CS-544 Optimization in Computer Vision

Choose one image per class from the CIFAR-10 dataset of images (look it up!). For each image, use k-means to reduce the number of colors to 32 (you can use a different colormap per image or one for all 10 images - your choice). Now for each image, prepare a noisy version using the following procedure. For each pixel, sample a Bernoulli random variable with probability 1/32 of coming up 1 (and 31/32 of coming up 0). If your sample has the value 1, then replace the pixel value with a value chosen uniformly and at random from the range 1-32.

Denoise your 10 images using the simple MRF model. You should choose 2 of the algorithms listed below, and compare their performance. You may use any codes you happen to find helpful -- this exercise isn't really about writing code. Notice you will have to choose the parameters of the model. Follow the guidelines in the MRF notes.

Options

• Graph cut algorithms. Keep in mind this is a multilabel problem, so you'll need to produce an approximate solution. Lots of good codes out there.
• Mean field algorithm. Again, cause it's multilabel, you'll have to do a (very little) more math than we did in class. It's probably easier to implement this than find a code.
• An approximation with a single tree, as we did in class.
• Loopy belief propagation. Likely easier to implement than find a code.
• Tree reweighted message passing. You'll have to look this up, but there are good codes.
• ADMM, using the decomposition we built in class. Likely easier to implement than find a code.

This is a broad MP intended to be educational. I will grade on quality of experimental concept and of argument from data. Submit PDF's to me by *DATE*. Email them to Xiaoming at xz23@illinois.edu, with "CS544" in the header