I can't guess a specific time, but I can guess that you will see changes sooner than you think. Be sure to take photos now and then so that you can keep track. It really helps whenever you are discouraged to see how far things do move over time.
Your front tooth that is sticking out towards the front looks very similar to the way mine did when I started treatment. My tooth took only 6 weeks to move back in line with my other teeth but then took many months to stabilise in that posistion - be warned that it may cause some pretty bad pain long after it looks like it's in it's right position. I found that for around 8 months that tooth was very sensitive at adjustments simply because it had moved so far in such a quick time.
I agree with KK in that tooth movement is very much an individual process - while mine moved within six weeks, you may find yours take a little longer depending on what your ortho focusses on.
Good Luck, you will be amazed at how quickly things start to change!
I can see the difference already and what you have to remember is that one tooth has to come forward and one has to move back. So i'm sure within the next two to three months you might be almost in line..
Congrats on the movement
Yes I agree... Why does it take people such a long time!!!! I took years and years to make the decision!