scholarly journals Landmark-free geometric methods in biological shape analysis

2015 ◽  
Vol 12 (113) ◽  
pp. 20150795 ◽  
Author(s):  
Patrice Koehl ◽  
Joel Hass
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Deformation Energy ◽  
Conformal Map ◽  
Success Rates ◽  
Genus Zero ◽  
Evolutionary Patterns ◽  
New Approach ◽  
Discrete Conformal Map ◽  
Biological Shape

In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy E sd ( f ) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

scholarly journals Minimum action principle and shape dynamics

2017 ◽  
Vol 14 (130) ◽  
pp. 20170031 ◽  
Author(s):  
Patrice Koehl
Keyword(s):  
Elastic Energy ◽  
Dimensional Space ◽  
Shape Recognition ◽  
Three Dimensional ◽  
The Other ◽  
Success Rates ◽  
Evolutionary Patterns ◽  
The Cost ◽  
Better Than ◽  
Three Dimensional Space

In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager–Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

scholarly journals FROM PLANAR GRAPHS TO EMBEDDED GRAPHS - A NEW APPROACH TO KAUFFMAN AND VOGEL'S POLYNOMIAL

2000 ◽  
Vol 09 (08) ◽  
pp. 975-986 ◽  
Author(s):  
RUI PEDRO CARPENTIER
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Direct Proof ◽  
Connected Components ◽  
Embedded Graphs ◽  
New Approach ◽  
Graphical Calculus ◽  
Embedded Graph

In [4] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [Formula: see text] and is defined in terms of a state-sum and the Dubrovnik polynomial for links. Using the graphical calculus of [4] it is shown that the polynomial of a planar graph can be calculated recursively from that of planar graphs with less vertices, which also allows the polynomial of an embedded graph to be calculated without resorting to links. The same approach is used to give a direct proof of uniqueness of the (normalized) polynomial restricted to planar graphs. In the case B=A-1 and a=A, it is proved that for a planar graph G we have [G]=2c-1(-A-A-1)v, where c is the number of connected components of G and v is the number of vertices of G. As a corollary, a necessary, but not sufficient, condition is obtained for an embedded graph to be ambient isotopic to a planar graph. In an appendix it is shown that, given a polynomial for planar graphs satisfying the graphical calculus, and imposing the first skein relation above, the polynomial extends to a rigid vertex regular isotopy invariant for embedded graphs, satisfying the remaining skein relations. Thus, when existence of the planar polynomial is guaranteed, this provides a direct way, not depending on results for the Dubrovnik polynomial, to show consistency of the polynomial for embedded graphs.

First U-Pb dating of fossilized soft tissue using a new approach to paleontological chronometry

Geology ◽  
2021 ◽  
Author(s):  
Heriberto Rochín-Bañaga ◽  
Donald W. Davis ◽  
Tobias Schwennicke
Keyword(s):  
Soft Tissue ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Uranium Content ◽  
New Approach ◽  
Inductively Coupled ◽  
Shark Teeth ◽  
Inductively Coupled Mass Spectrometry ◽  
Late Diagenesis ◽  
Three Dimensional Space

Previous U-Pb dating of fossils has had only limited success because of low uranium content and abundance of common Pb as well as element mobility during late diagenesis. We report the first accurate U-Pb dating of fossilized soft tissue from a Pliocene phosphatized bivalve mold using laser ablation–inductively coupled mass spectrometry (LA-ICPMS). The fossilized soft tissue yields a diagenetic U-Pb age of 3.16 ± 0.08 Ma, which is consistent with its late Pliocene stratigraphy and similar to the oldest U-Pb age measured on accompanying shark teeth. Phosphate extraclasts give a distinctly older age of 5.1 ± 1.7 Ma, indicating that they are likely detrital and may have furnished P, promoting phosphatization of the mold. The U-Pb ages reported here along with stratigraphic constraints suggest that diagenesis occurred shortly after the death of the bivalve and that the U-Pb system in the bivalve mold remained closed until the present. Shark teeth collected from the same horizon show variable resetting due to late diagenesis. Data were acquired as line scans in order to exploit the maximum Pb/U variation and were regressed as counts, rather than ratios, in three-dimensional space using a Bayesian statistical method.

