I've worked on a similar problem recently in javascript for my startup. In my case I needed to pick the most prevelant non dark color. So a bit different but some of the same principles should apply. My steps were as follows: 1. Get the colors 2. Get the weight of the colors (how prevelant each one is) 3. Convert RGB over to hex equivelant 4. Perform a luma check to get a brightness value for each color

From there you should be able to pick your color based on your criteria. Here are some of the utility functions I used.

function lumaCheck(c) {
    var c = c.substring(1);
    var rgb = parseInt(c, 16);
    var r = (rgb >> 16) & 0xff;
    var g = (rgb >> 8) & 0xff;
    var b = (rgb >> 0) & 0xff;
    var luma = 0.2126 * r + 0.7152 * g + 0.0722 * b;
    return luma;
}
function componentToHex(c) {
    var hex = c.toString(16);
    return hex.length == 1 ? "0" + hex : hex;
}
function rgbToHex(r, g, b) {
    return "#" + componentToHex(r) + componentToHex(g) + componentToHex(b);
}

In general what you'd probably want to do is get the most prevelant color. Get its brightness (lumaCheck). Then get the color with the furthest luma value away from the picked color in your color set. You can tweak your function to decide between weight & luma value until it's satisfactory. With your example the primary color would be derived from your data result and your compares against the backgrounds, I suppose.