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The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu-Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results., Comment: 58 pages, 23 figures

This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at least $C^2$-continuity, which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom., Comment: 44 pages, 36 figures

This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples., Comment: This document is the personal version of an article whose final publication is available at https://doi.org/10.1007/s00158-020-02803-0

An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space ${\Bbb R}^3$, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero stress conditions. Especially, the significance of considering correct surface loads rather than applying an equivalent load directly on the central axis is investigated. Incompatible linear in-plane strain components for the cross-section have been added to alleviate Poisson locking by using an enhanced assumed strain (EAS) method. In various numerical examples exhibiting large deformations, the accuracy and efficiency of the presented beam formulation is assessed in comparison to brick elements. We particularly use hyperelastic materials of the St. Venant-Kirchhoff and compressible Neo-Hookean types., Comment: 67 pages, 29 figures

The context of an image encapsulates rich information about how natural scenes and objects are related to each other. Such contextual information has the potential to enable a coherent understanding of natural scenes and images. However, context models have been evaluated mostly based on the improvement of object recognition performance even though it is only one of many ways to exploit contextual information. In this paper, we present a new scene understanding problem for evaluating and applying context models. We are interested in finding scenes and objects that are “out-of-context”. Detecting “out-of-context” objects and scenes is challenging because context violations can be detected only if the relationships between objects are carefully and precisely modeled. To address this problem, we evaluate different sources of context information, and present a graphical model that combines these sources. We show that physical support relationships between objects can provide useful contextual information for both object recognition and out-of-context detection.

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our algorithms can be applied to both discrete and Gaussian random variables and our learned models are such that all the observed and latent variables have the same domain (state space). Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures such as neighbor-joining) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world data sets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups data set.

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups. Our second and main algorithm, CLGrouping, starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step guides subsequent recursive grouping (or other latent-tree learning procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs.

There has been a growing interest in exploiting contextual information in addition to local features to detect and localize multiple object categories in an image. Context models can efficiently rule out some unlikely combinations or locations of objects and guide detectors to produce a semantically coherent interpretation of a scene. However, the performance benefit from using context models has been limited because most of these methods were tested on datasets with only a few object categories, in which most images contain only one or two object categories. In this paper, we introduce a new dataset with images that contain many instances of different object categories and propose an efficient model that captures the contextual information among more than a hundred of object categories. We show that our context model can be applied to scene understanding tasks that local detectors alone cannot solve., Shell International Exploration and Production, Inc, United States. Air Force Office of Scientific Research (award FA9550-06-1-0324)

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student submitted PDF version of thesis., Includes bibliographical references (p. 169-179)., Probabilistic models commonly assume that variables are independent of each other conditioned on a subset of other variables. Graphical models provide a powerful framework for encoding such conditional independence structure of a large collection of random variables. A special class of graphical models with significant theoretical and practical importance is the class of tree-structured graphical models. Tree models have several advantages: they can be easily learned given data, their structures are often intuitive, and inference in tree models is highly efficient. However, tree models make strong conditional independence assumptions, which limit their modeling power substantially. This thesis exploits the advantages of tree-structured graphical models and considers modifications to overcome their limitations. To improve the modeling accuracy of tree models, we consider latent trees in which variables at some nodes represent the original (observed) variables of interest while others represent the latent variables added during the learning procedure. The appeal of such models is clear: the additional latent variables significantly increase the modeling power, and inference on trees is scalable with or without latent variables. We propose two computationally efficient and statistically consistent algorithms for learning latent trees, and compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree models. We exploit the advantages of tree models in the application of modeling contextual information of an image. Object co-occurrences and spatial relationships can be important cues in recognizing and localizing object instances. We develop tree-based context models and demonstrate that its simplicity enables us to integrate many sources of contextual information efficiently. In addition to object recognition, we are interested in using context models to detect objects that are out of their normal context. This tas, by Myung Jin Choi., Ph.D.

We consider Gaussian multiresolution (MR) models in which coarser, hidden variables serve to capture statistical dependencies among the finest scale variables. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models that capture the residual correlations within each scale using sparse covariance structure. Our goal is to learn a tree-structured graphical model connecting variables across different scales, while at the same time learning sparse structure for the conditional covariance within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics., United States. Air Force Office of Scientific Research (Grant FA9550-08-1-1080), United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-06-1-0324), Shell International Exploration and Production B.V., Samsung Scholarship Foundation

In this paper, we consider the problem of learning Gaussian multiresolution (MR) models in which data are only available at the finest scale, and the coarser, hidden variables serve to capture long-distance dependencies. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models in which variables at each scale have sparse conditional covariance structure conditioned on other scales. Our goal is to learn a tree-structured graphical model connecting variables across scales (which translates into sparsity in inverse covariance), while at the same time learning sparse structure for the conditional covariance (not its inverse) within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics. We demonstrate the modeling and inference advantages of our approach over methods that use MR tree models and single-scale approximation methods that do not use hidden variables., United States. Air Force Office of Scientific Research (Grant FA9550-08-1-1080), Multidisciplinary University Research Initiative (MURI) (AFOSR Grant FA9550-06-1-0324), Shell International Exploration and Production, Inc

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset.

