ImageDev

ElasticRegistration2d

Computes the optimal elastic transformation to register a two-dimensional a moving image onto a fixed image.

Access to parameter description

For an introduction: section Image Registration.

Contrary to rigid tranformations, elastic transformations warp locally the moving image to align it with the fixed image. The implementation described here relies on the demon's algorithm published by Jean-Pierre Thirion [1].

This algorithm generates two images: ElasticRegistration2d has two levels of regularization: fluid and elastic. The fluid regularization corresponds to the force field regularization and the elastic one corresponds to the displacement field regularization.
The force field is an elementary displacement which is iteratively added to the current displacement field during the registration procedure. This force field tends to decrease the similarity measurement between both images.

ElasticRegistration2d also provides a multi-resolution approach which prevents the optimization procedure from falling into a local extrema and also speeds up the calculation.
The coarsest and the finest resolution levels of the multi-resolution can be user-defined. The registration is evaluated at the coarsest level first and then iteratively at each level until the finest one. The higher the finest level, the faster the computation. The lower the finest level, the more accurate the registration.

<b> (a) </b>
(a)
<b> (b) </b>
(b)
<b> (c) </b>
(c)
Figure 1. Elastic registration by demon's algorithm: (a) the fixed image,
(b) the moving image (artificially distorted image), (c) the moving image registered on the fixed image
This algorithm can notify some information during the processing (pyramid level, number of iterations, energy) and can be interrupted. These information can be intercepted with the progress data callback function defined by the setProgressDataCallback function. In this case, data sent to the callback will be a string containing a JSON structure including the pyramid level, the number of iterations, and the energy. Intercepting these events slows down the execution.
More information on the callback functions can be found in the Processing interaction section.


Reference: See also

Function Syntax

This function returns a ElasticRegistration2dOutput structure containing outputImage and outputDisplacementField. 
// Output structure of the elasticRegistration2d function.
struct ElasticRegistration2dOutput
{
    /// The moving image transformed by the output displacement field. Its dimensions are forced to the same values as the fixed image, its type is forced to floating point precision (32-bit).
    std::shared_ptr< iolink::ImageView > outputImage;
    /// The displacement field that maps a pixel of the moving image onto the corresponding pixel in the fixed image. Each pixel of the displacement image contains two values: the first one represents the displacement in the X direction and one in the Y direction. Its dimensions are forced to the same values as the moving image, and its type is forced to floating point precision (32-bit).
    std::shared_ptr< iolink::ImageView > outputDisplacementField;
};

// Function prototype
ElasticRegistration2dOutput
elasticRegistration2d( std::shared_ptr< iolink::ImageView > inputFixedImage,
                       std::shared_ptr< iolink::ImageView > inputMovingImage,
                       ElasticRegistration2d::MetricType metricType,
                       double tolerance,
                       iolink::Vector2u32 pyramidLevels,
                       iolink::Vector2d elasticStandardDeviation,
                       iolink::Vector2d fluidStandardDeviation,
                       std::shared_ptr< iolink::ImageView > outputImage = NULL,
                       std::shared_ptr< iolink::ImageView > outputDisplacementField = NULL );
This function returns a tuple containing output_image and output_displacement_field. 
// Function prototype.
elastic_registration_2d( input_fixed_image,
                         input_moving_image,
                         metric_type = ElasticRegistration2d.MetricType.MEAN_SQUARE_DIFFERENCE,
                         tolerance = 0.025,
                         pyramid_levels = [2, 0],
                         elastic_standard_deviation = [10, 10],
                         fluid_standard_deviation = [10, 10],
                         output_image = None,
                         output_displacement_field = None )
This function returns a ElasticRegistration2dOutput structure containing outputImage and outputDisplacementField. 
/// Output structure of the ElasticRegistration2d function.
public struct ElasticRegistration2dOutput
{
    /// 
    /// The moving image transformed by the output displacement field. Its dimensions are forced to the same values as the fixed image, its type is forced to floating point precision (32-bit).
    /// 
    public IOLink.ImageView outputImage;
    /// 
    /// The displacement field that maps a pixel of the moving image onto the corresponding pixel in the fixed image. Each pixel of the displacement image contains two values: the first one represents the displacement in the X direction and one in the Y direction. Its dimensions are forced to the same values as the moving image, and its type is forced to floating point precision (32-bit).
    /// 
    public IOLink.ImageView outputDisplacementField;
};

// Function prototype.
public static ElasticRegistration2dOutput
ElasticRegistration2d( IOLink.ImageView inputFixedImage,
                       IOLink.ImageView inputMovingImage,
                       ElasticRegistration2d.MetricType metricType = ImageDev.ElasticRegistration2d.MetricType.MEAN_SQUARE_DIFFERENCE,
                       double tolerance = 0.025,
                       uint[] pyramidLevels = null,
                       double[] elasticStandardDeviation = null,
                       double[] fluidStandardDeviation = null,
                       IOLink.ImageView outputImage = null,
                       IOLink.ImageView outputDisplacementField = null );

