Connectivity-Enforcing Hough Transform for the Robust Extraction of Line Segments

Global voting schemes based on the Hough transform (HT) have been widely used to robustly detect lines in images. However, since the votes do not take line connectivity into account, these methods do not deal well with cluttered images. In opposition, the so-called local methods enforce connectivity but lack robustness to deal with challenging situations that occur in many realistic scenarios, e.g., when line segments cross or when long segments are corrupted. In this paper, we address the critical limitations of the HT as a line segment extractor by incorporating connectivity in the voting process. This is done by only accounting for the contributions of edge points lying in increasingly larger neighborhoods and whose position and directional content agree with potential line segments. As a result, our method, which we call STRAIGHT (Segment exTRAction by connectivity-enforcInG HT), extracts the longest connected segments in each location of the image, thus also integrating into the HT voting process the usually separate step of individual segment extraction. The usage of the Hough space mapping and a corresponding hierarchical implementation make our approach computationally feasible. We present experiments that illustrate, with synthetic and real images, how STRAIGHT succeeds in extracting complete segments in several situations where current methods fail.Comment: Submitted for publicatio

A New Form of Path Integral for the Coherent States Representation and its Semiclassical Limit

The overcompleteness of the coherent states basis leads to a multiplicity of representations of Feynman's path integral. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. Two such semiclassical formulas were derived in \cite{Bar01} for the two corresponding path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}. Each of these formulas involve trajectories governed by a different classical representation of the Hamiltonian operator: the P representation in one case and the Q representation in other. In this paper we construct a third representation of the path integral whose semiclassical limit involves directly the Weyl representation of the Hamiltonian operator, i.e., the classical Hamiltonian itself.Comment: 16 pages, no figure

Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling

We study the formation of Majorana states in quasi-1D and 2D square lattices with open boundary conditions, with general anisotropic Rashba coupling, in the presence of an applied Zeeman field and in the proximity of a superconductor. For systems in which the length of the system is very large (quasi-1D) we calculate analytically the exact topological invariant, and we find a rich phase diagram which is strongly dependent on the width of the system. We compare our results with previous results based on a few-band approximation. We also investigate numerically open 2D systems of finite length in both directions. We use the recently introduced generalized Majorana polarization, which can locally evaluate the Majorana character of a given state. We find that the formation of Majoranas depends strongly on the geometry of the system and if the length and the width are comparable no Majorana states can form, however, one can show the formation of "quasi-Majorana" states that have a local Majorana character, but no global Majorana symmetry.Comment: 12 pages, 13 figure

Semiclassical Tunneling of Wavepackets with Real Trajectories

Semiclassical approximations for tunneling processes usually involve complex trajectories or complex times. In this paper we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunneling and interferences very accurately in the limit of small Plank's constant. We use these results to estimate the tunneling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height.Comment: 23 pages, 7 figures Revised text and figure

Universal quantum criticality at the Mott-Anderson transition

We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wavefunctions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime.Comment: 4 pages + references, 4 figures; v2: minor changes, accepted for publication in Phys. Rev. Let