RecursiveExponentialFilter2d

Smoothes a two-dimensional image with a recursive algorithm implementing an exponential filter.

Access to parameter description

This algorithm performs a 2D smoothing filter whose impulse response is an exponential function. The smoothing is achieved by a separable exponential decreasing filter with a variable scale factor.

• Response to horizontal impulse: $ f(x)=b(\alpha|x|+1)e^{-\alpha|x|} $
• Response to vertical impulse: $ ~~~~f(y)=b(\alpha|y|+1)e^{-\alpha|y|} $

Where:

• $x$ and $y$ represent the offsets from the pixel to process.
• $ \alpha $ is a sharpness factor. Low values produce high level of smoothing.
• $ b=\frac{\alpha}{4} $

The lower the $\alpha$ value, the smoother the result. Practically, this filter response is mostly visible in the [0.3, 5.3] range.
For convenience, the scale factor is controlled by a spread value in order to convert it between 0 et 100. A value of 0 applies a very limited smoothing, while 100 induces a strong smoothing: $$ SpreadValue=\frac{(5.3-\alpha)}{5}\times 100 $$ This filter is very close to a Gaussian filter. The main difference is the alpha coefficient, which has an inverse behavior compared to a Gaussian standard deviation.

This implementation is based on an Infinite Impulse Response (IIR) algorithm. It computes the sum of one causal and one anti-causal filter where previous results are used to compute the next result. Using this mode, the computation time is independent of the spread parameter.

See also

• GaussianFilter2d
• GradientOperator2d
• ExponentialFilter2d
• RecursiveExponentialFilter3d

// Function prototype.
std::shared_ptr< iolink::ImageView >
recursiveExponentialFilter2d( std::shared_ptr< iolink::ImageView > inputImage,
                              int32_t spreadValue,
                              std::shared_ptr< iolink::ImageView > outputImage = NULL );

// Function prototype.
recursive_exponential_filter_2d( input_image, spread_value = 60, output_image = None )

// Function prototype.
public static IOLink.ImageView
RecursiveExponentialFilter2d( IOLink.ImageView inputImage,
                              Int32 spreadValue = 60,
                              IOLink.ImageView outputImage = null );

// Command constructor.
RecursiveExponentialFilter2d();

// 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.
RecursiveExponentialFilter2d.input_image
// Property of the spreadValue parameter.
RecursiveExponentialFilter2d.spread_value
// Property of the outputImage parameter.
RecursiveExponentialFilter2d.output_image

// Method to launch the command.
execute()

// Command constructor.
RecursiveExponentialFilter2d()

// Property of the inputImage parameter.
RecursiveExponentialFilter2d.inputImage
// Property of the spreadValue parameter.
RecursiveExponentialFilter2d.spreadValue
// Property of the outputImage parameter.
RecursiveExponentialFilter2d.outputImage

// Method to launch the command.
Execute()

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

RecursiveExponentialFilter2d recursiveExponentialFilter2dAlgo;
recursiveExponentialFilter2dAlgo.setInputImage( polystyrene );
recursiveExponentialFilter2dAlgo.setSpreadValue( 60 );
recursiveExponentialFilter2dAlgo.execute();

std::cout << "outputImage:" << recursiveExponentialFilter2dAlgo.outputImage()->toString();

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

recursive_exponential_filter_2d_algo = imagedev.RecursiveExponentialFilter2d()
recursive_exponential_filter_2d_algo.input_image = polystyrene
recursive_exponential_filter_2d_algo.spread_value = 60
recursive_exponential_filter_2d_algo.execute()

print( "output_image:", str( recursive_exponential_filter_2d_algo.output_image ) );

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

RecursiveExponentialFilter2d recursiveExponentialFilter2dAlgo = new RecursiveExponentialFilter2d
{
    inputImage = polystyrene,
    spreadValue = 60
};
recursiveExponentialFilter2dAlgo.Execute();

Console.WriteLine( "outputImage:" + recursiveExponentialFilter2dAlgo.outputImage.ToString() );

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

auto result = recursiveExponentialFilter2d( polystyrene, 60 );

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

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

result = imagedev.recursive_exponential_filter_2d( polystyrene, 60 )

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

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

IOLink.ImageView result = Processing.RecursiveExponentialFilter2d( polystyrene, 60 );

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