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:
We present an end-to-end learned algorithm for seeded segmentation. Our method is based on the Random Walker algorithm, where we predict the edge weights of the underlying graph using a convolutional neural network. This can be interpreted as learning context-dependent diffusivities for a linear diffusion process. Besides calculating the exact gradient for optimizing these diffusivities, we also propose simplifications that sparsely sample the gradient and still yield competitive results. The proposed method achieves the currently best results on a seeded version of the CREMI neuron segmentation challenge.

Cited Abstract(s):
[1]: After a decade of rapid progress in image denoising, recent methods seem to have reached a performance limit. Nonetheless, we find that state-of-the-art denoising methods are visually clearly distinguishable and possess complementary strengths and failure modes. Motivated by this observation, we introduce a powerful non-parametric image restoration framework based on Regression Tree Fields (RTF). Our restoration model is a densely-connected tractable conditional random field that leverages existing methods to produce an image-dependent, globally consistent prediction. We estimate the conditional structure and parameters of our model from training data so as to directly optimize for popular performance measures. In terms of peak signal-to-noise-ratio (PSNR), our model improves on the best published denoising method by at least 0.26dB across a range of noise levels. Our most practical variant still yields statistically significant improvements, yet is over 20× faster than the strongest competitor. Our approach is well-suited for many more image restoration and low-level vision problems, as evidenced by substantial gains in tasks such as removal of JPEG blocking artefacts.
[1] have pioneered the use of flexible nonparametric classifiers to determine the potentials in a Conditional GMRF. However, they opted for ensembles of decision trees and had to estimate the impact of each possible split on the loss function, making a number of approximations necessary.