Why does a picture of a person seem to be looking in the same direction irrespective of the angle of observation? If you observe a picture of a person hanging on a wall who seems to be looking directly towards you always seems to be looking at you even though you change your angle of observation to the extremes. 
The same can be observed in a television. If a television is watched by many people from different angles all observe that a person on the screen is looking at them.
Why does it happen like that?
Update:
I First thought that it may be because of some data being lost due to conversion of 3D to 2D. But same is observed in a theater while watching a 3D movie.
 A: Seeing an object is seeing the light reflected from the surface. When we change the lighting on the object then we observe a different image. 

When we observe an object from different angles we see different images. This is because the reflected light goes in different directions and we see a particular ray only in one directions. For example when a ray is reflected from side of an object, we can see the ray only when we are in the path and if we are not in the path we cannot see the side of the object.

Coming to the case of a television. The image displayed on television is a 2-D image. Even if the angle of observance is change what we see is a 2-D image so we observe the same image. In case of 3-D pictures as seen in 3-D theaters we observe similar effect as in 2-D televisions. A 3-D image is formed by superimposition of multiple 2-D images of different polarization. 
A: A picture has only two dimensions. Ultimately all depth created through perspective and light and shadow is a trick, similarly eyes in a painting following you is also an illusion. The light, shadow and perspective depicted in a painting are fixed, meaning they don't shift. in a painting also it don't change, they look pretty much the same no matter from what angle you look at it. So if a person is painted to look at you, he or she will continue to look as you move. If a person is painted looking away from you, the light, shadow and perspective shouldn't allow him or her to ever look at you, even if you move yourself to the point where the person has been painted looking toward.
