  When pixel-level masks or partial annotations are not available for training
neural networks for semantic segmentation, it is possible to use higher-level
information in the form of bounding boxes, or image tags. In the imaging
sciences, many applications do not have an object-background structure and
bounding boxes are not available. Any available annotation typically comes from
ground truth or domain experts. A direct way to train without masks is using
prior knowledge on the size of objects/classes in the segmentation. We present
a new algorithm to include such information via constraints on the network
output, implemented via projection-based point-to-set distance functions. This
type of distance functions always has the same functional form of the
derivative, and avoids the need to adapt penalty functions to different
constraints, as well as issues related to constraining properties typically
associated with non-differentiable functions. Whereas object size information
is known to enable object segmentation from bounding boxes from datasets with
many general and medical images, we show that the applications extend to the
imaging sciences where data represents indirect measurements, even in the case
of single examples. We illustrate the capabilities in case of a) one or more
classes do not have any annotation; b) there is no annotation at all; c) there
are bounding boxes. We use data for hyperspectral time-lapse imaging, object
segmentation in corrupted images, and sub-surface aquifer mapping from
airborne-geophysical remote-sensing data. The examples verify that the
developed methodology alleviates difficulties with annotating non-visual
imagery for a range of experimental settings.