Dynamic Simulation of Multibody Mechanical Systems Using the Vector-Network Model

1988 ◽  
Vol 12 (1) ◽  
pp. 21-30 ◽  
Author(s):  
M.J. Richard
Keyword(s):  
Dynamic Models ◽  
Analytical Procedure ◽  
Dimensional Space ◽  
Digital Simulation ◽  
Three Dimensional ◽  
General Purpose ◽  
New Approach ◽  
Network Method ◽  
Definition Of ◽  
Three Dimensional Space

Pressing technological problems have created a growing interest in the development of dynamic models for the digital simulation of multibody systems. This paper describes a new approach to the problem of motion prediction. An extension of the “vector-network” method to rigid body systems in three-dimensional space is introduced. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics are combined. The analytical procedure was successfully implemented within a general-purpose digital simulation program since, from a minimal definition of the mechanism, it will automatically predict the behavior of the system as output, thereby giving the impression that the equations governing the motion of the mechanical system have been completely formulated and solved by the computer. Simulations of the response of a rail vehicle which demonstrate the validity, applicability and self-formulating aspect of the automated model are provided.

scholarly journals New Approach for Solving Three Dimensional Space Partial Differential Equation

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0786 ◽  
Author(s):  
Enadi Et al.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Partial Differential ◽  
Transform Method ◽  
New Approach ◽  
Practical Implications ◽  
Three Dimensional Space

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.        Finally, all algorithms in this paper are implemented in MATLAB version 7.12.

Design of 3-Dimensional Guidance Law of Missile Based on Discrete Sliding Mode

2013 ◽  
Vol 816-817 ◽  
pp. 976-980
Author(s):  
Nuan Wen ◽  
Zheng Hua Liu ◽  
Le Chang
Keyword(s):  
Discrete Time ◽  
Relative Motion ◽  
Sliding Mode ◽  
Dimensional Space ◽  
Three Dimensional ◽  
New Approach ◽  
3 Dimensional ◽  
Guidance Law ◽  
Guidance Laws ◽  
Three Dimensional Space

In this article, a new approach to design discrete-time sliding-mode guidance laws is presented based on the target-missile relative motion equation in three-dimensional space. This method significantly reduced system chattering and could be easily achieved on engineering. Furthermore, effectiveness of the proposed guidance laws is demonstrated through simulation by comparing with the traditional proportional guidance laws.

scholarly journals Complexation processes in “PbCl2-N2H4CS” aqueous solutions during deposition of lead sulphide films

2021 ◽  
Vol 23 (4) ◽  
pp. 543-547
Author(s):  
Victor N. Semenov ◽  
Vitaly V. Volkov ◽  
Natalia V. Pereslytskikh
Keyword(s):  
Aqueous Solutions ◽  
Coordination Compounds ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Lead Chloride ◽  
Lead Sulphide ◽  
New Approach ◽  
Complex Forms ◽  
Selection Of

In this study, we proposed a new approach to assessing the processes of complexation in aqueous solutions using the example of the interaction of lead chloride with thiourea. The goal of this study was the investigation of processes of complexation in “PbCl2-N2H4CS” aqueous solutions and determination of the regions of dominance of thiourea coordination compounds, which are precursors during the deposition of lead sulphide films.Based on the diagrams and cross section lines of equal fractions constructed in three-dimensional space, the regions of dominance of all complex forms existing in the studied solution were found. Such a graphic image is the most informative, since it allows selection of the concentration ranges of the predominance of certain coordination compounds, especially thiourea complexes, which are precursors during the deposition of lead sulphide films. It was shown that an increase in the concentration of N2H4CS led to an increase in the total fraction of thiourea complexes: for a twofold excess of N2H4CS its fraction was 0.25, for a threefold excess it was 0.35, for a fourfold excess it was 0.5, for a fivefold excess it was 0.7.

