Reconstructing vectorised photographic images

We address the problem of representing captured images in the continuous mathematical space more usually associated with certain forms of drawn ('vector') images. Such an image is resolution-independent so can be used as a master for varying resolution-specific formats. We briefly describe the main features of a vectorising codec for photographic images, whose significance is that drawing programs can access images and image components as first-class vector objects. This paper focuses on the problem of rendering from the isochromic contour form of a vectorised image and demonstrates a new fill algorithm which could also be used in drawing generally. The fill method is described in terms of level set diffusion equations for clarity. Finally we show that image warping is both simplified and enhanced in this form and that we can demonstrate real histogram equalisation with genuinely rectangular histograms

Automatic 2D-to-3D conversion of single low depth-of-field images

This research presents a novel approach to the automatic rendering of 3D stereoscopic disparity image pairs from single 2D low depth-of-field (LDOF) images. Initially a depth map is produced through the assignment of depth to every delineated object and region in the image. Subsequently the left and right disparity images are produced through depth imagebased rendering (DIBR). The objects and regions in the image are initially assigned to one of six proposed groups or labels. Labelling is performed in two stages. The first involves the delineation of the dominant object-of-interest (OOI). The second involves the global object and region grouping of the non-OOI regions. The matting of the OOI is also performed in two stages. Initially the in focus foreground or region-of-interest (ROI) is separated from the out of focus background. This is achieved through the correlation of edge, gradient and higher-order statistics (HOS) saliencies. Refinement of the ROI is performed using k-means segmentation and CIEDE2000 colour-difference matching. Subsequently the OOI is extracted from within the ROI through analysis of the dominant gradients and edge saliencies together with k-means segmentation. Depth is assigned to each of the six labels by correlating Gestalt-based principles with vanishing point estimation, gradient plane approximation and depth from defocus (DfD). To minimise some of the dis-occlusions that are generated through the 3D warping sub-process within the DIBR process the depth map is pre-smoothed using an asymmetric bilateral filter. Hole-filling of the remaining dis-occlusions is performed through nearest-neighbour horizontal interpolation, which incorporates depth as well as direction of warp. To minimising the effects of the lateral striations, specific directional Gaussian and circular averaging smoothing is applied independently to each view, with additional average filtering applied to the border transitions. Each stage of the proposed model is benchmarked against data from several significant publications. Novel contributions are made in the sub-speciality fields of ROI estimation, OOI matting, LDOF image classification, Gestalt-based region categorisation, vanishing point detection, relative depth assignment and hole-filling or inpainting. An important contribution is made towards the overall knowledge base of automatic 2D-to-3D conversion techniques, through the collation of existing information, expansion of existing methods and development of newer concepts

Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands

The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is energy absorption rate when the lattice depth is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid

Polylidar3D -- Fast Polygon Extraction from 3D Data

Flat surfaces captured by 3D point clouds are often used for localization, mapping, and modeling. Dense point cloud processing has high computation and memory costs making low-dimensional representations of flat surfaces such as polygons desirable. We present Polylidar3D, a non-convex polygon extraction algorithm which takes as input unorganized 3D point clouds (e.g., LiDAR data), organized point clouds (e.g., range images), or user-provided meshes. Non-convex polygons represent flat surfaces in an environment with interior cutouts representing obstacles or holes. The Polylidar3D front-end transforms input data into a half-edge triangular mesh. This representation provides a common level of input data abstraction for subsequent back-end processing. The Polylidar3D back-end is composed of four core algorithms: mesh smoothing, dominant plane normal estimation, planar segment extraction, and finally polygon extraction. Polylidar3D is shown to be quite fast, making use of CPU multi-threading and GPU acceleration when available. We demonstrate Polylidar3D's versatility and speed with real-world datasets including aerial LiDAR point clouds for rooftop mapping, autonomous driving LiDAR point clouds for road surface detection, and RGBD cameras for indoor floor/wall detection. We also evaluate Polylidar3D on a challenging planar segmentation benchmark dataset. Results consistently show excellent speed and accuracy.Comment: 40 page

Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that, they can be both described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it is a local symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, We find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly, which is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gapless-ness local in the parameter space.Comment: 14 + 3 pages, 1 figure. (The first two authors contributed equally to the work.

Spatial mapping of band bending in semiconductor devices using in-situ quantum sensors

Band bending is a central concept in solid-state physics that arises from local variations in charge distribution especially near semiconductor interfaces and surfaces. Its precision measurement is vital in a variety of contexts from the optimisation of field effect transistors to the engineering of qubit devices with enhanced stability and coherence. Existing methods are surface sensitive and are unable to probe band bending at depth from surface or bulk charges related to crystal defects. Here we propose an in-situ method for probing band bending in a semiconductor device by imaging an array of atomic-sized quantum sensing defects to report on the local electric field. We implement the concept using the nitrogen-vacancy centre in diamond, and map the electric field at different depths under various surface terminations. We then fabricate a two-terminal device based on the conductive two-dimensional hole gas formed at a hydrogen-terminated diamond surface, and observe an unexpected spatial modulation of the electric field attributed to a complex interplay between charge injection and photo-ionisation effects. Our method opens the way to three-dimensional mapping of band bending in diamond and other semiconductors hosting suitable quantum sensors, combined with simultaneous imaging of charge transport in complex operating devices.Comment: This is a pre-print of an article published in Nature Electronics. The final authenticated version is available online at https://dx.doi.org/10.1038/s41928-018-0130-