  We introduce a Gaussian Prototype Layer for gradient-based prototype learning
and demonstrate two novel network architectures for explainable segmentation
one of which relies on region proposals. Both models are evaluated on
agricultural datasets. While Gaussian Mixture Models (GMMs) have been used to
model latent distributions of neural networks before, they are typically fitted
using the EM algorithm. Instead, the proposed prototype layer relies on
gradient-based optimization and hence allows for end-to-end training. This
facilitates development and allows to use the full potential of a trainable
deep feature extractor. We show that it can be used as a novel building block
for explainable neural networks. We employ our Gaussian Prototype Layer in (1)
a model where prototypes are detected in the latent grid and (2) a model
inspired by Fast-RCNN with SLIC superpixels as region proposals. The earlier
achieves a similar performance as compared to the state-of-the art while the
latter has the benefit of a more precise prototype localization that comes at
the cost of slightly lower accuracies. By introducing a gradient-based GMM
layer we combine the benefits of end-to-end training with the simplicity and
theoretical foundation of GMMs which will allow to adapt existing
semi-supervised learning strategies for prototypical part models in future.
