A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

An Atomic Linear Stark Shift Violating P But Not T Arising From the Electroweak Nuclear Anapole Moment

We propose a direct method of detection of the nuclear anapole moment. It is based on the existence of a linear Stark shift for alkali atoms in their ground state perturbed by a quadrupolar interaction potential and a magnetic field. This shift is proportional to the T-even pseudoscalar built from the quadrupolar potential symmetry axis, the directions of the applied electric and magnetic fields.It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction and, on the other,the static electric dipole moment arising from electroweak interactions inside the nucleus. The case of ground state cesium atoms trapped in a uniaxial (hcp) phase of solid helium-4 is examined. From an explicit evaluation of both the hyperfine structure anisotropy and the static P-odd T-even dipole deduced from recent empirical data about the cesium nuclear anapole moment, we predict the Stark shift. It is three times the experimental upper bound to be set on the T-odd Stark shift of free cesium atoms in order to improve the present limit on the electron EDM.Comment: 31 pages, 3 PostScript figure

Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing

The Chern number, nu, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana zero modes. Here we show that such a winding can be faithfully identified for any superconducting system (p-wave or s-wave with spin-orbit coupling) through a set of time-of-flight measurements, making it a diagnostic tool also in actual cold atom experiments. As an application, we specialize the measurement scheme for a chiral topological model of spinless fermions. The proposed model only requires the experimentally accessible s-wave pairing and staggered tunnelling that mimics spin-orbit coupling. By adiabatically connecting this model to Kitaev's honeycomb lattice model, we show that it gives rise to nu = \pm 1 phases, where vortices bind Majorana fermions, and nu=\pm 2 phases that emerge as the unique collective state of such vortices. Hence, the preparation of these phases and the detection of their Chern numbers provide an unambiguous signature for the presence of Majorana modes. Finally, we demonstrate that our detection procedure is resilient against most inaccuracies in experimental control parameters as well as finite temperature.Comment: 9+4 pages, 11 figures, expanded versio

Wavelets and partial differential equations for image denoising

In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the wavelet domain and then allows to predict wavelet coefficients at each scale from the first one. This property combined with the theoretical results about the characterization of singularities in the wavelet domain enables to discard noise. Significant structures of the image are well recovered while some annoying artifacts along image edges are reduced. Some experimental results show that the proposed approach outperforms the most recent and effective wavelet based denoising schemes

Quantum scale biomimicry of low dimensional growth: An unusual complex amorphous precursor route to TiO2 band confinement by shape adaptive biopolymer-like flexibility for energy applications

Crystallization via an amorphous pathway is often preferred by biologically driven processes enabling living species to better regulate activation energies to crystal formation that are intrinsically linked to shape and size of dynamically evolving morphologies. Templated ordering of 3-dimensional space around amorphous embedded non-equilibrium phases at heterogeneous polymer-metal interfaces signify important routes for the genesis of low-dimensional materials under stress-induced polymer confinement. We report the surface induced catalytic loss of P=O ligands to bond activated aromatization of C-C C=C and Ti=N resulting in confinement of porphyrin-TiO(2 )within polymer nanocages via particle attachment. Restricted growth nucleation of TiO2 to the quantum scale (˂= 2 nm) is synthetically assisted by nitrogen, phosphine and hydrocarbon polymer chemistry via self-assembly. Here, the amorphous arrest phase of TiO, is reminiscent of biogenic amorphous crystal growth patterns and polymer coordination has both a chemical and biomimetic significance arising from quantum scale confinement which is atomically challenging. The relative ease in adaptability of non-equilibrium phases renders host structures more shape compliant to congruent guests increasing the possibility of geometrical confinement. Here, we provide evidence for synthetic biomimicry akin to bio-polymerization mechanisms to steer disorder-to-order transitions via solvent plasticization-like behaviour. This challenges the rationale of quantum driven confinement processes by conventional processes. Further, we show the change in optoelectronic properties under quantum confinement is intrinsically related to size that affects their optical absorption band energy range in DSSC.This work was supported by the National Research Foundation of Korea (NRF) grant funded by Korea government (MEST) NRF-2012R1A1A2008196, NRF 2012R1A2A2A01047189, NRF 2017R1A2B4008801, 2016R1D1A1A02936936, (NRF-2018R1A4A1059976, NRF-2018R1A2A1A13078704) and NRF Basic Research Programme in Science and Engineering by the Ministry of Education (No. 2017R1D1A1B03036226) and by the INDO-KOREA JNC program of the National Research Foundation of Korea Grant No. 2017K1A3A1A68. We thank BMSI (A*STAR) and NSCC for support. SJF is funded by grant IAF25 PPH17/01/a0/009 funded by A* STAR/NRF/EDB. CSV is the founder of a spinoff biotech Sinopsee Therapeutics. The current work has no conflicting interests with the company. We would like to express our very great appreciation to Ms. Hyoseon Kim for her technical expertise during HRTEM imaging