  This paper presents a novel selective constraint propagation method for
constrained image segmentation. In the literature, many pairwise constraint
propagation methods have been developed to exploit pairwise constraints for
cluster analysis. However, since most of these methods have a polynomial time
complexity, they are not much suitable for segmentation of images even with a
moderate size, which is actually equivalent to cluster analysis with a large
data size. Considering the local homogeneousness of a natural image, we choose
to perform pairwise constraint propagation only over a selected subset of
pixels, but not over the whole image. Such a selective constraint propagation
problem is then solved by an efficient graph-based learning algorithm. To
further speed up our selective constraint propagation, we also discard those
less important propagated constraints during graph-based learning. Finally, the
selectively propagated constraints are exploited based on $L_1$-minimization
for normalized cuts over the whole image. The experimental results demonstrate
the promising performance of the proposed method for segmentation with
selectively propagated constraints.
