  We consider the task of pixel-wise semantic segmentation given a small set of
labeled training images. Among two of the most popular techniques to address
this task are Decision Forests (DF) and Neural Networks (NN). In this work, we
explore the relationship between two special forms of these techniques: stacked
DFs (namely Auto-context) and deep Convolutional Neural Networks (ConvNet). Our
main contribution is to show that Auto-context can be mapped to a deep ConvNet
with novel architecture, and thereby trained end-to-end. This mapping can be
used as an initialization of a deep ConvNet, enabling training even in the face
of very limited amounts of training data. We also demonstrate an approximate
mapping back from the refined ConvNet to a second stacked DF, with improved
performance over the original. We experimentally verify that these mappings
outperform stacked DFs for two different applications in computer vision and
biology: Kinect-based body part labeling from depth images, and somite
segmentation in microscopy images of developing zebrafish. Finally, we revisit
the core mapping from a Decision Tree (DT) to a NN, and show that it is also
possible to map a fuzzy DT, with sigmoidal split decisions, to a NN. This
addresses multiple limitations of the previous mapping, and yields new insights
into the popular Rectified Linear Unit (ReLU), and more recently proposed
concatenated ReLU (CReLU), activation functions.
