It has been found that the statistics of textures in visual scenes are predictive of how easily human can distinguish the textures from random, uncorrelated noise. The existing method is to convert and split the original image into small patches consisting of binary pixels and to count the occurrences of all 16 possible 2x2 arrangements of binary pixels within each patch.

My summer project primarily involves the generalization of the binary method mentioned above to a continuous grayscale analysis. The research has two main components. The first component is to analyze images of natural scenes. Instead of converting original images into binary pixels, we convert them into real numbers between -1 and 1 and then conduct a similar analysis as in the binary case. The outcome of our analysis——images of natural scenes have the largest variation in pairwise correlations in the cardinal directions——conforms with the results of previous research.

The second component is to generate image patches with given values for the continuous grayscale statistics. After trying to use the Metropolis–Hastings algorithm and the Gibbs sampling algorithm, we are able to generate images patches with given values for one parameter. However, we have not yet found an efficient algorithm to generate image patches with given values for arbitrary number of parameters.

From the summer research experience, I have learned not only knowledge such as maximum entropy distribution, principal component analysis and sampling algorithms but also the idea of how to apply mathematics and statistics to a research in another subject. The experience also helps me to decide my future research directions.

It has been found that the statistics of textures in visual scenes are predictive of how easily human can distinguish the textures from random, uncorrelated noise. The existing method is to convert and split the original image into small patches consisting of binary pixels and to count the occurrences of all 16 possible 2x2 arrangements of binary pixels within each patch.

My summer project primarily involves the generalization of the binary method mentioned above to a continuous grayscale analysis. The research has two main components. The first component is to analyze images of natural scenes. Instead of converting original images into binary pixels, we convert them into real numbers between -1 and 1 and then conduct a similar analysis as in the binary case. The outcome of our analysis——images of natural scenes have the largest variation in pairwise correlations in the cardinal directions——conforms with the results of previous research.

The second component is to generate image patches with given values for the continuous grayscale statistics. After trying to use the Metropolis–Hastings algorithm and the Gibbs sampling algorithm, we are able to generate images patches with given values for one parameter. However, we have not yet found an efficient algorithm to generate image patches with given values for arbitrary number of parameters.

From the summer research experience, I have learned not only knowledge such as maximum entropy distribution, principal component analysis and sampling algorithms but also the idea of how to apply mathematics and statistics to a research in another subject. The experience also helps me to decide my future research directions.