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The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves.…
We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares…
It is well-known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not depend on the size or shape of the filter. These fast algorithms are generally referred to as constant-time or…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…
We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…
The network flow optimization approach is offered for Bayesian segmentation of gray-scale and color images. It is supposed image pixels are characterized by a feature function taking finite number of arbitrary rational values (it can be…
Deep Neural Networks now excel at image classification, detection and segmentation. When used to scan images by means of a sliding window, however, their high computational complexity can bring even the most powerful hardware to its knees.…
We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on…
Deep Convolutional Neural Networks (DCNNs) commonly use generic `max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic convolution as a building…
Convolutions are the fundamental building block of CNNs. The fact that their weights are spatially shared is one of the main reasons for their widespread use, but it also is a major limitation, as it makes convolutions content agnostic. We…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
Because of the powerful learning capability of deep neural networks, counting performance via density map estimation has improved significantly during the past several years. However, it is still very challenging due to severe occlusion,…
Existing deep convolutional neural networks (CNNs) require a fixed-size (e.g., 224x224) input image. This requirement is "artificial" and may reduce the recognition accuracy for the images or sub-images of an arbitrary size/scale. In this…
This paper introduces versatile filters to construct efficient convolutional neural networks that are widely used in various visual recognition tasks. Considering the demands of efficient deep learning techniques running on cost-effective…
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear…
Partitioning an image into superpixels based on the similarity of pixels with respect to features such as colour or spatial location can significantly reduce data complexity and improve subsequent image processing tasks. Initial algorithms…