->GetValue( translation );
Image Registration Lecture 8 11
Mean Squared DifferencesMean Squared Differences
MetricType::TransformParametersType translation( 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 );
}}
Image Registration Lecture 8 12
Evaluating many matchesEvaluating many matches
y
Fixed Image
Transform
x
y
Moving Image
x
Image Registration Lecture 8 13
Plotting the MetricPlotting the Metric
Mean Squared Differences
Transform Parametric Space
Image Registration Lecture 8 14
Plotting the MetricPlotting the Metric
Mean Squared Differences
Transform Parametric Space
Image Registration Lecture 8 15
Evaluating many matchesEvaluating many matches
y
Fixed Image
Transform
x
y
Moving Image
x
(-15,-25) mm
Image Registration Lecture 8 16
Plotting the MetricPlotting the Metric
Mean Squared Differences
Transform Parametric Space
Image Registration Lecture 8 17
Plotting the MetricPlotting the Metric
Mean Squared Differences
Transform Parametric Space
Image Registration Lecture 8 18
The Best Transform ParametersThe Best Transform Parameters
Evaluation of the full parameter space
is equivalent to performoptimization by
exhaustive search
Image Registration Lecture 8 19
The Best Transform ParametersThe Best Transform Parameters
Very Safe
but
Very Slow
Image Registration Lecture 8 20
The Best Transform ParametersThe Best Transform Parameters
Better Optimization Methods
for example
Gradient Descent
Image Registration Lecture 8 21
Image Registration FrameworkImage Registration Framework
FixedImage
MovingImage
Metric
Transform
Interpolator Optimizer
Parameters
Image Registration Lecture 8 22
Gradient Descent OptimizerGradient Descent Optimizer
f( x , y )
S = L ∙ G( x , y )f( x , y )
∆
G( x , y ) =
S = Step
L = LearningRate
Image Registration Lecture 8 23
Gradient Descent OptimizerGradient Descent Optimizer
f( x , y )
S = L ∙ G( x , y )f( x , y )
∆
G( x , y ) =
Image Registration Lecture 8 24
Gradient Descent OptimizerGradient Descent Optimizer
f( x , y )
S = L ∙ G( x , y )f( x , y )
∆
G( x , y ) =
L too large
Image Registration Lecture 8 25
Gradient Descent OptimizerGradient Descent Optimizer
f( x , y )
S = L ∙ G( x , y )f( x , y )
∆
G( x , y ) =
L too small
Image Registration Lecture 8 26
Gradient Descent OptimizerGradient Descent Optimizer
What’s wrong with this algorithm ?
Image Registration Lecture 8 27
Gradient Descent OptimizerGradient Descent Optimizer
S Units ? = millimeters
f(x,y) Units ? = intensity
G(x,y) Units ? = intensity / millimeters
L Units ? = millimeters2 / intensity
S = L ∙ G( x , y )
Image Registration Lecture 8 28
Gradient Descent OptimizerGradient Descent Optimizer
f( x )S = L ∙ G( x )
1
1
Image Registration Lecture 8 29
Gradient Descent OptimizerGradient Descent Optimizer
f( x )
1 1
S = L ∙ G( x )
S = Large in high gradients
S = Small in low gradients
Image Registration Lecture 8 30
Gradient Descent OptimizerGradient Descent Optimizer
f( x )S = L ∙ G( x )
Works great with this function
Works badly with this function
Image Registration Lecture 8 31
Gradient Descent VariantGradient Descent Variant
Driving Safe !
Image Registration Lecture 8 32
Regular Step Gradient DescentRegular Step Gradient Descent
f( x )
S = D ∙ G( x )^
Di = Di-1 / 2.0
D1
If G changes direction
D1
D1
D2
Image Registration Lecture 8 33
Regular Step Gradient DescentRegular Step Gradient Descent
f( x )
S = D ∙ G( x )^
D1
User Selects D1
D1
D1
D2
User Selects Dstop
User Selects Gstop
Image Registration Lecture 8 34
Optimizers are like a carOptimizers are like a car
Watch while you are driving !
