1. Mixture of Gaussians This is a probability distribution for random variables or N-D vectors such as… –intensity of an object in a gray scale image –color of an object in a colored image

2. Mixture of Gaussians Distribution may have the following forms in probability of “mode” k in this case where and standard Normal/Gaussian distribution in

3. Mixture of Gaussians Distribution may have the following form in probability of “mode” k where and

4. Mixture of Gaussians Suppose that your object pixels have colors which are distributed in as

5. Mixture of Gaussians Can we feet a “mixture of Gaussians” into a given sample of observed object colors ? What are for ? number of modes in the mixture

6. Mixture of Gaussians Use the following algorithm –Fix a number of modes you want to fit (say n=10 or 20) –Select initial guesses for from colors of n randomly selected pixels in the object –Select initial guesses for

7. Mixture of Gaussians Iterate two steps below 10-20 times –E step: for each object pixel p compute a probability that its color belongs to mode k –M step: update parameters analogous for and