Class Syntax

Parameters

Parameter Name Description Type Supported Values Default Value
input
inputFixedImage
The input fixed grayscale image on which the moving image has to be registered. Image Grayscale nullptr
input
inputMovingImage
The input moving grayscale image to be registered. Its dimensions and type can be different than the moving image input. Image Grayscale nullptr
input
metricType
The type of metric used to measure the similarity/dissimilarity between the fixed and the transformed image.
MEAN_SQUARE_DIFFERENCE The metric used is the Mean Squared Difference, it has to be minimized.
CORRELATION The metric used is the Normalized Correlation, it has to be maximized.
Enumeration MEAN_SQUARE_DIFFERENCE
input
tolerance
The maximum relative variation of the metric to stop the process. This variation is recomputed at each iteration. Float64 >0 0.025
input
pyramidLevels
The two-dimensional vector representing the coarsest (resp. finest) resolution level in its first (resp. second) element.
A value of 0 corresponds to the full resolution and a value of $N$ corresponds to a resolution of $ \frac{1}{2^N} $. 		Vector2u32 Any value {2, 0}
input
elasticStandardDeviation
The standard deviation of the gaussian kernel used to smooth the displacement field at each iteration. Vector2d >0 {10.f, 10.f}
input
fluidStandardDeviation
The standard deviation of the gaussian kernel used to smooth the forces field at each iteration. This parameter value is critical to reach large displacements. Vector2d >0 {10.f, 10.f}
output
outputImage
The moving image transformed by the output displacement field. Its dimensions are forced to the same values as the fixed image, its type is forced to floating point precision (32-bit). Image nullptr
output
outputDisplacementField
The displacement field that maps a pixel of the moving image onto the corresponding pixel in the fixed image. Each pixel of the displacement image contains two values: the first one represents the displacement in the X direction and one in the Y direction. Its dimensions are forced to the same values as the moving image, and its type is forced to floating point precision (32-bit). Image nullptr
Parameter Name Description Type Supported Values Default Value
input
input_fixed_image
The input fixed grayscale image on which the moving image has to be registered. image Grayscale None
input
input_moving_image
The input moving grayscale image to be registered. Its dimensions and type can be different than the moving image input. image Grayscale None
input
metric_type
The type of metric used to measure the similarity/dissimilarity between the fixed and the transformed image.
MEAN_SQUARE_DIFFERENCE The metric used is the Mean Squared Difference, it has to be minimized.
CORRELATION The metric used is the Normalized Correlation, it has to be maximized.
enumeration MEAN_SQUARE_DIFFERENCE
input
tolerance
The maximum relative variation of the metric to stop the process. This variation is recomputed at each iteration. float64 >0 0.025
input
pyramid_levels
The two-dimensional vector representing the coarsest (resp. finest) resolution level in its first (resp. second) element.
A value of 0 corresponds to the full resolution and a value of $N$ corresponds to a resolution of $ \frac{1}{2^N} $. 		vector2u32 Any value [2, 0]
input
elastic_standard_deviation
The standard deviation of the gaussian kernel used to smooth the displacement field at each iteration. vector2d >0 [10, 10]
input
fluid_standard_deviation
The standard deviation of the gaussian kernel used to smooth the forces field at each iteration. This parameter value is critical to reach large displacements. vector2d >0 [10, 10]
output
output_image
The moving image transformed by the output displacement field. Its dimensions are forced to the same values as the fixed image, its type is forced to floating point precision (32-bit). image None
output
output_displacement_field
The displacement field that maps a pixel of the moving image onto the corresponding pixel in the fixed image. Each pixel of the displacement image contains two values: the first one represents the displacement in the X direction and one in the Y direction. Its dimensions are forced to the same values as the moving image, and its type is forced to floating point precision (32-bit). image None
Parameter Name Description Type Supported Values Default Value
input
inputFixedImage
The input fixed grayscale image on which the moving image has to be registered. Image Grayscale null
input
inputMovingImage
The input moving grayscale image to be registered. Its dimensions and type can be different than the moving image input. Image Grayscale null
input
metricType
The type of metric used to measure the similarity/dissimilarity between the fixed and the transformed image.
MEAN_SQUARE_DIFFERENCE The metric used is the Mean Squared Difference, it has to be minimized.
CORRELATION The metric used is the Normalized Correlation, it has to be maximized.
Enumeration MEAN_SQUARE_DIFFERENCE
input
tolerance
The maximum relative variation of the metric to stop the process. This variation is recomputed at each iteration. Float64 >0 0.025
input
pyramidLevels
The two-dimensional vector representing the coarsest (resp. finest) resolution level in its first (resp. second) element.
A value of 0 corresponds to the full resolution and a value of $N$ corresponds to a resolution of $ \frac{1}{2^N} $. 		Vector2u32 Any value {2, 0}
input
elasticStandardDeviation
The standard deviation of the gaussian kernel used to smooth the displacement field at each iteration. Vector2d >0 {10f, 10f}
input
fluidStandardDeviation
The standard deviation of the gaussian kernel used to smooth the forces field at each iteration. This parameter value is critical to reach large displacements. Vector2d >0 {10f, 10f}
output
outputImage
The moving image transformed by the output displacement field. Its dimensions are forced to the same values as the fixed image, its type is forced to floating point precision (32-bit). Image null
output
outputDisplacementField
The displacement field that maps a pixel of the moving image onto the corresponding pixel in the fixed image. Each pixel of the displacement image contains two values: the first one represents the displacement in the X direction and one in the Y direction. Its dimensions are forced to the same values as the moving image, and its type is forced to floating point precision (32-bit). Image null

