Let the output of image sensor take values between 0 to 10. If the samples are quantized uniformly to 256 levels, show that transition and reconstruction levels are
$$t_k=\dfrac{10(k-1)}{256},\, k=1,\cdots,257$$ $$r_k=t_k+\dfrac{5}{256},\, k=1,\cdots,256,$$
respectively.
I asked the first formula, but the second I don't know how i will be able to do ...
It seems "transition levels" refers to the output levels at which there is a transition in the quantized value. Quantizing the interval from $0$ to $10$ uniformly with $256$ levels leads to $256$ intervals of length $10/256$ each, and the $257$ values $t_k$ are the boundary values of those intervals: $0,10/256,20/256,\dotsc,10$. Then when you want to reconstruct an output level from a quantized level, your best guess (e.g. in the sense of mean error or root mean square error) is the midpoint of the interval, and indeed the $256$ values $r_k$ are the midpoints of the intervals: $5/256,15/256,\dotsc$.