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Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Publications associées (32)

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Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

Projective transformations of structural equilibrium

Corentin Jean Dominique Fivet

Direct methods that transform the geometry of a structure and conserve its static equilibrium are of particular interest for designers. They allow the exploration of alternative solutions at minimum computational cost. While parallel transformations (stret ...

2016

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Martin Vetterli, Ivan Dokmanic, Juri Ranieri, Reza Parhizkar

Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireles ...

2015

A central theme of this thesis is using echoes to achieve useful, interesting, and sometimes surprising results. One should have no doubts about the echoes' constructive potential; it is, after all, demonstrated masterfully by Nature. Just think about the ...

EPFL2015

Relax and Unfold: Microphone Localization with Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Juri Ranieri

Recent methods for localization of microphones in a microphone array exploit sound sources at a priori unknown locations. This is convenient for ad-hoc arrays, as it requires little additional infrastructure. We propose a flexible localization algorithm by ...

2015

Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees

Hervé Bourlard, Philip Neil Garner, Afsaneh Asaei, Mohammadjavad Taghizadeh, Reza Parhizkar

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between the microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing ...

2015

While the question of the specification of spatial weight matrix is now largely discussed in the spatial econometrics literature, the definition of distance has attracted less attention. The choice of the distance measure is often glossed over, with the ul ...

2014

Theoretical Analysis of Euclidean Distance Matrix Completion for Ad hoc Microphone Array Calibration

Mohammadjavad Taghizadeh

We consider the problem of ad~hoc microphone array calibration where the distance matrix consisted of all microphones pairwise distances have entries missing corresponding to distances greater than

d_{\text{max}}

. Furthermore, the known entries are noisy ...

Idiap2014

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Because of their low weight, cost and energy consumption, optic-flow sensors attract growing interest in robotics for tasks such as self-motion estimation or depth measurement. Most applications require a large number of these sensors, which involves a fai ...

IEEE2012

The construction of low-dimensional models explaining high-dimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by in-plane geometric transformation ...

2011

Theoretical Analysis of Euclidean Distance Matrix Completion for Ad hoc Microphone Array Calibration

Mohammadjavad Taghizadeh

We consider the problem of ad~hoc microphone array calibration where the distance matrix consisted of all microphones pairwise distances have entries missing corresponding to distances greater than

d_{\text{max}}

. Furthermore, the known entries are noisy ...

Idiap2014