Can someone please tell me why this artifacts is so difficult to take away from the edges of the shadows ?
The file: pasteall.org/blend/4603
hmm… interesting way of adding a background… In the node editor i would turn up the premultiply on the alpha over node, and, it wasnt nessecary this time, but you should pack images before you upload .blend files 
Because these artifacts appear on the edges of shadows, I would say that they are being caused by alpha premultiplication. (You can look up those concepts in the Blender docs.) The problem might be caused by the edges of the casting object being semi-transparent, or by a similar process on the shadow itself.
I’m not going to try to tear into your blend-file but I can offer a few suggestions. The shadow-casting object probably needs to have alpha-calculations turned off, and the shadow that is cast should then be fed through a Blur node.
If there are some speedier ways to do this, I’ll be watching this thread closely for a while. 'Cuz what I tend to do is to handle objects and shadows separately, and some of the node networks that I’ve come up with in order to do that are, well, pretty funky. :spin:
Thanks guys ! It solved the problem, just turned on the “convert premul” on the “alpha over” node and here is the result: http://www.youtube.com/watch?v=wHZmz3E7_fE
Im almost totally newbeginner so Im am aware of that I have to go muck deeper in to materials, lights, shadows and such stuff before I can put things in by tracking and make it look totally natural.
By the way, Sundialsvs4 wrote… “I’m not going to try to tear into your blend-file but I can offer a few suggestions. The shadow-casting object probably needs to have alpha-calculations turned off, and the shadow that is cast should then be fed through a Blur node.”
Thats quite intresting ! I would really like to learn how to separate the object from the shadow and get some more controll over the appearance.
to separate it you should enable shadows as a pass in the layers panel. then you can mess around with them.
your camera tracking looks pretty good, do you have to pay for syntheyes? i use icarus and it’s horrible 
the things you need to focus on when camera tracking are
-lighting, you should try to reproduce it perfectly (including light bouncing off the floor etc.) however small it is.
-material, should look like they might exist in the real world
-story line, if you have an interesting story line, people focus on the story line and are less likely to pick out small details.
EDIT: almost forgot - resolution, your letters are much higher res than the rest of your movie. there are various ways to degrade the quality.
This is god stuff Casio ! Thanks ! I will try and come back with some feedback