Image Segmentation by Cascaded Region Agglomeration Supplementary material

In these supplementary materials we provide additional examples of segmentation with our method ISCRA compares to the results obtained with other methods. We also elaborate on some of the details that could not be fully included in the paper due to space limitations. Search for optimal α Here we describe in more detail the optimization for setting α, the parameters controlling the recall/precision tradeoff in the loss used to train a stage in the ISCRA cascade. We start with bracketing α between α1 = 0 and some number α2 large enough to ensure that no merges are made by the learned model; in practice, α2 = 600 is sufficiently high even for the first stage (subsequent stages, as shown in the paper, tend to get lower and lower αs). Since the recall obtained by the stage trained with α is in practice monotonic with α, we can proceed by bracketing α with smaller and smaller interval, until it becomes sufficiently small (we use 0.1 as the minimum interval size to continue binary search). It is important that the recall is evaluated on a set different from the set used to learnw(α). Our implementation uses 120 random images (out of 200 BSDS300 training images) as training set (drawn independently in each stage). In the first few stages, when computating the results of merging and evaluation of recall for every α is computationally expensive, we use 30 of the remaining 80 images as tuning set. Beyond these few stages we use the entire 80 images not used for training in the given stage as tuning. Note that since the training/tuning partition is done by independent sampling in each stage, the training and testing sets overlap only partially in subsequent stages, thus making the learning less prone to overfitting. Furthermore, since the algorithm keeps merging regions in each stage, after a few stages the set of regions in a given image changes quite a bit; this also reduces the danger of overfitting. Algorithm 1: Binary search for α Given: Training set {(Ri, Gi)}, tuning set {(Rj , Gj)}, ρ > 0 initialize α1 = 0, α2 = 〈large number〉 Starting recall: r0 ← REC({Ri}) while α2 − α1 > δ do α ← (α1 + α2)/2 compute recall with α on tuning set: r(α) ← REC(MERGE({Ii,Ri,w∗(α))) if r(α) > r0 − ρ then α2 ← α else α1 ← α Return: α2 Analysis of system components All the plots reported in this section are obtained on BSDS300 test set.