scholarly journals Dynamic Visual Measurement of Driver Eye Movements

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2217 ◽  
Author(s):  
Jin Zhang ◽  
Ze Yang ◽  
Huaxia Deng ◽  
Huan Yu ◽  
Mengchao Ma ◽  
...  
Keyword(s):  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Visual Fatigue ◽  
High Definition ◽  
Robust Algorithms ◽  
Visual Measurement ◽  
New Approach ◽  
The Face ◽  
Image Acquisition System

Vibrations often cause visual fatigue for drivers, and measuring the relative motion between the driver and the display is important for evaluating this visual fatigue. This paper proposes a non-contact videometric measurement method for studying the three-dimensional trajectories of the driver’s eyes based on stereo vision. The feasibility of this method is demonstrated by dynamic calibration. A high-speed dual-camera image acquisition system is used to obtain high-definition images of the face, and the relative trajectories between the eyes and the display are obtained by a set of robust algorithms. The trajectories of the eyes in three-dimensional space are then reconstructed during the vehicle driving process. This new approach provides three-dimensional information and is effective for assessing how vibration affects human visual performance.

Stresses in equilibrium configurations of inextensible nets with slack

2015 ◽  
Vol 22 (4) ◽  
pp. 649-665 ◽  
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Dimensional Space ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Deformation Energy ◽  
Equality Sign ◽  
Stress Concentrations ◽  
Equilibrium Configurations ◽  
Present Context ◽  
External Forces ◽  
Additive Measures

The paper deals with nets formed by two families of fibers (cords) which can grow shorter but not longer, in a deformation. The nets are treated as two-dimensional continua in the three-dimensional space. The inextensibility condition places unilateral constraint on the partial derivatives y,1 and y,2 of the deformation [Formula: see text] of the form [Formula: see text] [Formula: see text] There is no deformation energy, the total energy reduces to the potential energy of the net under external forces. Equilibrium configurations are those of minimum energy. The stresses in equilibrium configurations thus reduce to the reactions to the constraints. Nonzero stresses occur only in tense regions where one or two constraints are satisfied with the equality sign. The paper follows the work of Paroni in treating the stress problem via the dual variational problem in the sense of convex analysis. Unlike in the work of Paroni, where stresses are modeled as finitely additive set functions, here a (perhaps more economic) choice of spaces is made that leads to more accessible stresses represented by (countably additive) measures. The present development is made possible by an observation, of independent value, that the space of measures with divergence measure is the dual of another Banach space, in the present context naturally interpreted as the space of strains. Our measures generalize stress fields represented by ordinary functions to account for stress concentrations along folded lines in tension, frequently occurring in equilibrium configurations of the net.

scholarly journals HIGH QUALITY QUADRILATERAL SURFACE MESHING WITHOUT TEMPLATE RESTRICTIONS: A NEW APPROACH BASED ON NETWORK FLOW TECHNIQUES

2000 ◽  
Vol 10 (03) ◽  
pp. 285-307 ◽  
Author(s):  
MATTHIAS MÜLLER–HANNEMANN
Keyword(s):  
Network Flow ◽  
Local Density ◽  
Dimensional Space ◽  
Linear Equations ◽  
Three Dimensional ◽  
Minimum Cost ◽  
Second Phase ◽  
Mesh Quality ◽  
New Approach ◽  
Flow Techniques

We investigate a purely combinatorial approach to the following mesh refinement problem: Given a coarse mesh of polygons in three-dimensional space, find a decomposition into well-shaped quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. We present a new approach based on network flow techniques. In particular, we show that this problem can efficiently be solved by a reduction to a minimum cost bidirected flow problem, if the mesh does not contain branching edges, that is, edges incident to more than two polygons. This approach handles optimization criteria such as density, angles and regularity. In our model we get rid of restrictions on the set of feasible solutions imposed by templates. On the other hand, we still use advantages of general templates with respect to mesh quality for the individual refinement of the mesh polygons. For meshes with branchings, the problem is feasible if and only if a certain system of linear equations over GF(2) has a solution. To enhance the mesh quality for meshes with branchings, we introduce a two-stage approach which first decomposes the whole mesh into components without branchings, and then uses minimum cost bidirected flows on the components in a second phase. We report on our computational results which indicate that this approach usually leads to a very high mesh quality.

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