It is possible but a very difficult task.
It can be made easier your black dog is running on a grey background fetching a white stick.
A computer algorithm called "blob detection" can identify blobs of color in an image.
For example, you might track the black and white blobs frame be frame, and interpolate the motion.
For simple experiments, I recommend experimenting with this library:
http://v3ga.net/processing/BlobDetection/