49 research outputs found
Consensus Maximization: Theoretical Analysis and New Algorithms
The core of many computer vision systems is model fitting, which estimates a particular mathematical model given a set of input data. Due to the imperfection of the sensors, pre-processing steps and/or model assumptions, computer vision data usually contains outliers, which are abnormally distributed data points that can heavily reduce the accuracy of conventional model fitting methods. Robust fitting aims to make model fitting insensitive to outliers. Consensus maximization is one of the most popular paradigms for robust fitting, which is the main research subject of this thesis. Mathematically, consensus maximization is an optimization problem. To understand the theoretical hardness of this problem, a thorough analysis about its computational complexity is first conducted. Motivated by the theoretical analysis, novel techniques that improve different types of algorithms are then introduced. On one hand, an efficient and deterministic optimization approach is proposed. Unlike previous deterministic approaches, the proposed one does not rely on the relaxation of the original optimization problem. This property makes it much more effective at refining an initial solution. On the other hand, several techniques are proposed to significantly accelerate consensus maximization tree search. Tree search is one of the most efficient global optimization approaches for consensus maximization. Hence, the proposed techniques greatly improve the practicality of globally optimal consensus maximization algorithms. Finally, a consensus-maximization-based method is proposed to register terrestrial LiDAR point clouds. It demonstrates how to surpass the general theoretical hardness by using special problem structure (the rotation axis returned by the sensors), which simplify the problem and lead to application-oriented algorithms that are both efficient and globally optimal.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 202
Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior
In this work we address the problem of solving ill-posed inverse problems in
imaging where the prior is a variational autoencoder (VAE). Specifically we
consider the decoupled case where the prior is trained once and can be reused
for many different log-concave degradation models without retraining. Whereas
previous MAP-based approaches to this problem lead to highly non-convex
optimization algorithms, our approach computes the joint (space-latent) MAP
that naturally leads to alternate optimization algorithms and to the use of a
stochastic encoder to accelerate computations. The resulting technique (JPMAP)
performs Joint Posterior Maximization using an Autoencoding Prior. We show
theoretical and experimental evidence that the proposed objective function is
quite close to bi-convex. Indeed it satisfies a weak bi-convexity property
which is sufficient to guarantee that our optimization scheme converges to a
stationary point. We also highlight the importance of correctly training the
VAE using a denoising criterion, in order to ensure that the encoder
generalizes well to out-of-distribution images, without affecting the quality
of the generative model. This simple modification is key to providing
robustness to the whole procedure. Finally we show how our joint MAP
methodology relates to more common MAP approaches, and we propose a
continuation scheme that makes use of our JPMAP algorithm to provide more
robust MAP estimates. Experimental results also show the higher quality of the
solutions obtained by our JPMAP approach with respect to other non-convex MAP
approaches which more often get stuck in spurious local optima.Comment: arXiv admin note: text overlap with arXiv:1911.0637
A Novel Method for the Absolute Pose Problem with Pairwise Constraints
Absolute pose estimation is a fundamental problem in computer vision, and it
is a typical parameter estimation problem, meaning that efforts to solve it
will always suffer from outlier-contaminated data. Conventionally, for a fixed
dimensionality d and the number of measurements N, a robust estimation problem
cannot be solved faster than O(N^d). Furthermore, it is almost impossible to
remove d from the exponent of the runtime of a globally optimal algorithm.
However, absolute pose estimation is a geometric parameter estimation problem,
and thus has special constraints. In this paper, we consider pairwise
constraints and propose a globally optimal algorithm for solving the absolute
pose estimation problem. The proposed algorithm has a linear complexity in the
number of correspondences at a given outlier ratio. Concretely, we first
decouple the rotation and the translation subproblems by utilizing the pairwise
constraints, and then we solve the rotation subproblem using the
branch-and-bound algorithm. Lastly, we estimate the translation based on the
known rotation by using another branch-and-bound algorithm. The advantages of
our method are demonstrated via thorough testing on both synthetic and
real-world dataComment: 10 pages, 7figure
Unsupervised Learning for Robust Fitting:A Reinforcement Learning Approach
Robust model fitting is a core algorithm in a large number of computer vision
applications. Solving this problem efficiently for datasets highly contaminated
with outliers is, however, still challenging due to the underlying
computational complexity. Recent literature has focused on learning-based
algorithms. However, most approaches are supervised which require a large
amount of labelled training data. In this paper, we introduce a novel
unsupervised learning framework that learns to directly solve robust model
fitting. Unlike other methods, our work is agnostic to the underlying input
features, and can be easily generalized to a wide variety of LP-type problems
with quasi-convex residuals. We empirically show that our method outperforms
existing unsupervised learning approaches, and achieves competitive results
compared to traditional methods on several important computer vision problems.Comment: The preprint of paper accepted to CVPR 202
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