Results 1  10
of
48
Square Root SAM: Simultaneous localization and mapping via square root information smoothing
, 2006
"... Solving the SLAM (simultaneous localization and mapping) problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. Smoothing approaches have been investigated as a viable alternative to extended Kalman filter (EKF)based solutions to the problem. In parti ..."
Abstract

Cited by 142 (38 self)
 Add to MetaCart
(Show Context)
Solving the SLAM (simultaneous localization and mapping) problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. Smoothing approaches have been investigated as a viable alternative to extended Kalman filter (EKF)based solutions to the problem. In particular, approaches have been looked at that factorize either the associated information matrix or the measurement Jacobian into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact; they can be used in either batch or incremental mode; are better equipped to deal with nonlinear process and measurement models; and yield the entire robot trajectory, at lower cost for a large class of SLAM problems. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. This paper presents the theory underlying these methods, along with an interpretation of factorization in terms of the graphical model associated with the SLAM problem. Both simulation results and actual SLAM experiments in largescale environments are presented that underscore the potential of these methods as an alternative to EKFbased approaches.
Algorithm 887: Cholmod, supernodal sparse cholesky factorization and update/downdate
 ACM Transactions on Mathematical Software
, 2008
"... CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for b ..."
Abstract

Cited by 107 (8 self)
 Add to MetaCart
CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB TM interfaces. It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions.
Design of tangent vector fields
 ACM Trans. Graph
, 2007
"... Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and nonphotorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of ..."
Abstract

Cited by 62 (4 self)
 Add to MetaCart
(Show Context)
Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and nonphotorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of userprovided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1forms), we obtain an intrinsic, coordinatefree formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient prefactorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.
A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations
, 2005
"... ..."
Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
 ACM Trans. Math. Software
, 2006
"... The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorizatio ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
(Show Context)
The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a lowrank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLASbased) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MATLAB when A is sparse and symmetric positive definite. 1
Row modifications of a sparse Cholesky factorization
 SIAM J. Matrix Anal. Appl
, 2005
"... Abstract. Given a sparse, symmetric positive definite matrix C and an associated sparse Cholesky factorization LDLT, we develop sparse techniques for updating the factorization after a symmetric modification of a row and column of C. We show how the modification in the Cholesky factorization associa ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
(Show Context)
Abstract. Given a sparse, symmetric positive definite matrix C and an associated sparse Cholesky factorization LDLT, we develop sparse techniques for updating the factorization after a symmetric modification of a row and column of C. We show how the modification in the Cholesky factorization associated with this rank2 modification of C can be computed efficiently using a sparse rank1 technique developed in an earlier paper [SIAM J. Matrix Anal. Appl., 20 (1999), pp. 606627]. We also determine how the solution of a linear system Lx = b changes after changing a row and column of C or after a rankr change in C.
Algorithm 8xx: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate
, 2006
"... ..."
(Show Context)
Multifrontal multithreaded rankrevealing sparse QR factorization
"... SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
(Show Context)
SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase preeliminates singletons by permuting the input matrix into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fillreducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of A T A. Rankdetection is performed within each frontal matrix using Heath’s method, which does not require column pivoting. The resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.
Deformationbased Loop Closure for Large Scale Dense RGBD SLAM
"... Abstract — In this paper we present a system for capturing large scale dense maps in an online setting with a low cost RGBD sensor. Central to this work is the use of an “asrigidaspossible” space deformation for efficient dense map correction in a pose graph optimisation framework. By combining p ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
(Show Context)
Abstract — In this paper we present a system for capturing large scale dense maps in an online setting with a low cost RGBD sensor. Central to this work is the use of an “asrigidaspossible” space deformation for efficient dense map correction in a pose graph optimisation framework. By combining pose graph optimisation with nonrigid deformation of a dense map we are able to obtain highly accurate dense maps over large scale trajectories that are both locally and globally consistent. With low latency in mind we derive an incremental method for deformation graph construction, allowing multimillion point maps to be captured over hundreds of metres in realtime. We provide benchmark results on a well established RGBD SLAM dataset demonstrating the accuracy of the system and also provide a number of our own datasets which cover a wide range of environments, both indoors, outdoors and across multiple floors. I.