55 research outputs found
Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging
Under mild conditions on the noise level of the measurements, rotation
averaging satisfies strong duality, which enables global solutions to be
obtained via semidefinite programming (SDP) relaxation. However, generic
solvers for SDP are rather slow in practice, even on rotation averaging
instances of moderate size, thus developing specialised algorithms is vital. In
this paper, we present a fast algorithm that achieves global optimality called
rotation coordinate descent (RCD). Unlike block coordinate descent (BCD) which
solves SDP by updating the semidefinite matrix in a row-by-row fashion, RCD
directly maintains and updates all valid rotations throughout the iterations.
This obviates the need to store a large dense semidefinite matrix. We
mathematically prove the convergence of our algorithm and empirically show its
superior efficiency over state-of-the-art global methods on a variety of
problem configurations. Maintaining valid rotations also facilitates
incorporating local optimisation routines for further speed-ups. Moreover, our
algorithm is simple to implement; see supplementary material for a
demonstration program.Comment: Accepted to CVPR 2021 as an oral presentatio
Linear Global Translation Estimation with Feature Tracks
This paper derives a novel linear position constraint for cameras seeing a
common scene point, which leads to a direct linear method for global camera
translation estimation. Unlike previous solutions, this method deals with
collinear camera motion and weak image association at the same time. The final
linear formulation does not involve the coordinates of scene points, which
makes it efficient even for large scale data. We solve the linear equation
based on norm, which makes our system more robust to outliers in
essential matrices and feature correspondences. We experiment this method on
both sequentially captured images and unordered Internet images. The
experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3.
Move "Evaluation on synthetic data" out to supplementary file; 4. Divide
subsection "Evaluation on general data" to subsections "Experiment on
sequential data" and "Experiment on unordered Internet data"; 5. Change Fig.
1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some
symbols; 8. Correct some typo
Rotation Averaging and Strong Duality
In this paper we explore the role of duality principles within the problem of
rotation averaging, a fundamental task in a wide range of computer vision
applications. In its conventional form, rotation averaging is stated as a
minimization over multiple rotation constraints. As these constraints are
non-convex, this problem is generally considered challenging to solve globally.
We show how to circumvent this difficulty through the use of Lagrangian
duality. While such an approach is well-known it is normally not guaranteed to
provide a tight relaxation. Based on spectral graph theory, we analytically
prove that in many cases there is no duality gap unless the noise levels are
severe. This allows us to obtain certifiably global solutions to a class of
important non-convex problems in polynomial time.
We also propose an efficient, scalable algorithm that out-performs general
purpose numerical solvers and is able to handle the large problem instances
commonly occurring in structure from motion settings. The potential of this
proposed method is demonstrated on a number of different problems, consisting
of both synthetic and real-world data
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
Robust Camera Location Estimation by Convex Programming
D structure recovery from a collection of D images requires the
estimation of the camera locations and orientations, i.e. the camera motion.
For large, irregular collections of images, existing methods for the location
estimation part, which can be formulated as the inverse problem of estimating
locations in
from noisy measurements of a subset of the pairwise directions
, are
sensitive to outliers in direction measurements. In this paper, we firstly
provide a complete characterization of well-posed instances of the location
estimation problem, by presenting its relation to the existing theory of
parallel rigidity. For robust estimation of camera locations, we introduce a
two-step approach, comprised of a pairwise direction estimation method robust
to outliers in point correspondences between image pairs, and a convex program
to maintain robustness to outlier directions. In the presence of partially
corrupted measurements, we empirically demonstrate that our convex formulation
can even recover the locations exactly. Lastly, we demonstrate the utility of
our formulations through experiments on Internet photo collections.Comment: 10 pages, 6 figures, 3 table
GraphMatch: Efficient Large-Scale Graph Construction for Structure from Motion
We present GraphMatch, an approximate yet efficient method for building the
matching graph for large-scale structure-from-motion (SfM) pipelines. Unlike
modern SfM pipelines that use vocabulary (Voc.) trees to quickly build the
matching graph and avoid a costly brute-force search of matching image pairs,
GraphMatch does not require an expensive offline pre-processing phase to
construct a Voc. tree. Instead, GraphMatch leverages two priors that can
predict which image pairs are likely to match, thereby making the matching
process for SfM much more efficient. The first is a score computed from the
distance between the Fisher vectors of any two images. The second prior is
based on the graph distance between vertices in the underlying matching graph.
GraphMatch combines these two priors into an iterative "sample-and-propagate"
scheme similar to the PatchMatch algorithm. Its sampling stage uses Fisher
similarity priors to guide the search for matching image pairs, while its
propagation stage explores neighbors of matched pairs to find new ones with a
high image similarity score. Our experiments show that GraphMatch finds the
most image pairs as compared to competing, approximate methods while at the
same time being the most efficient.Comment: Published at IEEE 3DV 201
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