Sequential vs simultaneous stochastic segmentation

In past work, the Metropolis Algorithm along with Gibbs priors was used to successfully segment two-dimensional noisy gray images into a small finite number of labels. In applications where a clean signal is to be extracted from a noisy signal in real-time, the need for sequential segmentation arises. Here, we examine the success of using a column-sequential segmentation algorithm using the Metropolis Algorithm with Gibbs priors, and compare it to the column-simultaneous algorithm. What makes column-sequential algorithms harder than column-simultaneous algorithms is the lack of knowledge of pixel values to the right of the current column. Despite this difficulty, the column-sequential algorithm proposed here does relatively well. We conclude the paper with a discussion of methodologies that might further improve the quality of the column-sequential segmentation algorithms.