## Image Segmentation using Gaussian Mixture Model (GMM) and BIC

A while ago, I was so amazed about the image segmentation results using Gaussian Mixture Models (GMMs) because GMM gives pretty good results on normal/natural images. There are some results on my previous post. Of course, GMM is not the best for this job, but hey look at its speed and easiness to implement–it’s pretty good in that sense. However, one problem with GMM is that we need to pick the number of components. In general, the more component numbers we assume, the better log-likelihood it would be for GMM. In that case, we would simply send the number of components to infinity, right? Well…but there is nothing good come out of that because the segment would not be so meaningful–in fact, we overfit the data, which is bad.

Therefore, Bayesian Information Criteria (BIC) is introduced as a cost function composing of 2 terms; 1) minus of log-likelihood and 2) model complexity. Please see my old post. You will see that BIC prefers model that gives good result while the complexity remains small. In other words, the model whose BIC is smallest is the winner. Simple as that. Here is the MATLAB code. Below are some results from sweeping the number of components from 2 to 10. Unfortunately, the results are not what I (and maybe other audiences) desire or expect. As a human, my attention just focuses on skier, snow, sky/cloud and perhaps in the worst case, the shadows, so the suitable number of components should be 3-4. Instead, the BIC assigns 9-component model the winner which is far from I expected. So, Can I say that the straightforward BIC might not be a good model for image segmentation, in particular, for human perception? Well…give GMM-BIC a break– I think this is too early to blame BIC because I haven’t use other more sophisticated features like texture, shape, color histogram which might improve results from using GMM-BIC. The question is what are the suitable features and the number of components that makes the segmentation results using GMM-BIC similar to human perception? MATLAB code is made available here.