How to detect "light" colors with PHP

What I'd do in this situation is detect the lightness of the color using HSL, and compare that against a certain percentage. For example, the lightness attribute in the HSL algorithm takes the chroma (M - m where M is the largest RGB value and m is the smallest RGB value) and divides that by 2.

function lightness($R = 255, $G = 255, $B = 255) {
    return (max($R, $G, $B) + min($R, $G, $B)) / 510.0; // HSL algorithm
}

The above function would return a percentage of how light the color you've selected is (simple hex -> rgb conversions are required for this also, but that should be pretty easy). The reason I divided by 510 instead of 2 is because in order to get the percentage after dividing by 2, you divide by 255. To make it faster you can simply say: (x / 2) / 255 = x / 510. Then I'd compare the value returned by the above function to, say, 80%.

$r = hexdec($hex[0].$hex[1]);
$g = hexdec($hex[2].$hex[3]);
$b = hexdec($hex[4].$hex[5]);

if(lightness($r, $g, $b) >= .8) {
    // add border
} else {
    // no border
}

Transform HTML colour to RGB, then to Hue-Saturation-Lightnes (HSV)

<?php

function HTMLToRGB($htmlCode)
  {
    if($htmlCode[0] == '#')
      $htmlCode = substr($htmlCode, 1);

    if (strlen($htmlCode) == 3)
    {
      $htmlCode = $htmlCode[0] . $htmlCode[0] . $htmlCode[1] . $htmlCode[1] . $htmlCode[2] . $htmlCode[2];
    }

    $r = hexdec($htmlCode[0] . $htmlCode[1]);
    $g = hexdec($htmlCode[2] . $htmlCode[3]);
    $b = hexdec($htmlCode[4] . $htmlCode[5]);

    return $b + ($g << 0x8) + ($r << 0x10);
  }

function RGBToHSL($RGB) {
    $r = 0xFF & ($RGB >> 0x10);
    $g = 0xFF & ($RGB >> 0x8);
    $b = 0xFF & $RGB;

    $r = ((float)$r) / 255.0;
    $g = ((float)$g) / 255.0;
    $b = ((float)$b) / 255.0;

    $maxC = max($r, $g, $b);
    $minC = min($r, $g, $b);

    $l = ($maxC + $minC) / 2.0;

    if($maxC == $minC)
    {
      $s = 0;
      $h = 0;
    }
    else
    {
      if($l < .5)
      {
        $s = ($maxC - $minC) / ($maxC + $minC);
      }
      else
      {
        $s = ($maxC - $minC) / (2.0 - $maxC - $minC);
      }
      if($r == $maxC)
        $h = ($g - $b) / ($maxC - $minC);
      if($g == $maxC)
        $h = 2.0 + ($b - $r) / ($maxC - $minC);
      if($b == $maxC)
        $h = 4.0 + ($r - $g) / ($maxC - $minC);

      $h = $h / 6.0; 
    }

    $h = (int)round(255.0 * $h);
    $s = (int)round(255.0 * $s);
    $l = (int)round(255.0 * $l);

    return (object) Array('hue' => $h, 'saturation' => $s, 'lightness' => $l);
  }

$colour = '#F12346';
$rgb = HTMLToRGB($colour);
$hsl = RGBToHSL($rgb);

var_dump($hsl);

Usage:

$colour = '#F12346';
$rgb = HTMLToRGB($colour);
$hsl = RGBToHSL($rgb);
if($hsl->lightness > 200) {
  // this is light colour!
}

Source:

• http://www.caperna.org/computing/repository/hsl-rgb-color-conversion-php

Demo:

• http://codepad.org/X7KV4n4n

In addition to other formulas given by other answers, you may want to consider Luma.

function luma($r, $g, $b)
{
  return (0.2126 * $r + 0.7152 * $g + 0.0722 * $b) / 255;
}

$l = luma(0, 15, 255);

Values closer to 0 will be darker. Values closer to 1 will be lighter.