Supplementary Materials: Discriminative Re-ranking of Diverse Segmentations

In this supplementary document, we present how we characterize diversity in solutions along with some oracle statistics (Section 1.1) , and show some example success and failure cases of our re-ranker (Section 2). 1. Analyzing Diverse Segmentations In this section, we characterize the diversity achieved in the multiple segmentations. Specifically, we investigate the sources of diversity, and attempt to quantify the extent to which diversity enables potential gain in accuracy over the MAP solution. 1.1. Diversity and Oracles For the analysis reported in this section, we used the VOC 2012 training and validation sets. ALE and O2P models were trained on VOC2012 training set, and the models were used to produce 10 segmentations for each image in the validation set. Following [1], we tuned the Lagrangian multipliers via cross-val (λALE = 1.25 and λO2P = 0.08). 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 Number of Solutions M in im u m C o v e ri n g o f M A P O2P ALE (a) 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 Number of Solutions A v e ra g e P A S C A L A c c u ra c y O2P-oracle-label O2p-oracle ALE-oracle-label ALE-oracle (b) 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 Number of Solutions A v e ra g e P A S C A L A c c u ra c y O2P-oracle-mask O2p-oracle ALE-oracle-mask ALE-oracle (c) Figure 1: (a) Average minimum-covering (2) of MAP in the first M solutions vs. M . (b) Accuracy of an oracle restricted to labels present in the MAP, or (c) restricted to masks present in MAP. See text for details. Diversity of Solutions. In order to characterize the diversity in DivMBEST solutions, we define a covering measure, which for a given image i captures how much of the MAP segmentation is covered by one of the subsequent solutions. Let {s i,1 , . . . , s (m) i,K } denote the set of K segments in the m solution for image i and {s (1) i,1 , . . . , s (1) i,K′} denote the set of segments in MAP. The category-independent covering score is given by: D1(y (m) i ) = 1 ∑ k′ |s i,k′ | K′ ∑ k′=1 |s i,k′ | max k∈[K] O(s (1) i,k′ , s (m) i,k ), (1)