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One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
Reconstruction of geometric structures from images using supervised learning suffers from limited available amount of accurate data. One type of such data is accurate real-world RGB-D images. A major challenge in acquiring such ground truth…
We study array imaging of a sparse scene of point-like sources or scatterers in a homogeneous medium. For source imaging the sensors in the array are receivers that collect measurements of the wave field. For imaging scatterers the array…
Bio-image analysis is challenging due to inhomogeneous intensity distributions and high levels of noise in the images. Bayesian inference provides a principled way for regularizing the problem using prior knowledge. A fundamental choice is…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of…
We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…
This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is…
We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…
State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
In this paper a hierarchical model for pixel clustering and image segmentation is developed. In the model an image is hierarchically structured. The original image is treated as a set of nested images, which are capable to reversibly merge…