RecursiveLaplacian3d

Computes the Laplacian of a three-dimensional image with a recursive algorithm.

Access to parameter description

For an introduction:

• section Edge Detection
• section Laplacian
• section Images Filters

This algorithm is a recursive implementation for the determination of the Laplacian operator.

To minimize the effect of noise, the RecursiveLaplacian3d module smooths the image while computing the Laplacian by applying a second order derivative of the Deriche smoothing filter which has the three-dimensional form: $$ f(x,y,z)=b^3(\alpha|x|+1)e^{-\alpha|x|}\cdot(\alpha|y|+1)e^{-\alpha|y|}\cdot(\alpha|z|+1) e^{-\alpha|z|}~~where~~b=\frac{\alpha}{4} $$
The smoothing scale parameter determines the smoothing intensity. If the value is large, the noise will be reduced but edges will be less sharp and only the most important edges will appear in the output image.
It is important to select the right coefficient to lower the noise just enough without defocusing the edges.

Reference
R.Deriche. "Using Canny's criteria to derive a recursively implemented optimal edge detector". International Journal of Computer Vision, vol.1, no 2, pp. 167-187, Jun. 1987.

See also

• DobFilter3d
• RecursiveLaplacian2d
• GradientOperator3d

// Function prototype
std::shared_ptr< iolink::ImageView >
recursiveLaplacian3d( std::shared_ptr< iolink::ImageView > inputImage,
                      int32_t spreadValue,
                      std::shared_ptr< iolink::ImageView > outputImage = NULL );

// Function prototype.
recursive_laplacian_3d( input_image, spread_value = 60, output_image = None )

// Function prototype.
public static IOLink.ImageView
RecursiveLaplacian3d( IOLink.ImageView inputImage,
                      Int32 spreadValue = 60,
                      IOLink.ImageView outputImage = null );

// Command constructor.
RecursiveLaplacian3d();

/// Gets the inputImage parameter.
/// The input image.
std::shared_ptr< iolink::ImageView > inputImage() const;
/// Sets the inputImage parameter.
/// The input image.
void setInputImage( std::shared_ptr< iolink::ImageView > inputImage );

/// Gets the spreadValue parameter.
/// The smoothing factor defining the gradient sharpness. Its value must be between 0 and 100.
int32_t spreadValue() const;
/// Sets the spreadValue parameter.
/// The smoothing factor defining the gradient sharpness. Its value must be between 0 and 100.
void setSpreadValue( const int32_t& spreadValue );

/// Gets the outputImage parameter.
/// The output image.
std::shared_ptr< iolink::ImageView > outputImage() const;
/// Sets the outputImage parameter.
/// The output image.
void setOutputImage( std::shared_ptr< iolink::ImageView > outputImage );


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

# Property of the inputImage parameter.
RecursiveLaplacian3d.input_image
# Property of the spreadValue parameter.
RecursiveLaplacian3d.spread_value
# Property of the outputImage parameter.
RecursiveLaplacian3d.output_image

// Method to launch the command.
execute()

// Command constructor.
RecursiveLaplacian3d()

// Property of the inputImage parameter.
RecursiveLaplacian3d.inputImage
// Property of the spreadValue parameter.
RecursiveLaplacian3d.spreadValue
// Property of the outputImage parameter.
RecursiveLaplacian3d.outputImage

// Method to launch the command.
Execute()

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

RecursiveLaplacian3d recursiveLaplacian3dAlgo;
recursiveLaplacian3dAlgo.setInputImage( foam );
recursiveLaplacian3dAlgo.setSpreadValue( 60 );
recursiveLaplacian3dAlgo.execute();

std::cout << "outputImage:" << recursiveLaplacian3dAlgo.outputImage()->toString();

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

recursive_laplacian_3d_algo = imagedev.RecursiveLaplacian3d()
recursive_laplacian_3d_algo.input_image = foam
recursive_laplacian_3d_algo.spread_value = 60
recursive_laplacian_3d_algo.execute()

print( "output_image:", str( recursive_laplacian_3d_algo.output_image ) )

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

RecursiveLaplacian3d recursiveLaplacian3dAlgo = new RecursiveLaplacian3d
{
    inputImage = foam,
    spreadValue = 60
};
recursiveLaplacian3dAlgo.Execute();

Console.WriteLine( "outputImage:" + recursiveLaplacian3dAlgo.outputImage.ToString() );

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

auto result = recursiveLaplacian3d( foam, 60 );

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

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

result = imagedev.recursive_laplacian_3d( foam, 60 )

print( "output_image:", str( result ) )

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

IOLink.ImageView result = Processing.RecursiveLaplacian3d( foam, 60 );

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