Okay, for further reference: I updated my code, as there seemed to be some hiccups in it. 
But now it works pretty well! With this code, I can import a series of images (6x9 24-bit BMP, the least compression and errors in the pixels) with Processing, and project them onto the LED strip with Arduino (I cut the strip into a flexible matrix).
- First of all, the communication between Processing and Arduino was not going smoothly. There is no control over when the communication should begin.
- Second of all, I wanted to send rgb-values of the pixels from an 9x6 image (+ 6 extra pixels). The problem here is the amount of values (both min and max). Minimally, there would be 360 bytes ("x,x,x," * 60 = 360 bytes), and maximally 720 bytes ("xxx,xxx,xxx" * 60 = 720 bytes). Quite a variety! I'd better send it differently!
- Consequently, this floods the Arduino in data. As the serial buffer can only contain 128 bytes, the data should be divided into chunks, in order to control the input and make it consistent.
This resulted into a couple of additions/changes.
-
First of all, I integrated a function called establishContact(). With this function, I let Processing "initiate" the communication (Arduino responds, after which they both have isSerialStarted=true, so they both "know" the data that comes now is relevant).
-
Second of all, I used a different method for sending the pixel-values: through hexadecimal values. Always the same byte-length, namely 420 bytes ("xxxxxx," * 60 = 420). This required some encoding and decoding for both Processing and Arduino, but it works.
-
Thirdly, I chopped the data into chunks, by checking its length() in Processing. This means that, only when the length is smaller than 121 (128 minus the data to be added), it is safe to add another hex-value. Otherwise, start "filling up" the next chunk.
-
To let the Arduino make sense of the data, the entire hex-value data heap should have an SOP and EOP (e.g. start with "<" and end with ">"). This way, the Arduino knows when to update the entire LED strip, based on the collected data.
-
After having it up and running, the animation of images on the strip was not that fast (maybe 2 FPS, but heck, what is realistic?). I tried to turn up the speed, and it worked by increasing the baud-rate of the communication (115200 instead of 9600). The Arduino is able to handle all the code that I use, but it needs a moment to breathe in between. So after sending a chunk of data in Processing, I set a delay of 10ms to let the Arduino read out the serial buffer. It worked! I doubled the speed. 
So there you have it. A LED matrix that displays a sequence of 9x6 images, controlled by Arduino through Processing. I had to remove the comments from the code, otherwise I exceed a message length limit on this forum.. 
Arduino code:
#include <Adafruit_NeoPixel.h>
#define PIN 6
Adafruit_NeoPixel strip = Adafruit_NeoPixel(60, PIN, NEO_GRB + NEO_KHZ800);
uint16_t pixelID = 0;
char inChar = '\0';
char serialBuffer[6];
int sI = 0;
boolean isSerialOpen = false;
boolean isSerialStarted = false;
boolean isResponse = false;
void setup(){
strip.begin();
Serial.begin(115200);
strip.show();
}
void loop(){
while(Serial.available() > 0){
inChar = (char)Serial.read();
isResponse = true;
if(isSerialStarted==true){
if(inChar=='<'){
isSerialOpen = true;
}
else{
if((inChar==',')||(inChar=='>')){
long int r = strtol(String(serialBuffer).substring(0,2).c_str(),0,16);
long int g = strtol(String(serialBuffer).substring(2,4).c_str(),0,16);
long int b = strtol(String(serialBuffer).substring(4,6).c_str(),0,16);
strip.setPixelColor(pixelID,strip.Color(r,g,b));
pixelID++;
sI = 0;
serialBuffer[sI] = '\0';
if(inChar=='>'){
isSerialOpen = false;
strip.show();
pixelID = 0;
}
}
else {
if(isSerialOpen==true){
serialBuffer[sI] = inChar;
sI++;
serialBuffer[sI] = '\0';
}
}
}
}
else {
if(inChar=='A'){
Serial.println("B");
isSerialStarted=true;
}
}
}
if(Serial.available() == 0) {
if((isSerialStarted==true)&&(isSerialOpen == true)&&(isResponse==true)){
Serial.println("A");
isResponse = false;
}
}
}
Processing code:
import processing.serial.*;
Serial port;
byte[] serVal = new byte[2];
String[][] val = new String[7][4];
PImage[] images = new PImage[7];
int id = 0;
int bufID;
boolean justSend = true;
boolean isSerialStarted = false;
void setup(){
size(9,6);
colorMode(RGB,255);
port = new Serial(this, "COM9", 115200);
port.clear();
serVal = null;
for ( int i = 0; i< images.length; i++ )
{
images[i] = loadImage("imgs/g" + i + ".bmp" );
bufID = 0;
image(images[i], 0, 0);
loadPixels();
val[i][0] = "<";
val[i][1] = "";
val[i][2] = "";
val[i][3] = "";
for (int y = 0; y < 6; y++) {
for (int x = 0; x < 9; x++) {
if(val[i][bufID].length() > 121){
bufID++;
}
if((y < 3)&&(x==0)){
val[i][bufID] += (y==0) ? "c85000," : "c8c8c8,";
}
String pixelColor = hex(get(x,y),6);
if(val[i][bufID].length() > 121){
bufID++;
}
val[i][bufID] += pixelColor+",";
if(val[i][bufID].length() > 121){
bufID++;
}
if((y < 3)&&(x==8)){
val[i][bufID] += (y==0) ? "c85000," : "c8c8c8,";
}
if((y*x) == 40){
val[i][bufID] = val[i][bufID].substring(0,(val[i][bufID].length()-1));
val[i][bufID] += ">";
}
}
}
println("val["+i+"]:");
println(val[i]);
bufID = 0;
}
}
void draw(){
if(isSerialStarted == false){
establishContact(port);
}
else {
if(justSend==true){
delay(10);
port.write(val[id][bufID]);
if(bufID==3){
bufID = 0;
id = (id==6) ? 0 : id + 1;
}
else {
bufID++;
}
justSend = false;
}
}
}
void serialEvent(Serial port){
serVal = port.readBytes();
port.readBytes(serVal);
byte serialVal = serVal[0];
switch(serialVal){
case 65:
justSend = true;
break;
case 66:
isSerialStarted = true;
justSend = true;
break;
}
}
void establishContact(Serial port){
if(port.available() <= 0) {
port.write("A");
delay(300);
}
}