There has been a growing interest in exploiting contextual information in addition to local features to detect and localize multiple object categories in an image. A context model can rule out some unlikely combinations or locations of objects and guide detectors to produce a semantically coherent interpretation of a scene. However, the performance benefit of context models has been limited because most of the previous methods were tested on datasets with only a few object categories, in which most images contain one or two object categories. In this paper, we introduce a new dataset with images that contain many instances of different object categories, and propose an efficient model that captures the contextual information among more than a hundred object categories using a tree structure. Our model incorporates global image features, dependencies between object categories, and outputs of local detectors into one probabilistic framework. We demonstrate that our context model improves object recognition performance and provides a coherent interpretation of a scene, which enables a reliable image querying system by multiple object categories. In addition, our model can be applied to scene understanding tasks that local detectors alone cannot solve, such as detecting objects out of context or querying for the most typical and the least typicalscenes in a dataset., This research was partially funded by Shell International Exploration and Production Inc., by Army Research Office under award W911NF-06-1-0076, by NSF Career Award (ISI 0747120), and by the Air Force Office of Scientific Research under Award No.FA9550-06-1-0324. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Air Force.

There has been a growing interest in exploiting contextual information in addition to local features to detect and localize multiple object categories in an image. A context model can rule out some unlikely combinations or locations of objects and guide detectors to produce a semantically coherent interpretation of a scene. However, the performance benefit of context models has been limited because most of the previous methods were tested on datasets with only a few object categories, in which most images contain one or two object categories. In this paper, we introduce a new dataset with images that contain many instances of different object categories, and propose an efficient model that captures the contextual information among more than a hundred object categories using a tree structure. Our model incorporates global image features, dependencies between object categories, and outputs of local detectors into one probabilistic framework. We demonstrate that our context model improves object recognition performance and provides a coherent interpretation of a scene, which enables a reliable image querying system by multiple object categories. In addition, our model can be applied to scene understanding tasks that local detectors alone cannot solve, such as detecting objects out of context or querying for the most typical and the least typicalscenes in a dataset., This research was partially funded by Shell International Exploration and Production Inc., by Army Research Office under award W911NF-06-1-0076, by NSF Career Award (ISI 0747120), and by the Air Force Office of Scientific Research under Award No.FA9550-06-1-0324. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Air Force.

We consider Gaussian multiresolution (MR) models in which coarser, hidden variables serve to capture statistical dependencies among the finest scale variables. Tree-structured MR models have limited modeling capabilities, as variables at one scale are forced to be uncorrelated with each other conditioned on other scales. We propose a new class of Gaussian MR models that capture the residual correlations within each scale using sparse covariance structure. Our goal is to learn a tree-structured graphical model connecting variables across different scales, while at the same time learning sparse structure for the conditional covariance within each scale conditioned on other scales. This model leads to an efficient, new inference algorithm that is similar to multipole methods in computational physics.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007., Includes bibliographical references (p. 119-123)., Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long-range correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast algorithms in the spirit of multipole methods. The algorithms operate by guiding far-apart nodes to communicate through coarser scales and considering only local interactions at finer scales. The consistent stochastic structure of the pyramidal graph provides great flexibilities in designing and analyzing inference algorithms. Based on emerging techniques for inference on Gaussian graphical models, we propose several different inference algorithms to compute not only the optimal estimates but also approximate error variances as well. In addition, we consider the problem of rapidly updating the estimates based on some new local information, and develop a re-estimation algorithm on the pyramidal graph. Simulation results show that this algorithm can be applied to reconstruct discontinuities blurred during the estimation process or to update the estimates to incorporate a new set of measurements introduced in a local region., by Myung Jin Choi., S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007., Includes bibliographical references (p. 119-123)., Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long-range correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast algorithms in the spirit of multipole methods. The algorithms operate by guiding far-apart nodes to communicate through coarser scales and considering only local interactions at finer scales. The consistent stochastic structure of the pyramidal graph provides great flexibilities in designing and analyzing inference algorithms. Based on emerging techniques for inference on Gaussian graphical models, we propose several different inference algorithms to compute not only the optimal estimates but also approximate error variances as well. In addition, we consider the problem of rapidly updating the estimates based on some new local information, and develop a re-estimation algorithm on the pyramidal graph. Simulation results show that this algorithm can be applied to reconstruct discontinuities blurred during the estimation process or to update the estimates to incorporate a new set of measurements introduced in a local region., by Myung Jin Choi., S.M.