ImageDev

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
<b> Figure 1.</b> Graphic visualization of the 2D neighborhood analysis
Figure 1. Graphic visualization of the 2D neighborhood analysis

Examples

The examples below show the effect of the LocalMaxima2d algorithm with different parameters sets applied on the image illustrated in Figure 2.
<b> Figure 2.</b> Input image for local maxima extraction
Figure 2. Input image for local maxima extraction

Example 1

First parameter set: The extracted local maxima are the points higher than or equal to 4.

<b> Figure 3.</b> Extracted maxima with the first parameter set
Figure 3. Extracted maxima with the first parameter set

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:
<b> Figure 4.</b> Extracted maxima with the second parameter set
Figure 4. Extracted maxima with the second parameter set

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:
<b> Figure 5.</b> Extracted maxima with the third parameter set
Figure 5. Extracted maxima with the third parameter set

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

<b> Figure 6.</b> First maximum identified in example 3
Figure 6. First maximum identified in example 3


<b> Figure 7.</b> X sub-pixel position determined by parabola approximation
Figure 7. X sub-pixel position determined by parabola approximation


<b> Figure 8.</b> Y sub-pixel position determined by parabola approximation
Figure 8. Y sub-pixel position determined by parabola approximation

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

See also

Function Syntax

This function returns outputMeasurement. 
// 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 = NULL );
This function returns outputMeasurement. 
// Function prototype.
local_maxima_2d( input_gray_image,
                 local_window = [3, 3],
                 threshold_range = 0,
                 precision = LocalMaxima2d.Precision.PIXEL,
                 number_of_patterns = 1,
                 output_measurement = None )
This function returns outputMeasurement. 
// 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 );

Class Syntax

Parameters

Class Name LocalMaxima2d

Parameter Name Description Type Supported Values Default Value
input
inputGrayImage
The input grayscale image. Image Binary, Label or Grayscale nullptr
input
localWindow
The neighborhood size in pixels, along the X and Y directions. Vector2i32 >0 {3, 3}
input
thresholdRange
The threshold value higher than which maxima are retained. Float64 >=0 0
input
precision
The precision of the maxima localization.
PIXEL No sub-pixel approximation.
SUB_PIXEL Sub-pixel approximation determined by parabola fitting.
Enumeration PIXEL
input
numberOfPatterns
The maximum number of patterns to be detected. Int32 >=1 1
output
outputMeasurement
The result object containing the maxima positions. LocalMaximaMsr nullptr

Object Examples

std::shared_ptr< iolink::ImageView > 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( ) );

Function Examples

std::shared_ptr< iolink::ImageView > 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( )  );