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Probabilistic Joint Image Segmentation and Labeling by Figure-Ground Composition

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Abstract

We propose a layered statistical model for image segmentation and labeling obtained by combining independently extracted, possibly overlapping sets of figure-ground (FG) segmentations. The process of constructing consistent image segmentations, called tilings, is cast as optimization over sets of maximal cliques sampled from a graph connecting all non-overlapping figure-ground segment hypotheses. Potential functions over cliques combine unary, Gestalt-based figure qualities, and pairwise compatibilities among spatially neighboring segments, constrained by T-junctions and the boundary interface statistics of real scenes. Building on the segmentation layer, we further derive a joint image segmentation and labeling model (JSL) which, given a bag of FGs, constructs a joint probability distribution over both the compatible image interpretations (tilings) composed from those segments, and over their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, followed by sampling labelings conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly, based on maximum likelihood with a novel estimation procedure we refer to as incremental saddle-point approximation. The partition function over tilings and labelings is increasingly more accurately approximated by including incorrect configurations that are rated as probable by candidate models during learning. State of the art results are reported on the Berkeley, Stanford and Pascal VOC datasets, where an improvement of 28 % was achieved for the segmentation task only (tiling), and an accuracy of 47.8 % was obtained on the test set of VOC12 for semantic labeling (JSL).

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Notes

  1. The segments are defined by the contained pixels and have fixed positions in the image–they cannot be moved like puzzle pieces. Moreover, while disallowing overlap increases the exposure to imperfect boundary alignments between segments selected in any single tiling, it leads to a dramatic reduction in the solution space and does not raise additional issues with assigning pixels lying on segment intersections.

  2. We call a segmentation assembled from non-overlapping figure-ground segments a tiling, and the tiling together with the set of corresponding labels for its segments a labeling (rather than a labeled tiling). Assigning a label to a segment also assigns this label to all the pixels of the segment.

  3. This approximation is similar in spirit to the one in Sect. 2.2. By enforcing at least one tiling to be retained for each segment, we aim for a uniform spread of the sampled tilings, which at the same time correspond to modes of the probability distribution.

  4. For our implementations, the actual running-times where 180.3 h for the PMA and 1.3 h for the incremental saddle-point. The used computer was an Intel Xeon workstation.

  5. An alternative strategy to approximate the partition function by using samples from the target distribution is contrastive divergence (Hinton 2002). Samples are obtained by running an MCMC chain for a limited number of steps. The obtained estimate is biased, but has been observed to perform well in practice.

  6. As previously done by the method we compare to, when evaluating FG-Tiling, only the annotated regions are considered.

  7. The tiling parameters have been learned for BSDS on the training set, for Stanford over \(5\) folds, and for VOC2009 on the training set, respectively, using the methodology described in Sect. 2.2.

  8. We also selected the scale parameter that optimized the First score on each dataset.

  9. The 1 min slot given to Enum (1min) is about 7.5\(\times \) the average run-time of FG-Tiling on the BSDS test set. Without the time constraint, Enum did not finish enumerating cliques after 48 h on an image where a pool of \(|\mathcal {S}|=120\) figure-ground segmentations were used.

  10. Recall, the VOC score is defined as the average per-class overlap between pixels labeled in each class and the respective ground truth annotation.

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Acknowledgments

This work was supported, in part, by CNCS-UEFICSDI, under PCE-2011-3-0438, and CT-ERC-2012-1, and by FCT under PTDC/EEA-CRO/122812/2010. The authors thank the anonymous reviewers for their useful comments and suggestions.

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Authors and Affiliations

  1. Faculty of Informatics, Vienna University of Technology, Vienna, Austria

    Adrian Ion

  2. Institute of Systems and Robotics, University of Coimbra, Coimbra, Portugal

    João Carreira

  3. Department of Mathematics, Faculty of Engineering, Lund University, Lund, Sweden

    Cristian Sminchisescu

  4. Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Cristian Sminchisescu

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  1. Adrian Ion
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  2. João Carreira
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Correspondence to Cristian Sminchisescu.

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Ion, A., Carreira, J. & Sminchisescu, C. Probabilistic Joint Image Segmentation and Labeling by Figure-Ground Composition. Int J Comput Vis 107, 40–57 (2014). https://doi.org/10.1007/s11263-013-0663-7

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