Mat 256


Signal to Noise

Nithish Jayaraman

A video (series of images) is generated by starting with an image and determining the subsequent image using a three state markov chain. The three states represent pixel values of white, gray and black. The transition between them is governed by the structure of the chain and its probability of transition. The probability of transition of a pixel value from one frame to the next is determined by the mean of the neighboring pixel values.

Introduction:
Markov chain is an interesting concept to work with as it involves both probability and present values to determine the future values. The future values are not completely probabilistic and random as the markov chain has a rigid structure by having constant state values and only the transition between the states is determined by a probability value.

Conversations:
In the initial stages of the course, I was working on visual cryptography. Visual cryptography is method of hiding secret information in different images, the secret image or information is revealed when the different images are stacked together. Then I wasn’t able to make headway in making something interesting of that work and concept. The professors helped me in choosing a new work through a series of discussions. I continued working on images but now changing it with help of markov chain.

Development:
Initially started with a completely white image and observed results produced by the markov chain with fixed probability value. As a next step to increase the complexity, the probability value was determined depending upon the values of the neighboring pixels.

Conclusion:
After working on different individual projects on various methods to generate an image with the help of neighboring pixel values and modifying the current value, the images generated by markov chain variations seems to be promising. As an open ended project, there are lots of scopes for improvement. More complexities can be introduced to the markov chain depending upon what type of result you need obtain. For example, the number of states and the number of transitions possible from one state can be increased.

The a Markov value was determined on the basis of the pixel’s neighbors. The value of a is the mean value of all the neighboring pixel values. As the neighboring pixels have value between zero and one only, the probability value always lies between its bound. The programming language used to code and generate videos was Matlab. Matlab is an ideal choice for this type of work as it gives the best computation times due to its inbuilt matrix functions that are useful while working with images.