Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.

On Volumetric Shape Reconstruction from Implicit Forms

International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

Synthesis, structures and properties of inorganic framework materials

Chapter 1 reviews the literature on the structures and properties of inorganic framework materials that are of relevance to this thesis. In particular the phenomenon of negative thermal expansion and the AM(_2)O(_8)/AM(_2)O(_7) families of materials are discussed. Chapter 2 describes the methods of synthesis and characterisation of the materials investigated in this thesis. Chapter 3 discusses the dehydration reaction of M(_o)O(_2).H(_2)O.PO(_3)OH. The study involved the introduction of a new methodology for whole pattern powder fitting; this method was later verified by full Rietveld analysis. This investigation led to the discovery and structure solution of two new molybdenum phosphates using powder XRD. These materials have been named β-(MoO(_2))(_2)P(_2)0(_7) and β -(Mo0(_2))(_2)P(_2)0(_7). A structural pathway for the dehydration reactions has been proposed which is consistent with all of these structures and other analytical data obtained. Chapter 4 describes investigations into the structures of a-(Mo02)2P207 by powder diffraction and NMR methods. The high temperature structure was confirmed to be related to a literature model. The low temperature structure was further studied by electron diffraction, second harmonic generation and solid state NMR. The use of these complementary techniques with powder X-ray and neutron diffraction data, led to the solution of the complex superstructure. Chapter 5 describes a study into the structures of (MoO)(_2)P(_4)0(_13). The material undergoes a phase transition at 523 K. The low temperature structure contains 441 unique atoms and as such is the most crystallographically complex oxide solved to date. The high temperature structure contains 253 unique atoms and is the second most complex oxide in the ICSD. Chapter 6 describes the in-situ X-ray studies on the synthesis of M0P(_2)O(_7) from precursors Mo0(_2)(P0(_3))(_2) and (MoO)(_2)P(_4)0(_13) in an H(_2) environment. (Mo0(_2))(_2)P(_2)0(_7) was studied under similar conditions and found to decompose to an unidentifiable poorly crystalline phase. Chapter 7 describes the discovery of a new high temperature synthetic route to cubic ZrMo(_2)0(_8) using extremely rapid time-resolved XRD data recorded at the ESRF. The cubic material forms from its constituent oxides at 1350 K and can be isolated back at room temperature using a quench cooling method. A pure phase sample can be prepared using a Zr0(_2):Mo0(_3) ratio of 1:3. The entire synthesis occurs within seconds and precise control of temperature and time is crucial for this synthesis

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

New Models for High-Quality Surface Reconstruction and Rendering

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surface

Synthesis, crystal growth, magnetic and transport properties of Ln-M-X (Ln=lanthanide, M=transition metal, X=In, Ga) compounds

ABSTRACT This dissertation focuses on the structural stability, magnetic and transport properties of ternary lanthanide compounds grown using indium and gallium flux. Single crystals of TbRhIn5 were synthesized using indium flux. TbRhIn5 is isostructural to the well known LnnMIn3n+2 (n = 1, 2, ∞; Ln = La, Ce; M = Rh, Ir) and adopts the HoCoGa5 structure type and crystallizes in the space group P4/mmm, Z = 1. Lattice parameters are a = 4.6000(6) Å and c = 7.4370(11) Å, V = 157.29(6) Å3. A sharp antiferromagnetic transition is observed at TN = 48 K for TbRhIn5. Single crystals of SmPd2Ga2 have been synthesized by flux growth methods. SmPd2Ga2 adopts the tetragonal space group I4/mmm, Z=2, with lattice parameters, a = 4.2170(3) Å and c = 10.4140(3) Å. This new material has physical properties similar to other Sm intermetallics and has, most notably, a large positive magnetoresistance at low temperatures. Magnetic measurements indicate that SmPd2Ga2 is ferromagnetic with Tc ~ 5 K. Single crystals of Tb4MGa12 (M = Pd, Pt) have been synthesized. The isostructural compounds crystallize in the cubic space group, , with Z = 2 and lattice parameters: a = 8.5930(7) Å and a = 8.5850(3) Å for Tb4PdGa12 and Tb4PtGa12, respectively. Magnetic measurements suggest that Tb4PdGa12 and Tb4PtGa12 order antiferromagnetically Néel temperatures of 16 K and 12 K, respectively. Single crystals of Ln4MGa12 (Ln = Dy, Ho, Er; M = Pd, Pt) were synthesized and characterized by single crystal X-ray diffraction. Ln4MGa12 (Ln = Dy, Ho, Er; M = Pd, Pt) are isostructural to Tb4PdGa12. Magnetic measurements show that Dy4PdGa12 and Ho4PdGa12 do not show any magnetic ordering down to 2 K, while Er4PdGa12 shows an antiferromagnetic transition at TN = 3 K, as well as, magnetic transitions at 13 K and 21 K. Dy4PtGa12 orders antiferromagnetically at TN = 11 K and Ho4PtGa12 shows magnetic transitions at 26 K and 92 K. Er4PtGa12 shows an antiferromagnetic transition at TN = 5.5 K and magnetic transitions at 25 K and 93 K. The structure, magnetic, and transport behavior of these phases are discussed and compared

