As the title says can I perform image processing on Atmega-2560?
Basically I have to capture real time images and detect green or red color.
I have not thought of the frame rate but it is not that fast or slow.
No. Your question really is: Can an 8-bit processor, running at 16 MHz, with 8 KB of RAM, do image processing at an acceptable rate? Unless you are talking about 10 pixels by 10 pixels, at a frame rate of 1 frame per second, then I doubt it.
You may want to ask the "real" question. See The X-Y Problem. There are sensors around that detect colours. If you are making a maze-following robot that needs to stop if it gets near to a red wall, that is a much more achievable objective.