RecursiveLaplacian2d

Computes the Laplacian of a two-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 RecursiveLaplacian2d module smooths the image while computing the Laplacian by applying a second order derivative of the Deriche smoothing filter which has the two-dimensional form: $$ f(x,y)=b^2(\alpha|x|+1)e^{-\alpha|x|}\cdot(\alpha|y|+1)e^{-\alpha|y|}~~where~~b=\frac{\alpha}{4} $$
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

• DobFilter2d
• RecursiveLaplacian3d
• GradientOperator2d

// Function prototype.
std::shared_ptr< iolink::ImageView >
recursiveLaplacian2d( std::shared_ptr< iolink::ImageView > inputImage,
                      int32_t spreadValue,
                      std::shared_ptr< iolink::ImageView > outputImage = NULL );

// Function prototype.
recursive_laplacian_2d( input_image, spread_value = 60, output_image = None )

// Function prototype.
public static IOLink.ImageView
RecursiveLaplacian2d( IOLink.ImageView inputImage,
                      Int32 spreadValue = 60,
                      IOLink.ImageView outputImage = null );

// Command constructor.
RecursiveLaplacian2d();

// Get method of the inputImage parameter.
std::shared_ptr< iolink::ImageView > inputImage() const;
// Set method of the inputImage parameter.
void setInputImage( std::shared_ptr< iolink::ImageView > inputImage );

// Get method of the spreadValue parameter.
int32_t spreadValue() const;
// Set method of the spreadValue parameter.
void setSpreadValue( const int32_t& spreadValue );

// Get method of the outputImage parameter.
std::shared_ptr< iolink::ImageView > outputImage() const;
// Set method of the outputImage parameter.
void setOutputImage( std::shared_ptr< iolink::ImageView > outputImage );

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

// Property of the inputImage parameter.
RecursiveLaplacian2d.input_image
// Property of the spreadValue parameter.
RecursiveLaplacian2d.spread_value
// Property of the outputImage parameter.
RecursiveLaplacian2d.output_image

// Method to launch the command.
execute()

// Command constructor.
RecursiveLaplacian2d()

// Property of the inputImage parameter.
RecursiveLaplacian2d.inputImage
// Property of the spreadValue parameter.
RecursiveLaplacian2d.spreadValue
// Property of the outputImage parameter.
RecursiveLaplacian2d.outputImage

// Method to launch the command.
Execute()

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

RecursiveLaplacian2d recursiveLaplacian2dAlgo;
recursiveLaplacian2dAlgo.setInputImage( polystyrene );
recursiveLaplacian2dAlgo.setSpreadValue( 60 );
recursiveLaplacian2dAlgo.execute();

std::cout << "outputImage:" << recursiveLaplacian2dAlgo.outputImage()->toString();

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

recursive_laplacian_2d_algo = imagedev.RecursiveLaplacian2d()
recursive_laplacian_2d_algo.input_image = polystyrene
recursive_laplacian_2d_algo.spread_value = 60
recursive_laplacian_2d_algo.execute()

print( "output_image:", str( recursive_laplacian_2d_algo.output_image ) )

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

RecursiveLaplacian2d recursiveLaplacian2dAlgo = new RecursiveLaplacian2d
{
    inputImage = polystyrene,
    spreadValue = 60
};
recursiveLaplacian2dAlgo.Execute();

Console.WriteLine( "outputImage:" + recursiveLaplacian2dAlgo.outputImage.ToString() );

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

auto result = recursiveLaplacian2d( polystyrene, 60 );

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

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

result = imagedev.recursive_laplacian_2d( polystyrene, 60 )

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

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

IOLink.ImageView result = Processing.RecursiveLaplacian2d( polystyrene, 60 );

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