Understanding Image Kurtosis and Skewness in PHP with the ImageMagick Package

The getImageChannelKurtosis function accepts as a parameter any of the ImageMagick channel constants and returns an array containing elements with the two element values of 'kurtosis' and 'skewness.'

For the inputted color values, you have the ImageMagick channel constant values that look like imagick::CHANNEL_UNDEFINED, with "_VALUE" values of: undefined, red, gray, cyan, green, magenta, blue, yellow, alpha, opacity, matte, black, index, all, and default.  This is for measuring the particular channel for these colors of their own associated colorspaces.

According to Wikipedia, the Kurtosis is "any measure of the 'peakedness' of the probability distribution of a real-valued random variable" and Skewness (its opposite) is "a measure of the asymmetry of the probability distribution of a real-valued random variable."  The more colors vary from the inputted channel constant, you'll be more likely to get a skewness close to zero, and you'll get the opposite behavior from checking the kurtosis value, which makes sense, since skewness and kurtosis are considered mathematical antonyms.

Some sample code :

<?php

            // Author: holdoffhunger@gmail.com
   
        // Imagick Type
        // ---------------------------------------------

    $imagick_type = new Imagick();
   
        // Open File
        // ---------------------------------------------
       
    $file_to_grab = "image_workshop_directory/test.bmp";
   
    $file_handle_for_viewing_image_file = fopen($file_to_grab, 'a+');
   
        // Grab File
        // ---------------------------------------------

    $imagick_type->readImageFile($file_handle_for_viewing_image_file);
   
        // Get Quantum Range
        // ---------------------------------------------
       
    $imagick_type_channel_kurtosis_red = $imagick_type->getImageChannelKurtosis(imagick::CHANNEL_RED);
   
        // Print Results
        // ---------------------------------------------

    print("<pre>");
    print_r($imagick_type_channel_kurtosis_red);
    print("</pre>");

?>

The results for performing this function upon a photo of the ocean...

ImageMagick - Channel Kurtosis
  Channel - Undefined :

Kurtosis : 0
Skewness : 0

  Channel - Red :

Kurtosis : 0.920611158888
Skewness : 1.52701528976

  Channel - Gray :

Kurtosis : 0.920611158888
Skewness : 1.52701528976

  Channel - Cyan :

Kurtosis : 0.920611158888
Skewness : 1.52701528976

  Channel - Green :

Kurtosis : -0.286520845928
Skewness : 1.05203603783

  Channel - Magenta :

Kurtosis : -0.286520845928
Skewness : 1.05203603783

  Channel - Blue :

Kurtosis : -0.849997917796
Skewness : 0.807852655795

  Channel - Yellow :

Kurtosis : -0.849997917796
Skewness : 0.807852655795

  Channel - Alpha :

Kurtosis : 0
Skewness : 0

  Channel - Opacity :

Kurtosis : 0
Skewness : 0

  Channel - Matte :

Kurtosis : 0
Skewness : 0

  Channel - Black :

Kurtosis : 0
Skewness : 0

  Channel - Index :

Kurtosis : 0
Skewness : 0

  Channel - All :

Kurtosis : 0.509521246195
Skewness : 1.33491479552

  Channel - Default :

Kurtosis : -0.349955122843
Skewness : 1.00561407035

Official Function Page: http://www.php.net/manual/en/imagick.getimagechannelkurtosis.php

// Note: All code appearing on the PHP Revolution blog by the blog owner is released under the Hacktivismo Enhanced-Source Software License Agreement (HESSLA), unless otherwise noted.  http://www.hacktivismo.com/about/hessla.php