234 research outputs found
On Broken Triangles
A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP
On Broken Triangles (IJCAI 2016)
International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP
The complexity of finite-valued CSPs
We study the computational complexity of exact minimisation of
rational-valued discrete functions. Let be a set of rational-valued
functions on a fixed finite domain; such a set is called a finite-valued
constraint language. The valued constraint satisfaction problem,
, is the problem of minimising a function given as
a sum of functions from . We establish a dichotomy theorem with respect
to exact solvability for all finite-valued constraint languages defined on
domains of arbitrary finite size.
We show that every constraint language either admits a binary
symmetric fractional polymorphism in which case the basic linear programming
relaxation solves any instance of exactly, or
satisfies a simple hardness condition that allows for a
polynomial-time reduction from Max-Cut to
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
Tractability in Constraint Satisfaction Problems: A Survey
International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP
Robust surface modelling of visual hull from multiple silhouettes
Reconstructing depth information from images is one of the actively researched themes
in computer vision and its application involves most vision research areas from object
recognition to realistic visualisation. Amongst other useful vision-based reconstruction
techniques, this thesis extensively investigates the visual hull (VH) concept for volume
approximation and its robust surface modelling when various views of an object are
available. Assuming that multiple images are captured from a circular motion, projection
matrices are generally parameterised in terms of a rotation angle from a reference position
in order to facilitate the multi-camera calibration. However, this assumption is often
violated in practice, i.e., a pure rotation in a planar motion with accurate rotation angle
is hardly realisable. To address this problem, at first, this thesis proposes a calibration
method associated with the approximate circular motion.
With these modified projection matrices, a resulting VH is represented by a hierarchical
tree structure of voxels from which surfaces are extracted by the Marching
cubes (MC) algorithm. However, the surfaces may have unexpected artefacts caused by
a coarser volume reconstruction, the topological ambiguity of the MC algorithm, and
imperfect image processing or calibration result. To avoid this sensitivity, this thesis
proposes a robust surface construction algorithm which initially classifies local convex
regions from imperfect MC vertices and then aggregates local surfaces constructed by the
3D convex hull algorithm. Furthermore, this thesis also explores the use of wide baseline
images to refine a coarse VH using an affine invariant region descriptor. This improves
the quality of VH when a small number of initial views is given.
In conclusion, the proposed methods achieve a 3D model with enhanced accuracy.
Also, robust surface modelling is retained when silhouette images are degraded by
practical noise
Application of general semi-infinite Programming to Lapidary Cutting Problems
We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented
Robust surface modelling of visual hull from multiple silhouettes
Reconstructing depth information from images is one of the actively researched themes
in computer vision and its application involves most vision research areas from object
recognition to realistic visualisation. Amongst other useful vision-based reconstruction
techniques, this thesis extensively investigates the visual hull (VH) concept for volume
approximation and its robust surface modelling when various views of an object are
available. Assuming that multiple images are captured from a circular motion, projection
matrices are generally parameterised in terms of a rotation angle from a reference position
in order to facilitate the multi-camera calibration. However, this assumption is often
violated in practice, i.e., a pure rotation in a planar motion with accurate rotation angle
is hardly realisable. To address this problem, at first, this thesis proposes a calibration
method associated with the approximate circular motion.
With these modified projection matrices, a resulting VH is represented by a hierarchical
tree structure of voxels from which surfaces are extracted by the Marching
cubes (MC) algorithm. However, the surfaces may have unexpected artefacts caused by
a coarser volume reconstruction, the topological ambiguity of the MC algorithm, and
imperfect image processing or calibration result. To avoid this sensitivity, this thesis
proposes a robust surface construction algorithm which initially classifies local convex
regions from imperfect MC vertices and then aggregates local surfaces constructed by the
3D convex hull algorithm. Furthermore, this thesis also explores the use of wide baseline
images to refine a coarse VH using an affine invariant region descriptor. This improves
the quality of VH when a small number of initial views is given.
In conclusion, the proposed methods achieve a 3D model with enhanced accuracy.
Also, robust surface modelling is retained when silhouette images are degraded by
practical noise
- âŠ