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Markov Random Fields with Asymmetric Interactions for Modelling Spatial Context in Structured Scene Labelling

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Abstract

In this paper we propose a Markov random field with asymmetric Markov parameters to model the spatial and topological relationships between objects in structured scenes. The field is formulated in terms of conditional probabilities learnt from a set of training images. A locally consistent labelling of new scenes is achieved by relaxing the Markov random field directly using these conditional probabilities. We evaluate our model on a varied collection of several hundred hand-segmented images of buildings. The incorporation of spatial information is shown to improve greatly the performance of some trivial classifiers.

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Notes

  1. Note that although a directed graph for the computer vision community cannot be called an MRF, and as a consequence, according to the same community, asymmetric MRFs do not exist, from the mathematical point of view the concept is not only possible, but, in our opinion, also prevalent in nature: if the value of a node is assumed to be the outcome of a random experiment, we are clearly dealing with a random field; if we model this outcome by considering only the neighbours (defined in some pre-specified sense) of the node, we are clearly dealing with a Markovian random field. Nowhere in these two definitions enters the concept of directionality. We consider the assertion that a directed graph cannot be a Markov random field rather idiosyncratic of the computer vision community and not valid if strict mathematical definitions are applied. That is why in this paper we use the mathematically correct terms “asymmetric MRFs” or “non-Gibbsian MRFs”.

  2. The images alongside their annotation and segmentation information are available at http://www.commsp.ee.ic.ac.uk/~dheesch/ngmrf/data/.

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Acknowledgements

This work was supported by the FP6 European project eTRIMS.

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Authors and Affiliations

  1. Communications and Signal Processing Group, Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK

    Daniel Heesch & Maria Petrou

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  1. Daniel Heesch
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  2. Maria Petrou
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Correspondence to Maria Petrou.

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Heesch, D., Petrou, M. Markov Random Fields with Asymmetric Interactions for Modelling Spatial Context in Structured Scene Labelling. J Sign Process Syst 61, 95–103 (2010). https://doi.org/10.1007/s11265-009-0349-0

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