In Non-Local Means (NLM), each pixel is denoised by performing a weighted averaging of its neighboring pixels, where the weights are computed using image patches. We demonstrate that the denoising performance of NLM can be improved by pruning the neighboring pixels, namely, by rejecting neighboring pixels whose weights are below a certain threshold λ. While pruning can potentially reduce pixel ...

Pseudo-likelihood and contrastive divergence are two well-known examples of contrastive methods. These algorithms trade off the probability of the correct label with the probabilities of other “nearby” instantiations. In this paper we explore more general types of contrastive objectives, which trade off the probability of the correct label against an arbitrary set of other instantiations. We pr...

This article introduces a new image segmentation method that makes use of non-local comparisons between pairs of patches of features. A non-local energy is defined by summing the interactions between pairs of patches inside and outside the segmented domain. A maximum radius of interaction can be adapted to fit the amount of variation of the features inside and outside the region to segment. Thi...

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quan...

Both convolutional and recurrent operations are building blocks that process one local neighborhood at a time. In this paper, we present non-local operations as a generic family of building blocks for capturing long-range dependencies. Inspired by the classical non-local means method [4] in computer vision, our non-local operation computes the response at a position as a weighted sum of the fea...

In applications to spatial structure in biology and to the theory of phase transition, it has proved useful to generalize the idea of diffusion to a non-local dispersal with an integral operator replacing the Laplacian. We study the spectral problem for the linear scalar equation ut(x, t) = ∫ Ω K(x, y)u(y, t)dy+ h(x, t)u(x, t), and tackle the extra technical difficulties arising because of the ...