Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. 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

Let $Y$ be a measured (noisy) image $Y= X+ noise$, where $X$ is an image contains $0$(Background) and $200$(object). I need to create a decision rule that determines whether the true pixel value was $0$ or $200$ given the image $Y$.

the noise is Gaussian with mean=0 and standard deviation=sigma

I_true = [zeros(50,140);zeros(60,40),(ones(60,60)*200),zeros(60,40);zeros(50,140)];
[nrows ncolumns] = size(I_true);
sigma = 63.246;
gaussian_noise = sigma*randn(size(I_true));
I_noisy = I_true + gaussian_noise;

After adding the Gaussian noise to the true image the PDF of the intensity of a background pixel will be Gaussian with mean = $0$ and variance= $63.2462^2$ and the PDF of the intensity of an object pixel will be Gaussian with mean = $200$ and variance= $63.2462^2$

I used MAP rule and assumed that $P(Y=0)=P(Y=200)$

Likelihood ratio




so if $Y≥100$ the pixel will be considered as object.

my questions are :.

1) is my solution is right?

2) in the case of two objects with gray levels $150$ and $200$ what will be the steps of Map decision rule?

share|improve this question
Is your variance, $\sigma^2$ = 63.2462 or your standard deviation $\sigma$ = 63.2462? – Mohammad May 16 '12 at 20:19
@Mohammad sigma = standard deviation = 63.2462 – HforHesham May 16 '12 at 20:22
Yes, but you have written variance = 63.2462 – Mohammad May 16 '12 at 20:36
@Mohammad I have corrected it. – HforHesham May 16 '12 at 20:48
to learn it, you can go to my site – Ruslan Wahyudi Nov 18 '14 at 5:47
up vote 8 down vote accepted

1) Yes, your solution is correct.

2) If you assume that all a priori probabilities are equal, then the boundaries for AWGN is always the middle points between the possible values of X. In this case, then, the decision boundaries are at 75 and 175.

I believe that this rule (decision boundary at the middle points) can be generalised to applying to any noise probability distribution that is symmetric and monotonically decreases as the distance from zero increases.

share|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.