  For medical image segmentation, most fully convolutional networks (FCNs) need
strong supervision through a large sample of high-quality dense segmentations,
which is taxing in terms of costs, time and logistics involved. This burden of
annotation can be alleviated by exploiting weak inexpensive annotations such as
bounding boxes and anatomical landmarks. However, it is very difficult to
\textit{a priori} estimate the optimal balance between the number of
annotations needed for each supervision type that leads to maximum performance
with the least annotation cost. To optimize this cost-performance trade off, we
present a budget-based cost-minimization framework in a mixed-supervision
setting via dense segmentations, bounding boxes, and landmarks. We propose a
linear programming (LP) formulation combined with uncertainty and similarity
based ranking strategy to judiciously select samples to be annotated next for
optimal performance. In the results section, we show that our proposed method
achieves comparable performance to state-of-the-art approaches with
significantly reduced cost of annotations.
