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
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.
Function Syntax
This function returns outputMeasurement.
// Function prototype
CurvatureIntegralsMsr::Ptr curvatureIntegrals3d( std::shared_ptr< iolink::ImageView > inputBinaryImage, CurvatureIntegralsMsr::Ptr outputMeasurement = NULL );
This function returns outputMeasurement.
// Function prototype. curvature_integrals_3d( input_binary_image, output_measurement = None )
This function returns outputMeasurement.
// Function prototype. public static CurvatureIntegralsMsr CurvatureIntegrals3d( IOLink.ImageView inputBinaryImage, CurvatureIntegralsMsr outputMeasurement = null );
Class Syntax
Parameters
| Parameter Name | Description | Type | Supported Values | Default Value | |
|---|---|---|---|---|---|
 |
inputBinaryImage |
The 3D binary input image. | Image | Binary | nullptr |
 |
outputMeasurement |
The output measurement result. | CurvatureIntegralsMsr | nullptr | |
| Parameter Name | Description | Type | Supported Values | Default Value | |
|---|---|---|---|---|---|
|
input_binary_image |
The 3D binary input image. | image | Binary | None |
|
output_measurement |
The output measurement result. | CurvatureIntegralsMsr | None | |
| Parameter Name | Description | Type | Supported Values | Default Value | |
|---|---|---|---|---|---|
|
inputBinaryImage |
The 3D binary input image. | Image | Binary | null |
|
outputMeasurement |
The output measurement result. | CurvatureIntegralsMsr | null | |
Object Examples
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( ) );
Function Examples
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( ) );