305 research outputs found
Accelerating Globally Optimal Consensus Maximization in Geometric Vision
Branch-and-bound-based consensus maximization stands out due to its important
ability of retrieving the globally optimal solution to outlier-affected
geometric problems. However, while the discovery of such solutions caries high
scientific value, its application in practical scenarios is often prohibited by
its computational complexity growing exponentially as a function of the
dimensionality of the problem at hand. In this work, we convey a novel, general
technique that allows us to branch over an dimensional space for an
n-dimensional problem. The remaining degree of freedom can be solved globally
optimally within each bound calculation by applying the efficient interval
stabbing technique. While each individual bound derivation is harder to compute
owing to the additional need for solving a sorting problem, the reduced number
of intervals and tighter bounds in practice lead to a significant reduction in
the overall number of required iterations. Besides an abstract introduction of
the approach, we present applications to three fundamental geometric computer
vision problems: camera resectioning, relative camera pose estimation, and
point set registration. Through our exhaustive tests, we demonstrate
significant speed-up factors at times exceeding two orders of magnitude,
thereby increasing the viability of globally optimal consensus maximizers in
online application scenarios
New algorithmic developments in maximum consensus robust fitting
In many computer vision applications, the task of robustly estimating the set of parameters of
a geometric model is a fundamental problem. Despite the longstanding research efforts on robust
model fitting, there remains significant scope for investigation. For a large number of geometric
estimation tasks in computer vision, maximum consensus is the most popular robust fitting
criterion. This thesis makes several contributions in the algorithms for consensus maximization.
Randomized hypothesize-and-verify algorithms are arguably the most widely used class of
techniques for robust estimation thanks to their simplicity. Though efficient, these randomized
heuristic methods do not guarantee finding good maximum consensus estimates. To improve the
randomize algorithms, guided sampling approaches have been developed. These methods take
advantage of additional domain information, such as descriptor matching scores, to guide the
sampling process. Subsets of the data that are more likely to result in good estimates are prioritized
for consideration. However, these guided sampling approaches are ineffective when good
domain information is not available. This thesis tackles this shortcoming by proposing a new
guided sampling algorithm, which is based on the class of LP-type problems and Monte Carlo
Tree Search (MCTS). The proposed algorithm relies on a fundamental geometric arrangement
of the data to guide the sampling process. Specifically, we take advantage of the underlying tree
structure of the maximum consensus problem and apply MCTS to efficiently search the tree.
Empirical results show that the new guided sampling strategy outperforms traditional randomized
methods.
Consensus maximization also plays a key role in robust point set registration. A special case
is the registration of deformable shapes. If the surfaces have the same intrinsic shapes, their
deformations can be described accurately by a conformal model. The uniformization theorem
allows the shapes to be conformally mapped onto a canonical domain, wherein the shapes can be
aligned using a M¨obius transformation. The problem of correspondence-free M¨obius alignment
of two sets of noisy and partially overlapping point sets can be tackled as a maximum consensus
problem. Solving for the M¨obius transformation can be approached by randomized voting-type
methods which offers no guarantee of optimality. Local methods such as Iterative Closest Point
can be applied, but with the assumption that a good initialization is given or these techniques
may converge to a bad local minima. When a globally optimal solution is required, the literature
has so far considered only brute-force search. This thesis contributes a new branch-and-bound
algorithm that solves for the globally optimal M¨obius transformation much more efficiently.
So far, the consensus maximization problems are approached mainly by randomized algorithms,
which are efficient but offer no analytical convergence guarantee. On the other hand,
there exist exact algorithms that can solve the problem up to global optimality. The global methods,
however, are intractable in general due to the NP-hardness of the consensus maximization. To fill the gap between the two extremes, this thesis contributes two novel deterministic algorithms
to approximately optimize the maximum consensus criterion. The first method is based
on non-smooth penalization supported by a Frank-Wolfe-style optimization scheme, and another
algorithm is based on Alternating Direction Method of Multipliers (ADMM). Both of the
proposed methods are capable of handling the non-linear geometric residuals commonly used in
computer vision. As will be demonstrated, our proposed methods consistently outperform other
heuristics and approximate methods.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 201
Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior
Point cloud registration is challenging in the presence of heavy outlier
correspondences. This paper focuses on addressing the robust
correspondence-based registration problem with gravity prior that often arises
in practice. The gravity directions are typically obtained by inertial
measurement units (IMUs) and can reduce the degree of freedom (DOF) of rotation
from 3 to 1. We propose a novel transformation decoupling strategy by
leveraging screw theory. This strategy decomposes the original 4-DOF problem
into three sub-problems with 1-DOF, 2-DOF, and 1-DOF, respectively, thereby
enhancing the computation efficiency. Specifically, the first 1-DOF represents
the translation along the rotation axis and we propose an interval
stabbing-based method to solve it. The second 2-DOF represents the pole which
is an auxiliary variable in screw theory and we utilize a branch-and-bound
method to solve it. The last 1-DOF represents the rotation angle and we propose
a global voting method for its estimation. The proposed method sequentially
solves three consensus maximization sub-problems, leading to efficient and
deterministic registration. In particular, it can even handle the
correspondence-free registration problem due to its significant robustness.
Extensive experiments on both synthetic and real-world datasets demonstrate
that our method is more efficient and robust than state-of-the-art methods,
even when dealing with outlier rates exceeding 99%
Approximate least trimmed sum of squares fitting and applications in image analysis
The least trimmed sum of squares (LTS) regression estimation criterion is a robust statistical method for model fitting in the presence of outliers. Compared with the classical least squares estimator, which uses the entire data set for regression and is consequently sensitive to outliers, LTS identifies the outliers and fits to the remaining data points for improved accuracy. Exactly solving an LTS problem is NP-hard, but as we show here, LTS can be formulated as a concave minimization problem. Since it is usually tractable to globally solve a convex minimization or concave maximization problem in polynomial time, inspired by [1], we instead solve LTS’ approximate complementary problem, which is convex minimization. We show that this complementary problem can be efficiently solved as a second order cone program. We thus propose an iterative procedure to approximately solve the original LTS problem. Our extensive experiments demonstrate that the proposed method is robust, efficient and scalable in dealing with problems where data are contaminated with outliers. We show several applications of our method in image analysis.Fumin Shen, Chunhua Shen, Anton van den Hengel and Zhenmin Tan
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