21,303 research outputs found
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
Harmonic Exponential Families on Manifolds
In a range of fields including the geosciences, molecular biology, robotics
and computer vision, one encounters problems that involve random variables on
manifolds. Currently, there is a lack of flexible probabilistic models on
manifolds that are fast and easy to train. We define an extremely flexible
class of exponential family distributions on manifolds such as the torus,
sphere, and rotation groups, and show that for these distributions the gradient
of the log-likelihood can be computed efficiently using a non-commutative
generalization of the Fast Fourier Transform (FFT). We discuss applications to
Bayesian camera motion estimation (where harmonic exponential families serve as
conjugate priors), and modelling of the spatial distribution of earthquakes on
the surface of the earth. Our experimental results show that harmonic densities
yield a significantly higher likelihood than the best competing method, while
being orders of magnitude faster to train.Comment: fixed typ
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
ShapeFit and ShapeKick for Robust, Scalable Structure from Motion
We introduce a new method for location recovery from pair-wise directions
that leverages an efficient convex program that comes with exact recovery
guarantees, even in the presence of adversarial outliers. When pairwise
directions represent scaled relative positions between pairs of views
(estimated for instance with epipolar geometry) our method can be used for
location recovery, that is the determination of relative pose up to a single
unknown scale. For this task, our method yields performance comparable to the
state-of-the-art with an order of magnitude speed-up. Our proposed numerical
framework is flexible in that it accommodates other approaches to location
recovery and can be used to speed up other methods. These properties are
demonstrated by extensively testing against state-of-the-art methods for
location recovery on 13 large, irregular collections of images of real scenes
in addition to simulated data with ground truth
A reliable order-statistics-based approximate nearest neighbor search algorithm
We propose a new algorithm for fast approximate nearest neighbor search based
on the properties of ordered vectors. Data vectors are classified based on the
index and sign of their largest components, thereby partitioning the space in a
number of cones centered in the origin. The query is itself classified, and the
search starts from the selected cone and proceeds to neighboring ones. Overall,
the proposed algorithm corresponds to locality sensitive hashing in the space
of directions, with hashing based on the order of components. Thanks to the
statistical features emerging through ordering, it deals very well with the
challenging case of unstructured data, and is a valuable building block for
more complex techniques dealing with structured data. Experiments on both
simulated and real-world data prove the proposed algorithm to provide a
state-of-the-art performance
- …