  The recent emergence of deep learning has led to a great deal of work on
designing supervised deep semantic segmentation algorithms. As in many tasks
sufficient pixel-level labels are very difficult to obtain, we propose a method
which combines a Gaussian mixture model (GMM) with unsupervised deep learning
techniques. In the standard GMM the pixel values with each sub-region are
modelled by a Gaussian distribution. In order to identify the different
regions, the parameter vector that minimizes the negative log-likelihood (NLL)
function regarding the GMM has to be approximated. For this task, usually
iterative optimization methods such as the expectation-maximization (EM)
algorithm are used. In this paper, we propose to estimate these parameters
directly from the image using a convolutional neural network (CNN). We thus
change the iterative procedure in the EM algorithm replacing the
expectation-step by a gradient-step with regard to the networks parameters.
This means that the network is trained to minimize the NLL function of the GMM
which comes with at least two advantages. As once trained, the network is able
to predict label probabilities very quickly compared with time consuming
iterative optimization methods. Secondly, due to the deep image prior our
method is able to partially overcome one of the main disadvantages of GMM,
which is not taking into account correlation between neighboring pixels, as it
assumes independence between them. We demonstrate the advantages of our method
in various experiments on the example of myocardial infarct segmentation on
multi-sequence MRI images.