Incompressibility criteria for spun-normal surfaces

We give a simple sufficient condition for a spun-normal surface in an ideal triangulation to be incompressible, namely that it is a vertex surface with non-empty boundary which has a quadrilateral in each tetrahedron. While this condition is far from being necessary, it is powerful enough to give two new results: the existence of alternating knots with non-integer boundary slopes, and a proof of the Slope Conjecture for a large class of 2-fusion knots. While the condition and conclusion are purely topological, the proof uses the Culler-Shalen theory of essential surfaces arising from ideal points of the character variety, as reinterpreted by Thurston and Yoshida. The criterion itself comes from the work of Kabaya, which we place into the language of normal surface theory. This allows the criterion to be easily applied, and gives the framework for proving that the surface is incompressible. We also explore which spun-normal surfaces arise from ideal points of the deformation variety. In particular, we give an example where no vertex or fundamental surface arises in this way.Comment: 37 pages, 8 figures. V2: New remark in Section 9.1, additional references; V3 Minor edits, to appear in Trans. Amer. Math. So

Development of computational methods for electronic structural characterization of strongly correlated materials: from different ab-initio perspectives

The electronic correlations in materials drive a variety of fascinating phenomena from magnetism to metal-to-insulator transitions (MIT), which are due to the coupling between electron spin, charge, ionic displacements, and orbital ordering. Although Density Functional Theory (DFT) successfully describes the electronic structure of weakly interacting material systems, being a static mean-field approach, it fails to predict the properties of Strongly Correlated Materials (SCM) that include transition and rare earth metals where there is a prominent electron localization as in the case of d and f orbitals due to the nature of their spatial confinement. Dynamical Mean Field Theory (DMFT) is a Green’s function based method that has shown success in treating SCM. This dissertation focuses on the development of a user-friendly, open-source Python/Fortran framework, “DMFTwDFT” combining DFT and DMFT to characterize properties of both weakly and strongly correlated materials. The DFT Kohn- Sham orbitals are projected onto Maximally Localized Wannier Functions (MLWF) which essentially maps the Hubbard model to a local impurity model which we solve numerically using quantum Monte Carlo methods to capture both itinerant and localized nature of electrons. Additionally, we provide a library mode for computing the DMFT density matrix which can be linked and internally called from any DFT package allowing developers of other DFT codes to interface with our package and achieve full charge-self-consistency within DFT+DMFT. We then study the stability and diffusion of oxygen vacancies in the correlated material LaNiO3. By treating Ni-d as correlated orbitals along with a Ni-O hybridization manifold, we show that certain configurations undergo a MIT based on the environment of their vacancies. We also compute the transition path energy of a single oxygen vacancy through means of the nudged elastic band (NEB) method. We show that the diffusion energy profile calculated through DFT+U differs from that of DMFT, due to correlation effects that are not quite well captured with static mean-field theories. Additionally, DMFTwDFT was utilized to study strongly correlated alloys and materials useful for neuromorphic computing applications

Investigation of Antimonide Structure Types and the Structural Studies of Molybdates

This dissertation highlights the investigation of ternary lanthanide antimonide structure types and their physical properties. In particular, these ternary phases allow for the systematic investigation of the structure in an effort to correlate structure and properties. The ternary antimonides are layered structures with two-dimensional square sheets or nets, which influence the properties of these materials. In an effort to determine how structural changes influence the physical properties, various single crystals of compounds relating to the orthorhombic CeNiSb3 structure have been grown and characterized. The layered CeNiSb3 structure consists of Sb sheets, NiSb6 distorted octahedra, and CeSb9 monocapped square anti-prisms. LnNi(Sn,Sb)3 and LnPdSb3 differ slightly from the CeNiSb3 structure in the packing of the transition metal layer. The structures and physical properties of LnNi(Sn,Sb)3 (Ln = La-Nd, Sm, Gd, Tb) are studied as a function of lanthanide. The stability of the CeNiSb3 structure was investigated by the substitution of Co or Cu for Ni in CeNiSb3 resulting in CeNixCo1-xSb3 and Ln(Cu1-xNix)ySb2 compounds. Also, the effect of Ni substitution for Cu in Ce(Cu1-xNix)Sb2 (0 ≤ x ≤ 0.8) compounds on the magnetoresistance is investigated. This dissertation also explores the different structure types of molybdates Rb4M(MoO4)3 (M = Mn, Zn, and Cu). Each analogue adopts a different structure type and contain similar subunits. The full structure determinations of each of these compounds are important to be able to understand the promising magnetic and electrical properties

Robust and Accurate Superquadric Recovery: a Probabilistic Approach

Interpreting objects with basic geometric primitives has long been studied in computer vision. Among geometric primitives, superquadrics are well known for their ability to represent a wide range of shapes with few parameters. However, as the first and foremost step, recovering superquadrics accurately and robustly from 3D data still remains challenging. The existing methods are subject to local optima and sensitive to noise and outliers in real-world scenarios, resulting in frequent failure in capturing geometric shapes. In this paper, we propose the first probabilistic method to recover superquadrics from point clouds. Our method builds a Gaussian-uniform mixture model (GUM) on the parametric surface of a superquadric, which explicitly models the generation of outliers and noise. The superquadric recovery is formulated as a Maximum Likelihood Estimation (MLE) problem. We propose an algorithm, Expectation, Maximization, and Switching (EMS), to solve this problem, where: (1) outliers are predicted from the posterior perspective; (2) the superquadric parameter is optimized by the trust-region reflective algorithm; and (3) local optima are avoided by globally searching and switching among parameters encoding similar superquadrics. We show that our method can be extended to the multi-superquadrics recovery for complex objects. The proposed method outperforms the state-of-the-art in terms of accuracy, efficiency, and robustness on both synthetic and real-world datasets. The code is at http://github.com/bmlklwx/EMS-superquadric_fitting.git.Comment: Accepted to CVPR202