M for Gaussian Mixture Models代写 - GMMs代写 - MATLAB代写

Assignment 03: EM for Gaussian Mixture Models (GMMs): Image

Segmentation Appli ation

M for Gaussian Mixture Models代写 We will use Gaussian mixture models (GMMs) for image segmentation. And study the behavior of the algorithm on a simple ···

1.For this problem M for Gaussian Mixture Models代写

We will use Gaussian mixture models (GMMs) for image segmentation. And study the behavior of the algorithm on a simple image. The file “GMMSegmentTestImage.jpg” available on the website provides an image that is used as a test for olor blindness1. Color normal individuals viewing the image should see a lear message. In the image revealed by a partitioning of the image into distin t regions that are hara terized by homogeneity of some olor attributes. However, these regions also show variation in other attributes.

We will segment the image using Gaussian mixture modeling and assess the results we obtain. For the GMM tting in this assignment. You may hoose to use your own program using the equations provided during our dis ussion of GMMs in the ontext of the EM algorithm in lass. Or you may hoose to use an existing implementation from the web. Or from the appropriate MATLABtoolbox or python pa kage. (50 points)

(a) To simplify things and allow us to visualize our results, we will work in a 2-dimensional spa e instead of dire tly using the 3-dimensional RGB image data Convert the image RGB data from its native 3-dimensional RGB olor spa e into a 2-dimensional rg hromati ity spa e by applying the

transformation.

Transform the test image into rg hromati ity space M for Gaussian Mixture Models代写

And visualize your transformed image by mapping it ba k into an 8-bit RGB image via the transformation.

Comment on what attributes are preserved and what attributes are lost in the pro ess of onversion from the input RGB to the output RGB (equivalently from RGB spa e to rg hromati ity spa e. Hint: If you are using MATLAB, the fun tions imread() and imshow(), will be helpful for you in this exer ise.

(b) Cluster the pixels in the image by fitting a K = 3 omponent GMM to the hromati ities in the image. Specifically, model the observed rg hromati ity values a ross the pixels in the image as a set of iid d = 2-dimensional rg ve tor observations from a Gaussian mixture with unknown mean and ovarian e and use the Expe tation Maximization (EM) algorithm for GMM parameter estimation to estimate the unknown mean ve tors and ovarian e matri es for the GMM. M for Gaussian Mixture Models代写

Because the EM algorithm is only lo ally onvergent. You need to perform the GMM parameter estimation with multiple random initializations and sele t between these to obtain a “good” result. For determining a “good” result, you an either evaluate the likelihood fun tion, or (more readily) you an visualize your results as des ribed in the following parts. And assess the fit based on the visualizations. Hint: The MATLAB fun tion reshape() will be helpful for re-organizing the data from the 2D two rg hannel hromati ity image representation into a sequen e of 2D rg ve tors in this exer ise.