ImageDev

OrientationMatchingFourier3d

Estimates the probability of a sample to be locally oriented in a user-defined direction.

Access to parameter description

For an introduction: The direction is defined using angles Phi and Theta in spherical coordinates as explained in the ImageDev 3D orientation convention.
The orientation similarity of a local region with a user-defined orientation is computed by applying the transformation to the inertia matrix, taking into account the changes induced by the basis. Consider the basis change illustrated below.
<b> Figure 1.</b> Basis change from cartesian to spherical coordinate system
Figure 1. Basis change from cartesian to spherical coordinate system

One can demonstrate that the transformation of the vector $(V_x, V_y, V_z)$ in the basis $(e_x, e_y, e_z)$ to the vector $(V_r, V_\varphi, V_\theta)$ in the basis $(e_r, e_\varphi, e_\theta)$ is expressed as: $$ \left[ \begin{array}{c} V_r\\ V_\varphi\\ V_\theta\end{array}\right] = \left[ \begin{array}{ccc}; sin (\varphi) \cdot cos (\theta) & sin (\varphi) \cdot sin (\theta) & cos (\varphi)\\ cos (\varphi) \cdot cos (\theta) & cos (\varphi) \cdot sin (\theta) & sin (\varphi)\\ -sin (\theta) & cos (\theta) & 0 \end{array}\right] \left[ \begin{array}{c} V_x\\ V_y\\ V_z\end{array}\right] $$ We denote $P$ this transformation matrix.
Now let $M(x, y, z)$ be the inertia matrix in the basis $(e_x, e_y, e_z)$, the inertia matrix $M(r, \varphi, \theta)$ in the basis $(e_r, e_\varphi, e_\theta)$ is expressed as: $$ M(r, \varphi, \theta) = P \cdot M(x, y, z) \cdot P^{-1}$$
Finally, this algorithm provides two outputs:
<b> Figure 2.</b> Local orientation matching of a 3D image with user-defined direction
Figure 2. Local orientation matching of a 3D image with user-defined direction
See also

Function Syntax

This function returns a OrientationMatchingFourier3dOutput structure containing outputImage and outputMeasurement. 
// Output structure of the orientationMatchingFourier3d function.
struct OrientationMatchingFourier3dOutput
{
    /// The grayscale output image representing sticks oriented in the user-defined direction. Intensities correspond to a similarity score with the input orientation in percent. Image dimensions are forced to the same values as the input. Its type is unsigned 8-bit integer.
    std::shared_ptr< iolink::ImageView > outputImage;
    /// The output measurement result for each block.
    LocalOrientation3dMsr::Ptr outputMeasurement;
};

// Function prototype
OrientationMatchingFourier3dOutput
orientationMatchingFourier3d( std::shared_ptr< iolink::ImageView > inputImage,
                              int32_t blockSize,
                              OrientationMatchingFourier3d::BlockOverlap blockOverlap,
                              int32_t minThreshold,
                              int32_t maxThreshold,
                              double phiAngle,
                              double thetaAngle,
                              std::shared_ptr< iolink::ImageView > outputImage = NULL,
                              LocalOrientation3dMsr::Ptr outputMeasurement = NULL );
This function returns a tuple containing output_image and output_measurement. 
// Function prototype.
orientation_matching_fourier_3d( input_image,
                                 block_size = 64,
                                 block_overlap = OrientationMatchingFourier3d.BlockOverlap.YES,
                                 min_threshold = 100,
                                 max_threshold = 300,
                                 phi_angle = 0,
                                 theta_angle = 0,
                                 output_image = None,
                                 output_measurement = None )
This function returns a OrientationMatchingFourier3dOutput structure containing outputImage and outputMeasurement. 
/// Output structure of the OrientationMatchingFourier3d function.
public struct OrientationMatchingFourier3dOutput
{
    /// 
    /// The grayscale output image representing sticks oriented in the user-defined direction. Intensities correspond to a similarity score with the input orientation in percent. Image dimensions are forced to the same values as the input. Its type is unsigned 8-bit integer.
    /// 
    public IOLink.ImageView outputImage;
    /// The output measurement result for each block.
    public LocalOrientation3dMsr outputMeasurement;
};

// Function prototype.
public static OrientationMatchingFourier3dOutput
OrientationMatchingFourier3d( IOLink.ImageView inputImage,
                              Int32 blockSize = 64,
                              OrientationMatchingFourier3d.BlockOverlap blockOverlap = ImageDev.OrientationMatchingFourier3d.BlockOverlap.YES,
                              Int32 minThreshold = 100,
                              Int32 maxThreshold = 300,
                              double phiAngle = 0,
                              double thetaAngle = 0,
                              IOLink.ImageView outputImage = null,
                              LocalOrientation3dMsr outputMeasurement = null );

