10,212 research outputs found
A variational algorithm for the detection of line segments
In this paper we propose an algorithm for the detection of edges in images
that is based on topological asymptotic analysis. Motivated from the
Mumford--Shah functional, we consider a variational functional that penalizes
oscillations outside some approximate edge set, which we represent as the union
of a finite number of thin strips, the width of which is an order of magnitude
smaller than their length. In order to find a near optimal placement of these
strips, we compute an asymptotic expansion of the functional with respect to
the strip size. This expansion is then employed for defining a (topological)
gradient descent like minimization method. As opposed to a recently proposed
method by some of the authors, which uses coverings with balls, the usage of
strips includes some directional information into the method, which can be used
for obtaining finer edges and can also result in a reduction of computation
times
Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits
Motivated by applications in energy management, this paper presents the
Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the
exploration of risky arms, MARAB takes as arm quality its conditional value at
risk. When the user-supplied risk level goes to 0, the arm quality tends toward
the essential infimum of the arm distribution density, and MARAB tends toward
the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal
value. As a first contribution, this paper presents a theoretical analysis of
the MIN algorithm under mild assumptions, establishing its robustness
comparatively to UCB. The analysis is supported by extensive experimental
validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB
algorithms on artificial and real-world problems.Comment: 16 page
Blending Learning and Inference in Structured Prediction
In this paper we derive an efficient algorithm to learn the parameters of
structured predictors in general graphical models. This algorithm blends the
learning and inference tasks, which results in a significant speedup over
traditional approaches, such as conditional random fields and structured
support vector machines. For this purpose we utilize the structures of the
predictors to describe a low dimensional structured prediction task which
encourages local consistencies within the different structures while learning
the parameters of the model. Convexity of the learning task provides the means
to enforce the consistencies between the different parts. The
inference-learning blending algorithm that we propose is guaranteed to converge
to the optimum of the low dimensional primal and dual programs. Unlike many of
the existing approaches, the inference-learning blending allows us to learn
efficiently high-order graphical models, over regions of any size, and very
large number of parameters. We demonstrate the effectiveness of our approach,
while presenting state-of-the-art results in stereo estimation, semantic
segmentation, shape reconstruction, and indoor scene understanding
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
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