CurvatureIntegrals3d

Computes the integral of mean curvature and integral of total curvature of objects in a three-dimensional binary image.

Access to parameter description

For an introduction: section Image Analysis.

Intuitively, "curvature" is the amount by which a geometric object deviates from being "flat".

This algorithm computes a local measure. It is obtained as the sum of measurements in local 2x2x2 neighborhoods (a cube), for 13 planes associated with different normal directions and hitting three or four vertices of the cells (in the cubical lattice).

In the case of very elongated objects (needles or fibers), the integral of mean curvature $M$ can be used to measure the length $L$ of the object: $L=M/\pi$

For a convex object, the integral of mean curvature $M$ is (up to a constant) equivalent to the mean diameter; for instance, $$M=2\pi d ~~\mbox{, where} ~~ d=\frac{1}{13} \sum_{i=0}^{13} d_i$$ The Euler number and the Integral of total curvature carry the same information about the object. They differ by the constant factor $4\pi$. Considering a set $X$ of the 3-dimensional space and $\chi(X)$ being its Euler number, then the integral total curvature of $X$ is $K(X)=4\pi \chi(X)$.

Reference

• C.Lang, J.Ohser, R.Hilfer "On the Analysis of Spatial Binary Images". Journal of Microscopy, vol. 203, pp. 303-313, 2001.

See also

• ImageCurvature3d
• EulerNumber3d
• StructureModelIndex3d

// Function prototype
CurvatureIntegralsMsr::Ptr
curvatureIntegrals3d( std::shared_ptr< iolink::ImageView > inputBinaryImage, CurvatureIntegralsMsr::Ptr outputMeasurement = NULL );

// Function prototype.
curvature_integrals_3d( input_binary_image, output_measurement = None )

// Function prototype.
public static CurvatureIntegralsMsr
CurvatureIntegrals3d( IOLink.ImageView inputBinaryImage, CurvatureIntegralsMsr outputMeasurement = null );

// Command constructor.
CurvatureIntegrals3d();

/// Gets the inputBinaryImage parameter.
/// The 3D binary input image.
std::shared_ptr< iolink::ImageView > inputBinaryImage() const;
/// Sets the inputBinaryImage parameter.
/// The 3D binary input image.
void setInputBinaryImage( std::shared_ptr< iolink::ImageView > inputBinaryImage );

/// Gets the outputMeasurement parameter.
/// The output measurement result.
CurvatureIntegralsMsr::Ptr outputMeasurement() const;


// Method to launch the command.
void execute();

# Property of the inputBinaryImage parameter.
CurvatureIntegrals3d.input_binary_image
# Property of the outputMeasurement parameter.
CurvatureIntegrals3d.output_measurement

// Method to launch the command.
execute()

// Command constructor.
CurvatureIntegrals3d()

// Property of the inputBinaryImage parameter.
CurvatureIntegrals3d.inputBinaryImage
// Property of the outputMeasurement parameter.
CurvatureIntegrals3d.outputMeasurement

// Method to launch the command.
Execute()

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

CurvatureIntegrals3d curvatureIntegrals3dAlgo;
curvatureIntegrals3dAlgo.setInputBinaryImage( foam_sep );
curvatureIntegrals3dAlgo.execute();

std::cout << "meanCurvature: " << curvatureIntegrals3dAlgo.outputMeasurement()->meanCurvature( ) ;

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

curvature_integrals_3d_algo = imagedev.CurvatureIntegrals3d()
curvature_integrals_3d_algo.input_binary_image = foam_sep
curvature_integrals_3d_algo.execute()

print( "meanCurvature: ", str( curvature_integrals_3d_algo.output_measurement.mean_curvature( ) ) )

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

CurvatureIntegrals3d curvatureIntegrals3dAlgo = new CurvatureIntegrals3d
{
    inputBinaryImage = foam_sep
};
curvatureIntegrals3dAlgo.Execute();

Console.WriteLine( "meanCurvature: " + curvatureIntegrals3dAlgo.outputMeasurement.meanCurvature( ) );

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

auto result = curvatureIntegrals3d( foam_sep );

std::cout << "meanCurvature: " << result->meanCurvature( ) ;

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

result = imagedev.curvature_integrals_3d( foam_sep )

print( "meanCurvature: ", str( result.mean_curvature( ) )  )

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

CurvatureIntegralsMsr result = Processing.CurvatureIntegrals3d( foam_sep );

Console.WriteLine(  "meanCurvature: " + result.meanCurvature( )  );