Class Syntax

Parameters

Class Name OrientationMatchingFourier3d

Parameter Name Description Type Supported Values Default Value
input
inputImage
The grayscale input image. Image Grayscale nullptr
input
blockSize
The side size in pixels of the cubic blocks. Int32 >=1 64
input
blockOverlap
The policy for splitting the image into blocks.
NO The algorithm splits the image into contiguous blocks. The offset between two consecutive block origins is equal to the block size.
YES The algorithm splits the image into overlapping blocks. The offset between two consecutive block origins is equal to the half of the block size.
Enumeration YES
input
minThreshold
The minimum threshold value applied to the input grayscale image. Voxels having an intensity lower than this threshold are not considered by the algorithm. Int32 >=1 100
input
maxThreshold
The maximum threshold value applied to the input grayscale image. Voxels having an intensity greater than this threshold are not considered by the algorithm. Int32 >=1 300
input
phiAngle
The polar angle, in degrees, of the analysis orientation. Float64 Any value 0
input
thetaAngle
The azimuthal angle, in degrees, of the analysis orientation. Float64 Any value 0
output
outputImage
The grayscale output image representing sticks oriented in the user-defined direction. Intensities correspond to a similarity score with the input orientation in percent. Image dimensions are forced to the same values as the input. Its type is unsigned 8-bit integer. Image nullptr
output
outputMeasurement
The output measurement result for each block. LocalOrientation3dMsr nullptr

Object Examples

auto foam = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam.vip" );

OrientationMatchingFourier3d orientationMatchingFourier3dAlgo;
orientationMatchingFourier3dAlgo.setInputImage( foam );
orientationMatchingFourier3dAlgo.setBlockSize( 10 );
orientationMatchingFourier3dAlgo.setBlockOverlap( OrientationMatchingFourier3d::BlockOverlap::YES );
orientationMatchingFourier3dAlgo.setMinThreshold( 100 );
orientationMatchingFourier3dAlgo.setMaxThreshold( 300 );
orientationMatchingFourier3dAlgo.setPhiAngle( 0 );
orientationMatchingFourier3dAlgo.setThetaAngle( 0 );
orientationMatchingFourier3dAlgo.execute();

std::cout << "outputImage:" << orientationMatchingFourier3dAlgo.outputImage()->toString();
std::cout << "blockOriginX: " << orientationMatchingFourier3dAlgo.outputMeasurement()->blockOriginX( 0 ) ;

foam = imagedev.read_vip_image(imagedev_data.get_image_path("foam.vip"))

orientation_matching_fourier_3d_algo = imagedev.OrientationMatchingFourier3d()
orientation_matching_fourier_3d_algo.input_image = foam
orientation_matching_fourier_3d_algo.block_size = 10
orientation_matching_fourier_3d_algo.block_overlap = imagedev.OrientationMatchingFourier3d.YES
orientation_matching_fourier_3d_algo.min_threshold = 100
orientation_matching_fourier_3d_algo.max_threshold = 300
orientation_matching_fourier_3d_algo.phi_angle = 0
orientation_matching_fourier_3d_algo.theta_angle = 0
orientation_matching_fourier_3d_algo.execute()

print( "output_image:", str( orientation_matching_fourier_3d_algo.output_image ) )
print( "blockOriginX: ", str( orientation_matching_fourier_3d_algo.output_measurement.block_origin_x( 0 ) ) )

ImageView foam = Data.ReadVipImage( @"Data/images/foam.vip" );

OrientationMatchingFourier3d orientationMatchingFourier3dAlgo = new OrientationMatchingFourier3d
{
    inputImage = foam,
    blockSize = 10,
    blockOverlap = OrientationMatchingFourier3d.BlockOverlap.YES,
    minThreshold = 100,
    maxThreshold = 300,
    phiAngle = 0,
    thetaAngle = 0
};
orientationMatchingFourier3dAlgo.Execute();

Console.WriteLine( "outputImage:" + orientationMatchingFourier3dAlgo.outputImage.ToString() );
Console.WriteLine( "blockOriginX: " + orientationMatchingFourier3dAlgo.outputMeasurement.blockOriginX( 0 ) );

Function Examples

auto foam = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "foam.vip" );

auto result = orientationMatchingFourier3d( foam, 10, OrientationMatchingFourier3d::BlockOverlap::YES, 100, 300, 0, 0 );

std::cout << "outputImage:" << result.outputImage->toString();
std::cout << "blockOriginX: " << result.outputMeasurement->blockOriginX( 0 ) ;

foam = imagedev.read_vip_image(imagedev_data.get_image_path("foam.vip"))

result_output_image, result_output_measurement = imagedev.orientation_matching_fourier_3d( foam, 10, imagedev.OrientationMatchingFourier3d.YES, 100, 300, 0, 0 )

print( "output_image:", str( result_output_image ) )
print( "blockOriginX: ", str( result_output_measurement.block_origin_x( 0 ) )  )

ImageView foam = Data.ReadVipImage( @"Data/images/foam.vip" );

Processing.OrientationMatchingFourier3dOutput result = Processing.OrientationMatchingFourier3d( foam, 10, OrientationMatchingFourier3d.BlockOverlap.YES, 100, 300, 0, 0 );

Console.WriteLine( "outputImage:" + result.outputImage.ToString() );
Console.WriteLine(  "blockOriginX: " + result.outputMeasurement.blockOriginX( 0 )  );