LocalMaxima2d

Extracts the local maxima of an image using a two-dimensional neighborhood analysis.

Access to parameter description

This algorithm considers $I(i,j)$ as a local maximum of $I$ if the two conditions below are verified

1. $I(i,j)$ is a local maximum in a $(2p+1)\times(2q+1)$ neighborhood, i.e., considering $k \in [1,p]$, $l \in [1,q]$ and m in [-p,p], $I(i,j)$
• $I(i,j)>I(i+m,j-l)$
• $I(i,j)>I(i-k,j)$
• $I(i,j) \geq I(i+k,j)$
• $I(i,j) \geq I(i+m,j+l)$
2. $I(i,j)$ is higher than a specified threshold
• $I(i,j)>threshold$

Examples

The examples below show the effect of the LocalMaxima2d algorithm with different parameters sets applied on the image illustrated in Figure 2.

Example 1

First parameter set:

• p=0
• q=0
• threshold=4
• number=50

The extracted local maxima are the points higher than or equal to 4.


The actual number of local maxima detected is 7.
The local maxima are located at positions: (7,3), (6,5), (5,7), (6,7), (6,8), (2,9) and (6,9)
This algorithm configuration corresponds to a single thresholding operator.

Example 2

Second parameter set:

• p=1
• q=1
• threshold=3
• number=50

The actual number of local maxima detected is 4.
The local maxima are located at positions: (7,3), (6,5), (5,7) and (2,9)

Note: If there is an area in the image at constant level, the algorithm returns the upper left corner of this area. The other points of this area are not considered as "local maxima".

Example 3

Third parameter set:

• p=2
• q=2
• threshold=3
• number=50

The actual number of local maxima detected is 2.
The local maxima are located at positions: (7,3) and (5,7)

Note: The algorithm is not performed on the image border depending on the $n$ and $m$ values. This is the reason why the point (2,9) is not considered as a local maximum.

Sub-Pixel Position Determination

The maxima can be returned either as a discrete position in the image grid, or as a sub-pixel position by interpolation with parabola.
On example 3, the algorithm detects 2 local maxima. The positions are converted to sub-pixel positions as follows






The maximum detected in pixel precision at (7,3) becomes (6.95,4.05) with sub-pixel precision.

See also

• CrossCorrelation2d
• LocalMaxima3d

// Function prototype
LocalMaximaMsr::Ptr
localMaxima2d( std::shared_ptr< iolink::ImageView > inputGrayImage,
               iolink::Vector2i32 localWindow,
               double thresholdRange,
               LocalMaxima2d::Precision precision,
               int32_t numberOfPatterns,
               LocalMaximaMsr::Ptr outputMeasurement = nullptr );

// Function prototype.
local_maxima_2d(input_gray_image: idt.ImageType,
                local_window: Iterable[int] = [3, 3],
                threshold_range: float = 0,
                precision: LocalMaxima2d.Precision = LocalMaxima2d.Precision.PIXEL,
                number_of_patterns: int = 1,
                output_measurement: Union[Any, None] = None) -> LocalMaximaMsr

// Function prototype.
public static LocalMaximaMsr
LocalMaxima2d( IOLink.ImageView inputGrayImage,
               int[] localWindow = null,
               double thresholdRange = 0,
               LocalMaxima2d.Precision precision = ImageDev.LocalMaxima2d.Precision.PIXEL,
               Int32 numberOfPatterns = 1,
               LocalMaximaMsr outputMeasurement = null );

// Command constructor.
LocalMaxima2d();

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

/// Gets the localWindow parameter.
/// The neighborhood size in pixels, along the X and Y directions.
iolink::Vector2i32 localWindow() const;
/// Sets the localWindow parameter.
/// The neighborhood size in pixels, along the X and Y directions.
void setLocalWindow( const iolink::Vector2i32& localWindow );

/// Gets the thresholdRange parameter.
/// The threshold value higher than which maxima are retained.
double thresholdRange() const;
/// Sets the thresholdRange parameter.
/// The threshold value higher than which maxima are retained.
void setThresholdRange( const double& thresholdRange );

