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.
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
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|} $
- $x$ 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} $
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
Function Syntax
This function returns outputImage.
// Function prototype
std::shared_ptr< iolink::ImageView > recursiveExponentialFilter2d( std::shared_ptr< iolink::ImageView > inputImage, int32_t spreadValue, std::shared_ptr< iolink::ImageView > outputImage = NULL );
This function returns outputImage.
// Function prototype. recursive_exponential_filter_2d( input_image, spread_value = 60, output_image = None )
This function returns outputImage.
// Function prototype.
public static IOLink.ImageView
RecursiveExponentialFilter2d( IOLink.ImageView inputImage,
Int32 spreadValue = 60,
IOLink.ImageView outputImage = null );
Class Syntax
Parameters
| Class Name | RecursiveExponentialFilter2d |
|---|
| Parameter Name | Description | Type | Supported Values | Default Value | |
|---|---|---|---|---|---|
 |
inputImage |
The input image. | Image | Binary, Label, Grayscale or Multispectral | nullptr |
|
spreadValue |
The spread value between 0 and 100. The larger the value, the more intensive the smoothing. | Int32 | [0, 100] | 60 |
 |
outputImage |
The output image. Its dimensions are forced to the same values as the input. Its data type is promoted. | Image | nullptr | |
Object Examples
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() );
Function Examples
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() );