43 research outputs found
L1-rotation averaging using the Weiszfeld algorithm
We consider the problem of rotation averaging under the L1 norm. This problem is related to the classic Fermat-Weber problem for finding the geometric median of a set of points in IRn. We apply the classical Weiszfeld algorithm to this problem, adapting it iteratively in tangent spaces of SO(3) to obtain a provably convergent algorithm for finding the L1 mean. This results in an extremely simple and rapid averaging algorithm, without the need for line search. The choice of L1 mean (also called geometric median) is motivated by its greater robustness compared with rotation averaging under the L2 norm (the usual averaging process). We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global L1 optimum) and multiple rotation averaging (for which no such proof exists). The algorithm is demonstrated to give markedly improved results, compared with L2 averaging. We achieve a median rotation error of 0.82 degrees on the 595 images of the Notre Dame image set
Dilated FCN for Multi-Agent 2D/3D Medical Image Registration
2D/3D image registration to align a 3D volume and 2D X-ray images is a
challenging problem due to its ill-posed nature and various artifacts presented
in 2D X-ray images. In this paper, we propose a multi-agent system with an auto
attention mechanism for robust and efficient 2D/3D image registration.
Specifically, an individual agent is trained with dilated Fully Convolutional
Network (FCN) to perform registration in a Markov Decision Process (MDP) by
observing a local region, and the final action is then taken based on the
proposals from multiple agents and weighted by their corresponding confidence
levels. The contributions of this paper are threefold. First, we formulate
2D/3D registration as a MDP with observations, actions, and rewards properly
defined with respect to X-ray imaging systems. Second, to handle various
artifacts in 2D X-ray images, multiple local agents are employed efficiently
via FCN-based structures, and an auto attention mechanism is proposed to favor
the proposals from regions with more reliable visual cues. Third, a dilated
FCN-based training mechanism is proposed to significantly reduce the Degree of
Freedom in the simulation of registration environment, and drastically improve
training efficiency by an order of magnitude compared to standard CNN-based
training method. We demonstrate that the proposed method achieves high
robustness on both spine cone beam Computed Tomography data with a low
signal-to-noise ratio and data from minimally invasive spine surgery where
severe image artifacts and occlusions are presented due to metal screws and
guide wires, outperforming other state-of-the-art methods (single agent-based
and optimization-based) by a large margin.Comment: AAAI 201
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
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
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