At least two ways:

1. Use filter(INVERT) on a copy of the original image and use masking to display only the text area.
2. Use the pixel array to change the colors under the text area.

1. PImage img = loadImage("http://photo-dictionary.com/photofiles/list/2159/2822landscape.jpg");
2. PImage inverted;
3.  
4. void setup() {
5.   size(img.width, img.height);
6.   inverted = img.get();
7.   inverted.filter(INVERT);
8.   PGraphics mask = createGraphics(width, height, JAVA2D);
9.   mask.beginDraw();
10.   mask.smooth();
11.   mask.textAlign(CENTER, CENTER);
12.   mask.textSize(150);
13.   mask.text("INVERT", mask.width/2, mask.height/2);
14.   mask.filter(BLUR); // blurred version for better contrast and smooth display
    
15.   mask.text("INVERT", mask.width/2, mask.height/2);
16.   mask.endDraw();
17.   inverted.mask(mask);
18. }
19.  
20. void draw() {
21.   image(img, 0, 0);
22.   image(inverted, 0, 0);
23. }

i guess you could draw the text in an offscreen graphics buffer (PGraphics), then compare this buffer pixel per pixel with the location of the canvas it should be placed at. according to this comparison you could change individual pixels in the buffer before finally displaying it on the canvas using the image() function.