You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Differentiable programming is able to combine different functions or programs in a processing pipeline with the goal of applying end-to-end learning or optimization. A significant impediment is the non-differentiable nature of some algorithms. We propose to use synthetic gradients (SG) to overcome this difficulty. SG uses the universal function approximation property of neural networks. We apply SG to combine convolutional neural network (CNN) with dynamic programming (DP) in end-to-end learning for segmenting left ventricle from short axis view of heart MRI. Our experiments show that end-to-end combination of CNN and DP requires fewer labeled images to achieve a significantly better segmentation accuracy than using only CNN.

Cited Abstract(s):
[1]: Abstract We introduce a new methodology that combines deep learning and level set for the automated segmentation of the left ventricle of the heart from cardiac cine magnetic resonance (MR) data. This combination is relevant for segmentation problems, where the visual object of interest presents large shape and appearance variations, but the annotated training set is small, which is the case for various medical image analysis applications, including the one considered in this paper. In particular, level set methods are based on shape and appearance terms that use small training sets, but present limitations for modelling the visual object variations. Deep learning methods can model such variations using relatively small amounts of annotated training, but they often need to be regularised to produce good generalisation. Therefore, the combination of these methods brings together the advantages of both approaches, producing a methodology that needs small training sets and produces accurate segmentation results. We test our methodology on the MICCAI 2009 left ventricle segmentation challenge database (containing 15 sequences for training, 15 for validation and 15 for testing), where our approach achieves the most accurate results in the semi-automated problem and state-of-the-art results for the fully automated challenge.
In this work, we present a complementary approach to work with limited amount of labeled images. Our guiding principle is to inject the learning system with prior knowledge about the solution. A similar argument was made by Ngo, Lu, and Carneiro [1] for combining level set and CNN to work with limited labeled data for left ventricle segmentation. For this segmentation task, the prior knowledge is a smooth shape, which can be modeled as a closed contour drawn through a star pattern. To inject such knowledge into the learning system, we resort to the principle of differentiable programming, where more than one differentiable algorithms are stitched together. However, the added difficulty in our case is the non-differentiable nature of DP that we overcome using SG.