Soft Image Segmentation Using Gradient Graph Laplacian Regularizer

We revisit the well-studied image segmentation problem from a soft labeling perspective: instead of estimating integer labels per pixel indicating a finite set of classes, each pixel is assigned a real number that conveys the level of uncertainty in the estimated class label. Soft labels are useful, for example, for subsequent human editing or composition. Specifically, given a set of pre-computed super-pixel labels and feature vectors per pixel, we formulate a convex optimization objective regularized by signal-dependent gradient graph Laplacian regularizers (GGLR), which promotes piecewise planar (PWP) signal reconstruction. Unlike a previous well-known soft segmentation scheme that requires expensive computation of the first 100 eigenvectors, our optimization can be solved efficiently in linear time via conjugate gradient (CG). Experimental results show that our method produces satisfactory soft labels per pixel for images in two public datasets at a reduced computation cost compared to the previous soft segmentation scheme.