Extracting curve-skeletons from digital shapes using occluding contours

Curve-skeletons are compact and semantically relevant shape descriptors, able to summarize both topology and pose of a wide range of digital objects. Most of the state-of-the-art algorithms for their computation rely on the type of geometric primitives used and sampling frequency. In this paper we introduce a formally sound and intuitive definition of curve-skeleton, then we propose a novel method for skeleton extraction that rely on the visual appearance of the shapes. To achieve this result we inspect the properties of occluding contours, showing how information about the symmetry axes of a 3D shape can be inferred by a small set of its planar projections. The proposed method is fast, insensitive to noise, capable of working with different shape representations, resolution insensitive and easy to implement

Image processing for plastic surgery planning

This thesis presents some image processing tools for plastic surgery planning. In particular, it presents a novel method that combines local and global context in a probabilistic relaxation framework to identify cephalometric landmarks used in Maxillofacial plastic surgery. It also uses a method that utilises global and local symmetry to identify abnormalities in CT frontal images of the human body. The proposed methodologies are evaluated with the help of several clinical data supplied by collaborating plastic surgeons

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

Abstract We determine the generating functions of 1/4 BPS dyons in a class of 4d N $$\mathcal{N}$$ = 4 string vacua arising as CHL orbifolds of K3 × T 2, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be described as multiplicative lifts of certain supersymmetric indices (twining genera) on the worldsheet of the corresponding nonlinear sigma model on K3. As a consequence, our procedure also leads to an explicit derivation of almost all of these twining genera. The worldsheet indices singled out in this way match precisely a set of functions of interest in moonshine, as predicted by a recent conjecture

On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions

MHD equilibria with incompressible flows: symmetry approach

We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and in particular a special type of "weak" symmetries.Comment: Accepted for publication in Phys. Plasma

Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators

We study symmetry protected features in the quasiparticle interference (QPI) pattern of 2D systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier transformed local density of states (FT-LDOS), \rho(\bq,\omega), while the position of high intensity peaks generically depends on the geometric features of the iso-energy contour at energy $\omega$, the \emph{absence} of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror symmetric lines in the Brillouin zone (BZ) and (ii) separated by scattering vector \bq. We apply the general result to the QPI on the $<{001} >$-surface of topological crystalline insulator Pb$_{1-x}$Sn$_x$Te and predict all vanishing peaks in \rho(\bq,\omega). The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.Comment: Six-page text plus 2.5-page appendices, three figures and one table. Accepted versio

A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Comment: 10 pages, 8 figure