  Accurate segmentation of medical images is essential for diagnosis and
treatment of diseases. These problems are solved by highly complex models, such
as deep networks (DN), requiring a large amount of labeled data for training.
Thereby, many DNs possess task- or imaging modality specific architectures with
a decision-making process that is often hard to explain and interpret. Here, we
propose a framework that embeds existing DNs into a low-dimensional subspace
induced by the learnable explicit feature map (LEFM) layer. Compared to the
existing DN, the framework adds one hyperparameter and only modestly increase
the number of learnable parameters. The method is aimed at, but not limited to,
segmentation of low-dimensional medical images, such as color histopathological
images of stained frozen sections. Since features in the LEFM layer are
polynomial functions of the original features, proposed LEFM-Nets contribute to
the interpretability of network decisions. In this work, we combined LEFM with
the known networks: DeepLabv3+, UNet, UNet++ and MA-net. New LEFM-Nets are
applied to the segmentation of adenocarcinoma of a colon in a liver from images
of hematoxylin and eosin (H&E) stained frozen sections. LEFM-Nets are also
tested on nuclei segmentation from images of H&E stained frozen sections of ten
human organs. On the first problem, LEFM-Nets achieved statistically
significant performance improvement in terms of micro balanced accuracy and
$F_1$ score than original networks. LEFM-Nets achieved only better performance
in comparison with the original networks on the second problem. The source code
is available at https://github.com/dsitnik/lefm.
