Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of $SE(2)$ and $SE(3)$. Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of $SE(2)$ or $SE(3)$ - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.Comment: ICRA 2014 Preprin

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

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration.Comment: In Press, available online, August 1, 2014. http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal Processing, 201

Computational limitations of model based recognition

Includes bibliographical references (p. 13-14).Cover title.Research supported by the U.S. Army Research Office. DAAL03-86-K-0171 Research supported by the Office of Naval Research under an Air Force Contract. F196128-90-C-0002Haim Shvaytser (Schweitzer), Sanjeev R. Kulkarni

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

OA-SLAM: Leveraging Objects for Camera Relocalization in Visual SLAM

In this work, we explore the use of objects in Simultaneous Localization and Mapping in unseen worlds and propose an object-aided system (OA-SLAM). More precisely, we show that, compared to low-level points, the major benefit of objects lies in their higher-level semantic and discriminating power. Points, on the contrary, have a better spatial localization accuracy than the generic coarse models used to represent objects (cuboid or ellipsoid). We show that combining points and objects is of great interest to address the problem of camera pose recovery. Our main contributions are: (1) we improve the relocalization ability of a SLAM system using high-level object landmarks; (2) we build an automatic system, capable of identifying, tracking and reconstructing objects with 3D ellipsoids; (3) we show that object-based localization can be used to reinitialize or resume camera tracking. Our fully automatic system allows on-the-fly object mapping and enhanced pose tracking recovery, which we think, can significantly benefit to the AR community. Our experiments show that the camera can be relocalized from viewpoints where classical methods fail. We demonstrate that this localization allows a SLAM system to continue working despite a tracking loss, which can happen frequently with an uninitiated user. Our code and test data are released at gitlab.inria.fr/tangram/oa-slam.Comment: ISMAR 202

Stable Camera Motion Estimation Using Convex Programming

We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy measurements of $\pm (t_i - t_j)/\|t_i - t_j\|$ for some pairs (i,j) (where the signs are unknown). This problem is at the core of the structure from motion (SfM) problem in computer vision, where the $t_i$'s represent camera locations in $R^3$. The noiseless version of the problem, with exact line measurements, has been considered previously under the general title of parallel rigidity theory, mainly in order to characterize the conditions for unique realization of locations. For noisy pairwise line measurements, current methods tend to produce spurious solutions that are clustered around a few locations. This sensitivity of the location estimates is a well-known problem in SfM, especially for large, irregular collections of images. In this paper we introduce a semidefinite programming (SDP) formulation, specially tailored to overcome the clustering phenomenon. We further identify the implications of parallel rigidity theory for the location estimation problem to be well-posed, and prove exact (in the noiseless case) and stable location recovery results. We also formulate an alternating direction method to solve the resulting semidefinite program, and provide a distributed version of our formulation for large numbers of locations. Specifically for the camera location estimation problem, we formulate a pairwise line estimation method based on robust camera orientation and subspace estimation. Lastly, we demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts updated, some typos correcte

NMDA-based pattern discrimination in a modeled cortical neuron

Compartmental simulations of an anatomically characterized cortical pyramidal cell were carried out to study the integrative behavior of a complex dendritic tree. Previous theoretical (Feldman and Ballard 1982; Durbin and Rumelhart 1989; Mel 1990; Mel and Koch 1990; Poggio and Girosi 1990) and compartmental modeling (Koch et al. 1983; Shepherd et al. 1985; Koch and Poggio 1987; Rall and Segev 1987; Shepherd and Brayton 1987; Shepherd et al. 1989; Brown et al. 1991) work had suggested that multiplicative interactions among groups of neighboring synapses could greatly enhance the processing power of a neuron relative to a unit with only a single global firing threshold. This issue was investigated here, with a particular focus on the role of voltage-dependent N-methyl-D-asparate (NMDA) channels in the generation of cell responses. First, it was found that when a large proportion of the excitatory synaptic input to dendritic spines is carried by NMDA channels, the pyramidal cell responds preferentially to spatially clustered, rather than random, distributions of activated synapses. Second, based on this mechanism, the NMDA-rich neuron is shown to be capable of solving a nonlinear pattern discrimination task. We propose that manipulation of the spatial ordering of afferent synaptic connections onto the dendritic arbor is a possible biological strategy for pattern information storage during learning

Robust and affordable localization and mapping for 3D reconstruction. Application to architecture and construction

La localización y mapeado simultáneo a partir de una sola cámara en movimiento se conoce como Monocular SLAM. En esta tesis se aborda este problema con cámaras de bajo coste cuyo principal reto consiste en ser robustos al ruido, blurring y otros artefactos que afectan a la imagen. La aproximación al problema es discreta, utilizando solo puntos de la imagen significativos para localizar la cámara y mapear el entorno. La principal contribución es una simplificación del grafo de poses que permite mejorar la precisión en las escenas más habituales, evaluada de forma exhaustiva en 4 datasets. Los resultados del mapeado permiten obtener una reconstrucción 3D de la escena que puede ser utilizada en arquitectura y construcción para Modelar la Información del Edificio (BIM). En la segunda parte de la tesis proponemos incorporar dicha información en un sistema de visualización avanzada usando WebGL que ayude a simplificar la implantación de la metodología BIM.Departamento de Informática (Arquitectura y Tecnología de Computadores, Ciencias de la Computación e Inteligencia Artificial, Lenguajes y Sistemas Informáticos)Doctorado en Informátic