See also ImageMagick v6 Examples - Image Transformations — Sigmoidal Non-linearity Contrast
Adjusts the contrast of an image with a non-linear sigmoidal contrast algorithm. Increase the contrast of the image using a sigmoidal transfer function without saturating highlights or shadows. Contrast indicates how much to increase the contrast (0 is none; 3 is typical; 20 is pushing it); mid-point indicates where midtones fall in the resultant image (0 is white; 50 is middle-gray; 100 is black). Set sharpen to true to increase the image contrast otherwise the contrast is reduced.
Adjusts the contrast of an image with a non-linear sigmoidal contrast algorithm. Increase the contrast of the image using a sigmoidal transfer function without saturating highlights or shadows. Contrast indicates how much to increase the contrast (0 is none; 3 is typical; 20 is pushing it); mid-point indicates where midtones fall in the resultant image (0 is white; 50 is middle-gray; 100 is black). Set sharpen to true to increase the image contrast otherwise the contrast is reduced.
function sigmoidalContrastImage($image_path, $sharpening, $midpoint, $sigmoidalContrast)
{
    $imagick = new \Imagick(realpath($image_path));
    $imagick->sigmoidalcontrastimage(
        $sharpening,
        $midpoint,
        $sigmoidalContrast * \Imagick::getQuantum()
    );
    header("Content-Type: image/jpeg");
    echo $imagick->getImageBlob();
}