A Markovian Model For Contour Grouping

In order to interpret and analyse a scene, determining the contours is a fundamental step. Classical methods of contour extration do not always allow the detection of all the controus. We notice, for exemple, that the contours obtained by a Canny-Deriche filter have some gaps, especially at corners or at T-junctions. In short, the boundaries which are detected are not always closed. In this report, we present an algorith that restores incomplete contours. We model the image by Markov Random Fields and we define the Gibbs Distribution associated with it. In order to complete the contours, several criteria are defined and introduced in an energy function, which has to be optimized. The deterministic ICM "Iterated Conditional Mode" relaxation algorithm is implemented to minimize this energy function. The result is a contour image consisting of closed contours. This method has been tested on different images which present different types of difficulties (indoors, outdoors, satellite (SPOT), industrial and medical images)

Density-operator evolution: Complete positivity and the Keldysh real-time expansion

We study the reduced time-evolution of open quantum systems by combining quantum-information and statistical field theory. Inspired by prior work [EPL 102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling. This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage defines the dissipative timescales of the system --before having integrated out the environment completely-- the second stage sums up elementary physical processes described by CP superoperators. This allows us to establish the nontrivial relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit. Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by 'cutting' a group of Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schr\"odinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.Comment: Submission to SciPost Physics, 49 pages including 6 appendices, 13 figures. Significant improvement of introduction and conclusion, added discussions, fixed typos, no results change

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of two-dimensional harmonic oscillators that contains the conventional Brownian motion as a particular instance. This description is derived from first principles in the framework of the so-called Maxwell-Chern-Simons electrodynamics, or also known, Abelian topological massive gauge theory. Disregarding backreaction effects and endowing the system Hamiltonian with a suitable renormalized potential interaction, the conceived description is equivalent to a minimal-coupling theory with a gauge field giving rise to a fluctuating force that mimics the Lorentz force induced by a particle-attached magnetic flux. We show that the underlying symmetry structure of the theory (i.e. time-reverse asymmetry and parity violation) yields an interacting vortex-like Brownian dynamics for the system particles. An explicit comparison to the conventional Brownian motion in the quantum Markovian limit reveals that the proposed description represents a second-order correction to the well-known damped harmonic oscillator, which manifests that there may be dissipative phenomena intrinsic to the dimensionality of the interesting system.Comment: 20+11 pages, 3 figures. Comments are welcome. Discussion in Sec. III and IV improved. Several typos and a misleading remark corrected, and figure replaced. Close to the published versio