This is an interesting problem and I used to use it years ago to keep image file sizes down but I can’t remember what software I used. So it piqued my interest enough to create a sketch that uses the Quantize class code in the link provided by @jb4x (thanks).
So here is the result ouput from my sketch
I have simply created a new tab called Quantize.java and copied the code from the link into it. NOTE that the tab name must match precisely the class name to make it a top level class.
The Quatize class expects the pixel data to be in a 2D array wheres PImage stores pixel data in a 1D array so I have created a class called QImage which performs all the conversion and use the Quatize class to do its stuff.
Anyway the main tab sketch code is shown below but if you want you can download the entire sketch from here
Enjoy 
PImage img;
QImage qimg256, qimg64, qimg16;
void setup() {
size(520, 400);
img = loadImage("london.jpg");
textSize(14);
fill(0);
background(255);
// Make sonme quantized images
qimg256 = new QImage(img, 256);
qimg64 = new QImage(img, 64);
qimg16 = new QImage(img, 16);
text("32 bit ARGB", 10, 18);
image(img, 0, 20);
text("256 colors", 270, 18);
image(qimg256.getImage(), 260, 20);
text("64 colors", 10, 218);
image(qimg64.getImage(), 0, 220);
text("16 colors", 270, 218);
image(qimg16.getImage(), 260, 220);
save("sample.png");
}
/**
This class is used to store the result of the image quantization.
The final image comprises a color table and a 2D array containing
an index into the color table.
It also creates a new PImage with the reduced color set for
convenience.
*/
public class QImage {
final int[][] pixels;
final int w, h;
final int[] colortable;
final PImage reducedImage;
/**
img = the PImage we want to quantize
maxNbrColors - color table size
*/
public QImage(PImage img, int maxNbrColors) {
// Pixel data needs to be in 2D array for Quantize class.
w = img.width;
h = img.height;
pixels = new int[h][w];
img.loadPixels();
int[] p = img.pixels;
int n = 0;
for (int y = 0; y < h; y++) {
for (int x = 0; x < w; x++) {
pixels[y][x] = p[n++];
}
}
// Quantize the image
colortable = Quantize.quantizeImage(pixels, maxNbrColors);
//Create a PImage with the reduced color pallette
reducedImage = createImage(w, h, ARGB);
for (int y = 0; y < h; y++) {
for (int x = 0; x < w; x++) {
reducedImage.set(x, y, colortable[pixels[y][x]]);
}
}
}
/**
Convenience method to draw the quatized image at a
given position.
*/
public void displayRAW(int px, int py) {
for (int y = 0; y < h; y++) {
for (int x = 0; x < w; x++) {
set(px + x, py+y, colortable[pixels[y][x]]);
}
}
}
/**
Get the pixel color index data
*/
public int[][] getPixels() {
return pixels;
}
/**
Get the color table data
*/
public int[] getColorTable() {
return colortable;
}
/**
Get the maximum number of colors in the reduced image.
The actual number of unique colors maybe less than this.
*/
public int nbrColors() {
return colortable.length;
}
/**
Convenience method to get the quatized image as a PImage
that can be used directly in processing
*/
public PImage getImage() {
return reducedImage;
}
}