  Instance Segmentation, which seeks to obtain both class and instance labels
for each pixel in the input image, is a challenging task in computer vision.
State-of-the-art algorithms often employ two separate stages, the first one
generating object proposals and the second one recognizing and refining the
boundaries. Further, proposals are usually based on detectors such as faster
R-CNN which search for boxes in the entire image exhaustively. In this paper,
we propose a novel algorithm that directly utilizes a fully convolutional
network (FCN) to predict instance labels. Specifically, we propose a
variational relaxation of instance segmentation as minimizing an optimization
functional for a piecewise-constant segmentation problem, which can be used to
train an FCN end-to-end. It extends the classical Mumford-Shah variational
segmentation problem to be able to handle permutation-invariant labels in the
ground truth of instance segmentation. Experiments on PASCAL VOC 2012, Semantic
Boundaries dataset(SBD), and the MSCOCO 2017 dataset show that the proposed
approach efficiently tackle the instance segmentation task. The source code and
trained models will be released with the paper.
