Image segmentation is the task of grouping pixels in an image into semantically similar segments. If the image is an aerial photograph, then a good segmentation will have assigned the pixels to segments corresponding to various land features, such as water, road, forest, and building. Unsupervised image segmentation involves doing this without example data of pixels and their true feature labels. This paper introduces a new method, called triplet Markov fields, for doing unsupervised image segmentation.

The proposed method is an extension of previous probabilistic models, including hidden Markov fields and pairwise Markov fields. Each model in the hierarchy is more expressive than earlier models, which means they can potentially represent more complex segment shapes, such as crinkly lakes or a complex network of roads. The tradeoff is the additional complexity in deriving, implementing, and computing the estimation methods. Are the additional hassles worth the gain in image segment quality?

First, we see the quality: the triplet Markov fields are tested on synthetic images and a radar image of a city, and are compared to the simpler variants. The improvement is significant. Second, and more surprising, the authors show that the triplet Markov fields require only minor changes to the parameter estimation methods for the earlier variants. The complexity penalty here is small for a good gain in model expressiveness.