/// Gets the precision parameter.
/// The precision of the maxima localization.
LocalMaxima2d::Precision precision() const;
/// Sets the precision parameter.
/// The precision of the maxima localization.
void setPrecision( const LocalMaxima2d::Precision& precision );

/// Gets the numberOfPatterns parameter.
/// The maximum number of patterns to be detected.
int32_t numberOfPatterns() const;
/// Sets the numberOfPatterns parameter.
/// The maximum number of patterns to be detected.
void setNumberOfPatterns( const int32_t& numberOfPatterns );

/// Gets the outputMeasurement parameter.
/// The result object containing the maxima positions.
LocalMaximaMsr::Ptr outputMeasurement() const;


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

# Property of the inputGrayImage parameter.
LocalMaxima2d.input_gray_image
# Property of the localWindow parameter.
LocalMaxima2d.local_window
# Property of the thresholdRange parameter.
LocalMaxima2d.threshold_range
# Property of the precision parameter.
LocalMaxima2d.precision
# Property of the numberOfPatterns parameter.
LocalMaxima2d.number_of_patterns
# Property of the outputMeasurement parameter.
LocalMaxima2d.output_measurement

// Method to launch the command.
execute()

// Command constructor.
LocalMaxima2d()

// Property of the inputGrayImage parameter.
LocalMaxima2d.inputGrayImage
// Property of the localWindow parameter.
LocalMaxima2d.localWindow
// Property of the thresholdRange parameter.
LocalMaxima2d.thresholdRange
// Property of the precision parameter.
LocalMaxima2d.precision
// Property of the numberOfPatterns parameter.
LocalMaxima2d.numberOfPatterns
// Property of the outputMeasurement parameter.
LocalMaxima2d.outputMeasurement

// Method to launch the command.
Execute()

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

LocalMaxima2d localMaxima2dAlgo;
localMaxima2dAlgo.setInputGrayImage( polystyrene );
localMaxima2dAlgo.setLocalWindow( {3, 3} );
localMaxima2dAlgo.setThresholdRange( 0 );
localMaxima2dAlgo.setPrecision( LocalMaxima2d::Precision::PIXEL );
localMaxima2dAlgo.setNumberOfPatterns( 1 );
localMaxima2dAlgo.execute();

std::cout << "value: " << localMaxima2dAlgo.outputMeasurement()->value( ) ;

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

local_maxima_2d_algo = imagedev.LocalMaxima2d()
local_maxima_2d_algo.input_gray_image = polystyrene
local_maxima_2d_algo.local_window = [3, 3]
local_maxima_2d_algo.threshold_range = 0
local_maxima_2d_algo.precision = imagedev.LocalMaxima2d.PIXEL
local_maxima_2d_algo.number_of_patterns = 1
local_maxima_2d_algo.execute()

print("value: ", str(local_maxima_2d_algo.output_measurement.value()))

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

LocalMaxima2d localMaxima2dAlgo = new LocalMaxima2d
{
    inputGrayImage = polystyrene,
    localWindow = new int[]{3, 3},
    thresholdRange = 0,
    precision = LocalMaxima2d.Precision.PIXEL,
    numberOfPatterns = 1
};
localMaxima2dAlgo.Execute();

Console.WriteLine( "value: " + localMaxima2dAlgo.outputMeasurement.value( ) );

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

auto result = localMaxima2d( polystyrene, {3, 3}, 0, LocalMaxima2d::Precision::PIXEL, 1 );

std::cout << "value: " << result->value( ) ;

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

result = imagedev.local_maxima_2d(polystyrene, [3, 3], 0, imagedev.LocalMaxima2d.PIXEL, 1)

print("value: ", str(result.value()))

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

LocalMaximaMsr result = Processing.LocalMaxima2d( polystyrene, new int[]{3, 3}, 0, LocalMaxima2d.Precision.PIXEL, 1 );

Console.WriteLine(  "value: " + result.value( )  );