scholarly journals User-defined B-Spline template snake

2021 ◽  
Author(s):  
Hoda Dehmeshki
Keyword(s):  
Critical Points ◽  
Degrees Of Freedom ◽  
Automatic Segmentation ◽  
Initial Position ◽  
Object Boundary ◽  
Snake Model ◽  
B Spline ◽  
Deformable Template ◽  
Object Based ◽  
Minimum Number

This thesis has created a new Snake model that overcomes many of the limitations of the traditional finite difference snake. This new deformable model combines a novel user initialization process with a finite element B-spline snake to create a powerful semi-automatic segmentation method. Using the simple but powerful initialization process, the user recognizes critical points and regions in a specified order, and transfers this knowledge to the model. By drawing lines across the object of interest, importatn information pertaining to the global shape of the object, such as width and symmetry, is imparted to the model. The snake is parameterized using minimum number of model degrees of freedom necessary and these degrees of freedom are placed in optimal positions around the object, based on the critical points and features recognized by the user via the input lines. Thus, the model is more like a deformable template than a local snake model - it is less sensitive to noise and more amenable to propagation to subsequent image slices in a volume image or time series. Unlike a traditional deformable template model however, it is constructed and positioned by the user rather than preconstructed and automatically initialized by the segmentation system. The template snake isinitialized very close to the object boundary and is very similar in shape. Furthermore, it is "aware" of its position with respect to the object. This thesis also describes the computation of the external image forces and how the known initial position and shape of the snake can be used to design object-specific image forces.

scholarly journals User-defined B-Spline template snake

2021 ◽  
Author(s):  
Hoda Dehmeshki
Keyword(s):  
Critical Points ◽  
Degrees Of Freedom ◽  
Automatic Segmentation ◽  
Initial Position ◽  
Object Boundary ◽  
Snake Model ◽  
B Spline ◽  
Deformable Template ◽  
Object Based ◽  
Minimum Number

This thesis has created a new Snake model that overcomes many of the limitations of the traditional finite difference snake. This new deformable model combines a novel user initialization process with a finite element B-spline snake to create a powerful semi-automatic segmentation method. Using the simple but powerful initialization process, the user recognizes critical points and regions in a specified order, and transfers this knowledge to the model. By drawing lines across the object of interest, importatn information pertaining to the global shape of the object, such as width and symmetry, is imparted to the model. The snake is parameterized using minimum number of model degrees of freedom necessary and these degrees of freedom are placed in optimal positions around the object, based on the critical points and features recognized by the user via the input lines. Thus, the model is more like a deformable template than a local snake model - it is less sensitive to noise and more amenable to propagation to subsequent image slices in a volume image or time series. Unlike a traditional deformable template model however, it is constructed and positioned by the user rather than preconstructed and automatically initialized by the segmentation system. The template snake isinitialized very close to the object boundary and is very similar in shape. Furthermore, it is "aware" of its position with respect to the object. This thesis also describes the computation of the external image forces and how the known initial position and shape of the snake can be used to design object-specific image forces.

scholarly journals A VISIBILITY-BASED PURSUIT-EVASION PROBLEM

1999 ◽  
Vol 09 (04n05) ◽  
pp. 471-493 ◽  
Author(s):  
LEONIDAS J. GUIBAS ◽  
JEAN-CLAUDE LATOMBE ◽  
STEVEN M. LAVALLE ◽  
DAVID LIN ◽  
RAJEEV MOTWANI
Keyword(s):  
Finite Graph ◽  
Initial Position ◽  
Moving Target ◽  
Multiply Connected ◽  
Pursuit Evasion ◽  
Minimum Number ◽  
Evasion Problem ◽  
Free Spaces ◽  
Simply Connected ◽  
Motion Strategy

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ( lg  n). For multiply-connected free spaces, the bound is [Formula: see text] pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

scholarly journals Degrees-Of-Freedom in Multi-Cloud Based Sectored Cellular Networks

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 668
Author(s):  
Samet Gelincik ◽  
Ghaya Rekaya-Ben Othman
Keyword(s):  
Cellular Networks ◽  
Degrees Of Freedom ◽  
Signal To Noise Ratio ◽  
Base Stations ◽  
Processing Capacity ◽  
Coding Schemes ◽  
Minimum Number ◽  
Cut Set ◽  
Base Band ◽  
Multi Cloud

This paper investigates the achievable per-user degrees-of-freedom (DoF) in multi-cloud based sectored hexagonal cellular networks (M-CRAN) at uplink. The network consists of N base stations (BS) and K ≤ N base band unit pools (BBUP), which function as independent cloud centers. The communication between BSs and BBUPs occurs by means of finite-capacity fronthaul links of capacities C F = μ F · 1 2 log ( 1 + P ) with P denoting transmit power. In the system model, BBUPs have limited processing capacity C BBU = μ BBU · 1 2 log ( 1 + P ) . We propose two different achievability schemes based on dividing the network into non-interfering parallelogram and hexagonal clusters, respectively. The minimum number of users in a cluster is determined by the ratio of BBUPs to BSs, r = K / N . Both of the parallelogram and hexagonal schemes are based on practically implementable beamforming and adapt the way of forming clusters to the sectorization of the cells. Proposed coding schemes improve the sum-rate over naive approaches that ignore cell sectorization, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. We derive a lower bound on per-user DoF which is a function of μ BBU , μ F , and r. We show that cut-set bound are attained for several cases, the achievability gap between lower and cut-set bounds decreases with the inverse of BBUP-BS ratio 1 r for μ F ≤ 2 M irrespective of μ BBU , and that per-user DoF achieved through hexagonal clustering can not exceed the per-user DoF of parallelogram clustering for any value of μ BBU and r as long as μ F ≤ 2 M . Since the achievability gap decreases with inverse of the BBUP-BS ratio for small and moderate fronthaul capacities, the cut-set bound is almost achieved even for small cluster sizes for this range of fronthaul capacities. For higher fronthaul capacities, the achievability gap is not always tight but decreases with processing capacity. However, the cut-set bound, e.g., at 5 M 6 , can be achieved with a moderate clustering size.

scholarly journals Two degrees of freedom, dynamic, hand-wrist EMG-force using a minimum number of electrodes

2019 ◽  
Vol 47 ◽  
pp. 10-18 ◽  
Author(s):  
Chenyun Dai ◽  
Ziling Zhu ◽  
Carlos Martinez-Luna ◽  
Thane R. Hunt ◽  
Todd R. Farrell ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Two Degrees Of Freedom ◽  
Minimum Number

scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

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