Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider the function $z = x^2 + y^2$ , for $0 \leq x \leq 10$ and $0 \leq y \leq 10$. Take a regular discretization with steps $\Delta x = \Delta y = 0.1$ and its histogram as the probability distribution. Then, apply the LLOYD-MAX quantizer to get a 8-bits grey level image.

How I will be able to fix this problem?

The transition, $t_k$, and reconstruction, $r_k$ levels are the fórmulas:

$$t_k = \dfrac{r_k+r_{k-1}}{2}$$ $$r_k = \dfrac{\int_{t_k}^{t_{k+1}}up(u)du}{\int_{t_k}^{t_{k+1}}p(u)du}$$

where $u$ a real scalar random variable with a continuous probability density function $p(u).$

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.