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]: Accurate segmentation of the heart is an important step towards evaluating cardiac function. In this paper, we present a fully automated framework for segmentation of the left (LV) and right (RV) ventricular cavities and the myocardium (Myo) on short-axis cardiac MR images. We investigate various 2D and 3D convolutional neural network architectures for this task. We investigate the suitability of various state-of-the art 2D and 3D convolutional neural network architectures, as well as slight modifications thereof, for this task. Experiments were performed on the ACDC 2017 challenge training dataset comprising cardiac MR images of 100 patients, where manual reference segmentations were made available for end-diastolic (ED) and end-systolic (ES) frames. We find that processing the images in a slice-by-slice fashion using 2D networks is beneficial due to a relatively large slice thickness. However, the exact network architecture only plays a minor role. We report mean Dice coefficients of @math (LV), @math (RV), and @math (Myo), respectively with an average evaluation time of 1.1 seconds per volume on a modern GPU.

[2]: In this paper, we present a novel convolutional neural network architecture to segment images from a series of short-axis cardiac magnetic resonance slices (CMRI). The proposed model is an extension of the U-net that embeds a cardiac shape prior and involves a loss function tailored to the cardiac anatomy. Since the shape prior is computed offline only once, the execution of our model is not limited by its calculation. Our system takes as input raw magnetic resonance images, requires no manual preprocessing or image cropping and is trained to segment the endocardium and epicardium of the left ventricle, the endocardium of the right ventricle, as well as the center of the left ventricle. With its multiresolution grid architecture, the network learns both high and low-level features useful to register the shape prior as well as accurately localize the borders of the cardiac regions. Experimental results obtained on the Automatic Cardiac Diagnostic Challenge - Medical Image Computing and Computer Assisted Intervention (ACDC-MICCAI) 2017 dataset show that our model segments multislices CMRI (left and right ventricle contours) in 0.18 s with an average Dice coefficient of @math and an average 3-D Hausdorff distance of @math mm.

[3]: Abstract The sequel to the popular lecture book entitled Biomedical Image Analysis: Tracking, this book on Biomedical Image Analysis: Segmentation tackles the challenging task of segmenting biological and medical images. The problem of partitioning multidimensional biomedical data into meaningful regions is perhaps the main roadblock in the automation of biomedical image analysis. Whether the modality of choice is MRI, PET, ultrasound, SPECT, CT, or one of a myriad of microscopy platforms, image segmentation is a vital step in analyzing the constituent biological or medical targets. This book provides a state-of-the-art, comprehensive look at biomedical image segmentation that is accessible to well-equipped undergraduates, graduate students, and research professionals in the biology, biomedical, medical, and engineering fields. Active model methods that have emerged in the last few years are a focus of the book, including parametric active contour and active surface models, active shape models, and geomet...
The left ventricle appears as a blob'' object in short axis MRI. Traditionally active contours and level set based methods were used for blob object segmentation [3] . While these methods offer object shape constraints, they typically look for strong edges or statistical modeling for successful segmentation. These techniques lack a way to work with labeled images in a supervised machine learning framework. For complex segmentation tasks, such as cardiac MRI segmentation [1] these methods are inadequate. Deep learning (DL) has invigorated interest for these classic techniques in the recent years, including our present work, because starting from raw pixels DL can be trained end-to-end with labeled images. With the exception of limited literature, such as shape prior CNN [2] , DL lacks any inherent mechanism to incorporate prior knowledge about object shapes; instead, DL relies on the volume of labeled images to implicitly learn about object shapes or constraints. Hence, there is a need to combine CNN with these traditional methods so that the latter can provide adequate prior knowledge.