A hierarchical 3D segmentation method and the definition of vertebral body coordinate systems for QCT of the lumbar spine

2006 ◽  
Vol 10 (4) ◽  
pp. 560-577 ◽  
Author(s):  
André Mastmeyer ◽  
Klaus Engelke ◽  
Christina Fuchs ◽  
Willi A. Kalender
Keyword(s):  
Lumbar Spine ◽  
Vertebral Body ◽  
Segmentation Method ◽  
Coordinate Systems ◽  
3D Segmentation ◽  
Definition Of

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

scholarly journals The Celestial Reference System in Relativistic Framework

1990 ◽  
Vol 141 ◽  
pp. 99-110
Author(s):  
Han Chun-Hao ◽  
Huang Tian-Yi ◽  
Xu Bang-Xin
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference System ◽  
Light Deflection ◽  
Coordinate Systems ◽  
Definition Of ◽  
Celestial Sphere ◽  
Celestial Reference System ◽  
Relativistic Framework

The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5.

scholarly journals Lumbar Intervertebral Motion in Healthy Male Participants: Protocol for a Motion Analysis During Flexion and Extension Cinematographic Recordings

10.2196/14741 ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. e14741
Author(s):  
Inge J M H Caelers ◽  
Toon F M Boselie ◽  
Kim Rijkers ◽  
Wouter L W Van Hemert ◽  
Rob A De Bie ◽  
...  
Keyword(s):  
Lumbar Spine ◽  
Health Care Professionals ◽  
Healthy Male ◽  
Motion Patterns ◽  
Maximum Flexion ◽  
Adequate Definition ◽  
Physiological Motion ◽  
Definition Of ◽  
Medical Research Ethics ◽  
Flexion And Extension

Background Physiological motion of the lumbar spine is a subject of interest for musculoskeletal health care professionals, as abnormal motion is believed to be related to lumbar conditions and complaints. Many researchers have described ranges of motion for the lumbar spine, but only a few have mentioned specific motion patterns of each individual segment during flexion and extension. These motion patterns mostly comprise the sequence of segmental initiation in sagittal rotation. However, an adequate definition of physiological motion of the lumbar spine is still lacking. The reason for this is the reporting of different ranges of motion and sequences of segmental initiation in previous studies. Furthermore, due to insufficient fields of view, none of these papers have reported on maximum flexion and extension motion patterns of L1 to S1. In the lower cervical spine, a consistent pattern of segmental contributions was recently described. In order to understand physiological motion of the lumbar spine, it is necessary to systematically study motion patterns, including the sequence of segmental contribution, of vertebrae L1 to S1 in healthy individuals during maximum flexion and extension. Objective This study aims to define the lumbar spines’ physiological motion pattern of vertebrae L1, L2, L3, L4, L5, and S1 by determining the sequence of segmental contribution and the sequence of segmental initiation of motion in sagittal rotation of each vertebra during maximum flexion and extension. The secondary endpoint will be exploring the possibility of analyzing the intervertebral horizontal and vertical translation of each vertebra during maximum flexion and extension. Methods Cinematographic recordings will be performed on 11 healthy male participants, aged 18-25 years, without a history of spine problems. Cinematographic flexion and extension recordings will be made at two time points with a minimum 2-week interval in between. Results The study has been approved by the local institutional medical ethical committee (Medical Research Ethics Committee of Zuyderland and Zuyd University of Applied Sciences) on September 24, 2018. Inclusion of participants will be completed in 2020. Conclusions If successful, these physiological motion patterns can be compared with motion patterns of patients with lumbar conditions before or after surgery. Ultimately, researchers may be able to determine differences in biomechanics that can potentially be linked to physical complaints like low back pain. Trial Registration ClinicalTrials.gov NCT03737227; https://clinicaltrials.gov/ct2/show/NCT03737227 International Registered Report Identifier (IRRID) DERR1-10.2196/14741

Identification of principal screws of two- and three-screw systems

2007 ◽  
Vol 221 (12) ◽  
pp. 1701-1715 ◽  
Author(s):  
J-S Zhao ◽  
F Chu ◽  
Z-J Feng
Keyword(s):  
Screw Theory ◽  
Coordinate Systems ◽  
Third Order ◽  
Analytical Methodology ◽  
Partial Derivatives ◽  
Spatial Mechanisms ◽  
Analysis Theory ◽  
Definition Of ◽  
Derivatives Of ◽  
Homogeneous Linear

The current paper proposes a unified analytical methodology to identify the principal screws of two- and three-screw systems. Based on the definition of the pitch of a screw, it first obtains an identical homogeneous quadric equation. According to functional analysis theory, it is known that the partial derivatives of an identical quadric equation with respect to its variables must be zero. Therefore, the paper deduces a set of linear homogeneous equations that are made up of the partial derivatives of the quadric equation. With the existing criteria of non-zero solutions for homogeneous linear algebra equations, it ultimately obtains the formulas of the principal pitches and the associated principal screws of the system. The most outstanding contribution of this methodology is that it proposes a unified analytical approach to identify the principal pitches and the principal coordinate systems of the second-order and the third-order screw systems. This should be a new contribution to the screw theory and will boost its applications to the kinematics analysis of robots and spatial mechanisms.

Applications of the Global Coordinate System

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Coordinate System ◽  
Critical Points ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Analytical Characterization ◽  
Equilibrium Manifold ◽  
System P ◽  
Definition Of

The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ‎, ω‎) where b = φ‎((ρ‎, ω‎) = (ρ‎, ρ‎ · ρ‎1, …, ρ‎ · ρ‎m); and (2) the determination of the location of the equilibrium (ρ‎, ω‎) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ‎, ω‎), there are different ways of representing the equilibrium (ρ‎, ω‎) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.

A LEARNING ALGORITHM FOR OPTIMAL REPRESENTATION OF EXPERIMENTAL DATA

1994 ◽  
Vol 04 (02) ◽  
pp. 311-326 ◽  
Author(s):  
JOSEPH L. BREEDEN ◽  
NORMAN H. PACKARD
Keyword(s):  
Experimental Data ◽  
Time Delays ◽  
Optimality Criterion ◽  
Learning Algorithm ◽  
Space Representation ◽  
Coordinate Systems ◽  
State Space Representation ◽  
Optimal Representation ◽  
Definition Of ◽  
General Tool

We have developed a procedure for finding optimal representations of experimental data. Criteria for optimality vary according to context; an optimal state space representation will be one that best suits one’s stated goal for reconstruction. We consider an ∞-dimensional set of possible reconstruction coordinate systems that include time delays, derivatives, and many other possible coordinates; and any optimality criterion is specified as a real valued functional on this space. We present a method for finding the optima using a learning algorithm based upon the genetic algorithm and evolutionary programming. The learning algorithm machinery for finding optimal representations is independent of the definition of optimality, and thus provides a general tool useful in a wide variety of contexts.

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