Image Registration Lecture 8 35
Watch over your optimizerWatch over your optimizer
Example:
Optimizer registering an image with itself starting at (-15mm, -25mm)
Image Registration Lecture 8 36
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 1.0 mm
Image Registration Lecture 8 37
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 2.0 mm
Image Registration Lecture 8 38
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 5.0 mm
Image Registration Lecture 8 39
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 10.0 mm
Image Registration Lecture 8 40
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 20.0 mm
Image Registration Lecture 8 41
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 40.0 mm
Image Registration Lecture 8 42
Watch over your optimizerWatch over your optimizer
Example:
Optimizer registering an image shifted by (-15mm, -25mm)
The optimizer starts at (0mm,0mm)
Image Registration Lecture 8 43
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 1.0 mm
Image Registration Lecture 8 44
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 2.0 mm
Image Registration Lecture 8 45
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 5.0 mm
Image Registration Lecture 8 46
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 10.0 mm
Image Registration Lecture 8 47
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 20.0 mm
Image Registration Lecture 8 48
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Mean Squared Differences
Step Length = 40.0 mm
Image Registration Lecture 8 49
Other Image MetricsOther Image Metrics
Normalized Correlation
Image Registration Lecture 8 50
Normalized CorrelationNormalized Correlation
Image A Image B
For each pixel in A
SumAB += A( index ) ∙ B( index )
Match( A , B ) = SumAB / √ ( SumAA ∙ SumBB )
SumAA += A( index ) ∙ A( index )SumBB += B( index ) ∙ B( index )
Image Registration Lecture 8 51
Evaluating many matchesEvaluating many matches
y
Fixed Image
Transform
x
y
Moving Image
x
Image Registration Lecture 8 52
Plotting the MetricPlotting the Metric
Normalized Correlation Metric
Transform Parametric Space
Image Registration Lecture 8 53
Plotting the MetricPlotting the Metric
Normalized Correlation Metric
Transform Parametric Space
Image Registration Lecture 8 54
Normalized Correlation MetricNormalized Correlation Metric
#include "itkImage.h"#include "itkNormalizedCorrelationImageToImageMetric.h"#include "itkLinearInterpolateImageFunction.h"#include "itkTranslationTransform.h"
typedef itk::Image< char, 2 > ImageType;
ImageType::ConstPointer fixedImage = GetFixedImage(); ImageType::ConstPointer movingImage = GetMovingImage();
typedef itk::LinearInterpolateImageFunction< ImageType, double > InterpolatorType;
InterpolatorType::Pointer interpolator = InterpolatorType::New();
typedef itk::TranslationTransform< double, 2 > TransformType;
TransformType::Pointer transform = TransformType::New();
Image Registration Lecture 8 55
Normalized Correlation MetricNormalized Correlation Metric
typedef itk::NormalizedCorrelationImageToImageMetric< ImageType, ImageType > MetricType;
MetricType::Pointer metric = MetricType::New();
metric->SetInterpolator( interpolator );metric->SetTransform( transform );
metric->SetFixedImage( fixedImage );metric->SetMovingImage( movingImage );
MetricType::TransformParametersType translation( Dimension );
translation[0] = 12;translation[1] = 27;
double value = metric->GetValue( translation );
Image Registration Lecture 8 56
Watch over your optimizerWatch over your optimizer
Example:
Optimizer registering an image with itself starting at (-15mm, -25mm)
Image Registration Lecture 8 57
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 1.0 mm
Image Registration Lecture 8 58
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 2.0 mm
Image Registration Lecture 8 59
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 5.0 mm
Image Registration Lecture 8 60
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 10.0 mm
Image Registration Lecture 8 61
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 20.0 mm
Image Registration Lecture 8 62
Plotting the Optimizer’s PathPlotting the Optimizer’s Path
Normalized Correlation Metric
Step Length = 40.0 mm
Image Registration Lecture 8 63
Evaluating many matchesEvaluating many matches
y
Fixed Image
Transform
x
y
Moving Image
x
(-15,-25) mm
Image Registration Lecture 8 64
Plotting the MetricPlotting the Metric
Normalized Correlation Metric
Transform Parametric Space
Image Registration Lecture 8 65
Plotting the MetricPlotting the Metric
Normalized Correlation Metric
Transform Parametric Space
Image Registration Lecture 8 66
Watch over your optimizerWatch over your optimizer
Example:
Optimizer registering an image shifted by (-15mm, -25mm)
The optimizer starts at (0mm,0mm)
Image Registration Lecture 8 67
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 1.0 mm
Image Registration Lecture 8 68
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 2.0 mm
Image Registration Lecture 8 69
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 5.0 mm
Image Registration Lecture 8 70
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 10.0 mm
Image Registration Lecture 8 71
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 20.0 mm
Image Registration Lecture 8 72
Plotting the Optimizer PathPlotting the Optimizer Path
Normalized Correlation Metric
Step Length = 40.0 mm
Image Registration Lecture 8 73
Watch over your optimizerWatch over your optimizer
How much can you blindly
trust your optimizer…
Image Registration Lecture 8 74
I left my Optimizer working…I left my Optimizer working…
Image Registration Lecture 8 75
I think it’s going to finish soon…I think it’s going to finish soon…
Image Registration Lecture 8 76
EndEnd
Enjoy ITK !