9,822 research outputs found
A Spectral Learning Approach to Range-Only SLAM
We present a novel spectral learning algorithm for simultaneous localization
and mapping (SLAM) from range data with known correspondences. This algorithm
is an instance of a general spectral system identification framework, from
which it inherits several desirable properties, including statistical
consistency and no local optima. Compared with popular batch optimization or
multiple-hypothesis tracking (MHT) methods for range-only SLAM, our spectral
approach offers guaranteed low computational requirements and good tracking
performance. Compared with popular extended Kalman filter (EKF) or extended
information filter (EIF) approaches, and many MHT ones, our approach does not
need to linearize a transition or measurement model; such linearizations can
cause severe errors in EKFs and EIFs, and to a lesser extent MHT, particularly
for the highly non-Gaussian posteriors encountered in range-only SLAM. We
provide a theoretical analysis of our method, including finite-sample error
bounds. Finally, we demonstrate on a real-world robotic SLAM problem that our
algorithm is not only theoretically justified, but works well in practice: in a
comparison of multiple methods, the lowest errors come from a combination of
our algorithm with batch optimization, but our method alone produces nearly as
good a result at far lower computational cost
A Collaborative Kalman Filter for Time-Evolving Dyadic Processes
We present the collaborative Kalman filter (CKF), a dynamic model for
collaborative filtering and related factorization models. Using the matrix
factorization approach to collaborative filtering, the CKF accounts for time
evolution by modeling each low-dimensional latent embedding as a
multidimensional Brownian motion. Each observation is a random variable whose
distribution is parameterized by the dot product of the relevant Brownian
motions at that moment in time. This is naturally interpreted as a Kalman
filter with multiple interacting state space vectors. We also present a method
for learning a dynamically evolving drift parameter for each location by
modeling it as a geometric Brownian motion. We handle posterior intractability
via a mean-field variational approximation, which also preserves tractability
for downstream calculations in a manner similar to the Kalman filter. We
evaluate the model on several large datasets, providing quantitative evaluation
on the 10 million Movielens and 100 million Netflix datasets and qualitative
evaluation on a set of 39 million stock returns divided across roughly 6,500
companies from the years 1962-2014.Comment: Appeared at 2014 IEEE International Conference on Data Mining (ICDM
Inverse, forward and other dynamic computations computationally optimized with sparse matrix factorizations
We propose an algorithm to compute the dynamics of articulated rigid-bodies
with different sensor distributions. Prior to the on-line computations, the
proposed algorithm performs an off-line optimisation step to simplify the
computational complexity of the underlying solution. This optimisation step
consists in formulating the dynamic computations as a system of linear
equations. The computational complexity of computing the associated solution is
reduced by performing a permuted LU-factorisation with off-line optimised
permutations. We apply our algorithm to solve classical dynamic problems:
inverse and forward dynamics. The computational complexity of the proposed
solution is compared to `gold standard' algorithms: recursive Newton-Euler and
articulated body algorithm. It is shown that our algorithm reduces the number
of floating point operations with respect to previous approaches. We also
evaluate the numerical complexity of our algorithm by performing tests on
dynamic computations for which no gold standard is available.Comment: 8 pages, 2 figure, conference RCAR 201
GSLAM: Initialization-robust Monocular Visual SLAM via Global Structure-from-Motion
Many monocular visual SLAM algorithms are derived from incremental
structure-from-motion (SfM) methods. This work proposes a novel monocular SLAM
method which integrates recent advances made in global SfM. In particular, we
present two main contributions to visual SLAM. First, we solve the visual
odometry problem by a novel rank-1 matrix factorization technique which is more
robust to the errors in map initialization. Second, we adopt a recent global
SfM method for the pose-graph optimization, which leads to a multi-stage linear
formulation and enables L1 optimization for better robustness to false loops.
The combination of these two approaches generates more robust reconstruction
and is significantly faster (4X) than recent state-of-the-art SLAM systems. We
also present a new dataset recorded with ground truth camera motion in a Vicon
motion capture room, and compare our method to prior systems on it and
established benchmark datasets.Comment: 3DV 2017 Project Page: https://frobelbest.github.io/gsla
The Incremental Multiresolution Matrix Factorization Algorithm
Multiresolution analysis and matrix factorization are foundational tools in
computer vision. In this work, we study the interface between these two
distinct topics and obtain techniques to uncover hierarchical block structure
in symmetric matrices -- an important aspect in the success of many vision
problems. Our new algorithm, the incremental multiresolution matrix
factorization, uncovers such structure one feature at a time, and hence scales
well to large matrices. We describe how this multiscale analysis goes much
farther than what a direct global factorization of the data can identify. We
evaluate the efficacy of the resulting factorizations for relative leveraging
within regression tasks using medical imaging data. We also use the
factorization on representations learned by popular deep networks, providing
evidence of their ability to infer semantic relationships even when they are
not explicitly trained to do so. We show that this algorithm can be used as an
exploratory tool to improve the network architecture, and within numerous other
settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page
A factorization approach to inertial affine structure from motion
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives
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