Object Examples

std::shared_ptr< iolink::ImageView > polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

ElasticRegistration2d elasticRegistration2dAlgo;
elasticRegistration2dAlgo.setInputFixedImage( polystyrene );
elasticRegistration2dAlgo.setInputMovingImage( polystyrene );
elasticRegistration2dAlgo.setMetricType( ElasticRegistration2d::MetricType::MEAN_SQUARE_DIFFERENCE );
elasticRegistration2dAlgo.setTolerance( 0.025 );
elasticRegistration2dAlgo.setPyramidLevels( {2, 0} );
elasticRegistration2dAlgo.setElasticStandardDeviation( {10.0, 10.0} );
elasticRegistration2dAlgo.setFluidStandardDeviation( {10.0, 10.0} );
elasticRegistration2dAlgo.execute();

std::cout << "outputImage:" << elasticRegistration2dAlgo.outputImage()->toString();
std::cout << "outputDisplacementField:" << elasticRegistration2dAlgo.outputDisplacementField()->toString();

polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))

elastic_registration_2d_algo = imagedev.ElasticRegistration2d()
elastic_registration_2d_algo.input_fixed_image = polystyrene
elastic_registration_2d_algo.input_moving_image = polystyrene
elastic_registration_2d_algo.metric_type = imagedev.ElasticRegistration2d.MEAN_SQUARE_DIFFERENCE
elastic_registration_2d_algo.tolerance = 0.025
elastic_registration_2d_algo.pyramid_levels = [2, 0]
elastic_registration_2d_algo.elastic_standard_deviation = [10.0, 10.0]
elastic_registration_2d_algo.fluid_standard_deviation = [10.0, 10.0]
elastic_registration_2d_algo.execute()

print( "output_image:", str( elastic_registration_2d_algo.output_image ) )
print( "output_displacement_field:", str( elastic_registration_2d_algo.output_displacement_field ) )

ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" );

ElasticRegistration2d elasticRegistration2dAlgo = new ElasticRegistration2d
{
    inputFixedImage = polystyrene,
    inputMovingImage = polystyrene,
    metricType = ElasticRegistration2d.MetricType.MEAN_SQUARE_DIFFERENCE,
    tolerance = 0.025,
    pyramidLevels = new uint[]{2, 0},
    elasticStandardDeviation = new double[]{10.0, 10.0},
    fluidStandardDeviation = new double[]{10.0, 10.0}
};
elasticRegistration2dAlgo.Execute();

Console.WriteLine( "outputImage:" + elasticRegistration2dAlgo.outputImage.ToString() );
Console.WriteLine( "outputDisplacementField:" + elasticRegistration2dAlgo.outputDisplacementField.ToString() );

Function Examples

std::shared_ptr< iolink::ImageView > polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

auto result = elasticRegistration2d( polystyrene, polystyrene, ElasticRegistration2d::MetricType::MEAN_SQUARE_DIFFERENCE, 0.025, {2, 0}, {10.0, 10.0}, {10.0, 10.0} );

std::cout << "outputImage:" << result.outputImage->toString();
std::cout << "outputDisplacementField:" << result.outputDisplacementField->toString();

polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))

result_output_image, result_output_displacement_field = imagedev.elastic_registration_2d( polystyrene, polystyrene, imagedev.ElasticRegistration2d.MEAN_SQUARE_DIFFERENCE, 0.025, [2, 0], [10.0, 10.0], [10.0, 10.0] )

print( "output_image:", str( result_output_image ) )
print( "output_displacement_field:", str( result_output_displacement_field ) )

ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" );

Processing.ElasticRegistration2dOutput result = Processing.ElasticRegistration2d( polystyrene, polystyrene, ElasticRegistration2d.MetricType.MEAN_SQUARE_DIFFERENCE, 0.025, new uint[]{2, 0}, new double[]{10.0, 10.0}, new double[]{10.0, 10.0} );

Console.WriteLine( "outputImage:" + result.outputImage.ToString() );
Console.WriteLine( "outputDisplacementField:" + result.outputDisplacementField.ToString() );