6,542 research outputs found
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
A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching
We propose a combinatorial solution for the problem of non-rigidly matching a
3D shape to 3D image data. To this end, we model the shape as a triangular mesh
and allow each triangle of this mesh to be rigidly transformed to achieve a
suitable matching to the image. By penalising the distance and the relative
rotation between neighbouring triangles our matching compromises between image
and shape information. In this paper, we resolve two major challenges: Firstly,
we address the resulting large and NP-hard combinatorial problem with a
suitable graph-theoretic approach. Secondly, we propose an efficient
discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge
this is the first combinatorial formulation for non-rigid 3D shape-to-image
matching. In contrast to existing local (gradient descent) optimisation
methods, we obtain solutions that do not require a good initialisation and that
are within a bound of the optimal solution. We evaluate the proposed method on
the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image
registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure
Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape
We present a full pipeline for computing the medial axis transform of an
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
Robust and Optimal Methods for Geometric Sensor Data Alignment
Geometric sensor data alignment - the problem of finding the
rigid transformation that correctly aligns two sets of sensor
data without prior knowledge of how the data correspond - is a
fundamental task in computer vision and robotics. It is
inconvenient then that outliers and non-convexity are inherent to
the problem and present significant challenges for alignment
algorithms. Outliers are highly prevalent in sets of sensor data,
particularly when the sets overlap incompletely. Despite this,
many alignment objective functions are not robust to outliers,
leading to erroneous alignments. In addition, alignment problems
are highly non-convex, a property arising from the objective
function and the transformation. While finding a local optimum
may not be difficult, finding the global optimum is a hard
optimisation problem. These key challenges have not been fully
and jointly resolved in the existing literature, and so there is
a need for robust and optimal solutions to alignment problems.
Hence the objective of this thesis is to develop tractable
algorithms for geometric sensor data alignment that are robust to
outliers and not susceptible to spurious local optima.
This thesis makes several significant contributions to the
geometric alignment literature, founded on new insights into
robust alignment and the geometry of transformations. Firstly, a
novel discriminative sensor data representation is proposed that
has better viewpoint invariance than generative models and is
time and memory efficient without sacrificing model fidelity.
Secondly, a novel local optimisation algorithm is developed for
nD-nD geometric alignment under a robust distance measure. It
manifests a wider region of convergence and a greater robustness
to outliers and sampling artefacts than other local optimisation
algorithms. Thirdly, the first optimal solution for 3D-3D
geometric alignment with an inherently robust objective function
is proposed. It outperforms other geometric alignment algorithms
on challenging datasets due to its guaranteed optimality and
outlier robustness, and has an efficient parallel implementation.
Fourthly, the first optimal solution for 2D-3D geometric
alignment with an inherently robust objective function is
proposed. It outperforms existing approaches on challenging
datasets, reliably finding the global optimum, and has an
efficient parallel implementation. Finally, another optimal
solution is developed for 2D-3D geometric alignment, using a
robust surface alignment measure.
Ultimately, robust and optimal methods, such as those in this
thesis, are necessary to reliably find accurate solutions to
geometric sensor data alignment problems
- …