7,027 research outputs found
Image reconstruction with a non-parallelism constraint
No full textWe consider the problem of restoration of images corrupted by blur and noise.
We find the minimum of the primal energy
function, which has two terms. The former is related to
faithfulness to the data and the latter is associated with
smoothness constraints. In general, we have to estimate
the discontinuities of the ideal image. We require that the
obtained images are piecewise continuous and with thin edges. We associate with
the primal energy function a dual
energy function, which treats discontinuities implicitly.
In order to have thin edges, we determine a dual energy function, which is convex
and takes into account non-parallelism constraints.
The proposed dual energy can be used as initial function in a
GNC (Graduated Non-Convexity)-type algorithm,
to obtain reconstructed images with Boolean discontinuities.
In the experimental results, we show that
the parallel lines are inhibited
The Traveling salesman problem in circulant weighted graphs with two stripes
No full textThe Symmetric Circulant Traveling Salesman Problem asks for the minimum cost of a Hamiltonian cycle in a circulant weighted undirected graph. The computational complexity of this problem is not known.
Just a constructive upper bound, and a good lower bound have been determined.
This paper provides a characterization of the two stripe case. Instances where the minimum cost of a Hamiltonian cycle is equal either to the upper bound, or to the lower bound are recognized. A new construction providing Hamiltonian cycles, whose cost is in many cases lower than the upper bound, is
proposed for the remaining instances
The Travelling Salesman Problem in Symmetric Circulant Matrices with Two Stripes
No full textThe Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one
A deterministic algorithm for optical flow estimation
No full textIn this paper we propose a new deterministic algorithm for determining optical flow through regularization techniques so that the solution of the problem is defined as the minimum of an appropriate energy function. We also assume that the displacements are piecewise continuous and that the discontinuities are variable to be estimated. More precisely, we introduce a hierarchical three-step optimization strategy to minimize the constructed energy function, which is not convex. In the first step we find a suitable initial guess of the displacements field by a gradient-based GNC algorithm. In the second step we define the local energy of a displacement field as the energy function obtained by fixing all the field with the exception of a row or of a column. Then, through an application of the shortest path technique we minimize iteratively each local energy function restricted to a row or to a column until we arrive at a fixed point. In the last step we use again a GNC algorithm to recover a sub-pixel accuracy. The experimental results confirm the goodness of this technique
Half-Quadratic Image Restoration with a Non-parallelism Constraint
No full textThe problem of image restoration from blur and noise is studied.
By regularization techniques, a solution of the problem is found as the minimum of a
primal energy function, which is formed by two terms. The former deals with
faithfulness to the data, and the latter is associated with the smoothness constraints.
We impose that the obtained results are images piecewise continuous and with thin edges. In correspondence with the primal energy function, there is a dual energy function, which deals with discontinuities implicitly.
We present a unified approach of the duality theory, also to consider the non-parallelism constraint.
We construct a dual energy function, which is convex and imposes
such a constraint. To reconstruct images with Boolean discontinuities,
the proposed energy function can be used as an initial approximation in a
Graduated Non-Convexity algorithm.
The experimental results confirm that such a technique
inhibits the formation of parallel lines
A Blind Source Separation Technique for Document Restoration
No full textWe examine an instance of the blind source separation problem, namely, the reconstruction of digital
documents degraded by bleed-through and show-through eects. We introduce a nonstationary,
locally linear data model and a solution approach based on the assumption of cross-correlated ideal
sources. In order to solve the ill-posed local linear problem, we impose that the sum of all rows
of the mixture matrix is equal to one, and we assume that the ideal sources are nonnegative and
with an estimated level of overlapping (i.e., estimated cross-correlation). The solutions we obtain
are related to a factorization of the covariance matrix of the data, which allows the given constraints
to be satised at best. Our experimental results conrm the eectiveness of the method we propose
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